TransPL: VQ-Code Transition Matrices for Pseudo-Labeling of Time Series Unsupervised Domain Adaptation
Authors: Jaeho Kim
Seulki Lee
Venue: ICML 2025 poster (2025)
Keywords: Time Series
Transition Matrices
VQVAE
Adaptation
Primary area: deep_learning->sequential_models_time_series
TL;DR: Construct VQ code transition matrix for time series unsupervised domain adaptation

Abstract: Unsupervised domain adaptation (UDA) for time series data remains a critical challenge in deep learning, with traditional pseudo-labeling strategies failing to capture temporal patterns and channel-wise shifts between domains, producing sub-optimal pseudo labels. As such, we introduce TransPL, a novel approach that addresses these limitations by modeling the joint distribution $P(X,y)$ of the source domain through code transition matrices, where the codes are derived from vector quantization (VQ) of time series patches. Our method constructs class- and channel-wise code transition matrices from the source domain and employs Bayes' rule for target domain adaptation, generating pseudo-labels based on channel-wise weighted class-conditional likelihoods. TransPL offers three key advantages: explicit modeling of temporal transitions and channel-wise shifts between different domains, versatility towards different UDA scenarios (e.g., weakly-supervised UDA), and explainable pseudo-label generation. We validate TransPL's effectiveness through extensive analysis on four time series UDA benchmarks and confirm that it consistently outperforms state-of-the-art pseudo-labeling methods by a strong margin (6.1\% accuracy improvement, 4.9\% F1 improvement), while providing interpretable insights into the domain adaptation process through its learned code transition matrices.

TransPL: VQ-Code Transition Matrices for Pseudo-Labeling of Time Series Unsupervised Domain Adaptation
Jaeho Kim
Seulki Lee!
Abstract
ral transitions and inherent sensor characteristics. As such, model trained on one specific domain (i.e. source) may not generalize to previously unseen domains (i.e. target), For instance, in human activity recognition using wearable devices, the accelerometer's gravity component may re- main stable across users but the gyroscope readings can shift dramatically when users wear devices with varying tightness (Parkka et al., 2007). Therefore, characterizing the temporal transitions within time series and incorpo- rating selective shift in sensors (channels) for time se- ries domain adaptation potentially enhances both the model adaptation process and the transparency of the black- methodology, as we understand "what" needs to be adapted.
Unsupervised domain adaptation (UDA) for time series data remains a critical challenge in deep learning, with traditional pseudo-labeling strate- gies failing capture temporal patterns and channel-wise shifts between domains, producing sub-optimal pseudo labels. As such, we intro- duce TransPL, a novel approach that addresses these limitations by modeling the joint distri- bution P(X.y) y) of the source domain through code transition matrices, where the codes are de- rived from vector quantization (VQ) of time se- ries patches. Our method constructs class- and channel-wise code transition matrices from the source domain and employs Bayes' rule for tar- get domain adaptation, generating pseudo-labels based on channel- weighted class-conditional likelihoods. TransPL offers three key advan- tages: explicit modeling of temporal transitions and channel-wise shifts between different do- mains, versatility towards different UDA sce- narios (e.g. weakly-supervised UDA), and ex- plainable pseudo-label generation. We validate TransPL's effectiveness through extensive analy- sis on four time series UDA benchmarks and con- firm that it consistently outperforms state-of-the- art pseudo-labeling methods by strong margin (6. % accuracy improvement, 4.9% F1 improve- ment), while providing interpretable insights into the domain adaptation process through its learned code transition matrices.
In this work, we propose TransPL, a novel unsupervised domain adaptation (UDA) pseudo-labeling strategy for time series classification. TransPL models the temporal transi- tions via vector quantized (VQ) codebooks (Van Den Oord et al., 2017) and applies selective channel adaptation strat- egy by quantifying the alignment between the channel code transition matrices of the source and target domains. In the UDA setup, the target model has access to both the labeled source and the unlabeled target domain training sets. TransPL models the jointP(X y) of the labeled source do- main through the construction of code transition matrices, where the transition matrices used for pseudo-labeling the unlabeled target's training set using Bayes' rule. Previ- ous pscudo-labeling strategies (He et al., 2023b) are mostly derived from image domains (Lee et al., 2013; Liu et al., 2023b), where they operate as black boxes that fail to ex- plicitly model the temporal dynamics and selective channel shifts inherent to time series. Instead, they rely on the source domain's 's classifier or the clustering of the target domain, resulting in sub-par model performance and black- box pseudo-labels. In light of this, TransPL provides the following contributions:
1. Introduction
Time series often exhibit strong variability across different domains (e.g. users, devices) due to both dynamic tempo-
We formulate unsupervised domain adaptation (UDA) for time series as learning discrete transitions between vector quantized (VQ) codes that characterize tempo- ral dynamics based on our novel coarse and fine VQ structure. The learned codes are used to construct class-
Artificiil Intelligence Graduate School, Ulsan National In- stitute of Science and Technology (UNIST), Ulsan, South Korea. Correspondence to: Sculki Lee <seulki.lee@ ur.s.
Proceedings of the ndnd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).
'https://githii com/ eai 1ab/TransPI.

---

TransPL: VQ-Code Transition Matrices for Pscudo-Labeling of Time Series Unsupervised Domain Adaptation
and channel-wise transition matrices.
text (Kim et al., 2024). As such, the UDA setup is partic- ularly important for time series, where obtaining laheled data from different domains (e.g. users) is expensive. Co- DATS (Wilson et al., 2020) is an extension of DANN (Ganin et al., 2016), a domain adversarial approach that aligns source and target through adversarial training. Notably, Co- DATS introduced the concept of weak supervision (WS) in time series through target label distributions, which is espe- cially relevant in practical scenarios such as activity recog- nition where users can provide self-reported estimates of time spent on different activities. Here, the WS in CoDATS is provided through an ad-hoc minimization of Kullback- Leibler (KL) divergence between the expectation of the target prediction distribution and the weakly-supervised la- bel distribution. In contrast, TransPL can integrate WS directly into the pseudo label formulation through Bayes' rule, providing a mathematically principled approach to incorporating prior knowledge of target label distributions.
2. Using Bayes' rule, we calculate the class posteriors in chan manner, where the posteriors are calcu- lated from the class-conditional likelihoods and prior. This widens TransPL's applicabilitty to various UDA setups, including weakly supervised scenarios, where the label distribution (i.e. prior) is known. Further- more, we quantify channel alignment scores using the optimal transport (Flamary et al., 2021), allowing us to weight channel-wise confidence of the class posteriors. 3. We demonstrate that TransPL, outperforms existing pseudo-labeling strategies, resulting in enhanced UDA performance across time series benchmarks, as well being interpretable, providing transparent explanations for the generated pseudo-labele
2. Backgrounds and Related Works
2.1. Pseudo Labeling in UDA
More recent approaches have explored various aspects of time series adaptation. SASA (Cai et al., 2021) constructs and aligns sparse associative structures between domains using attention maps. RAINCOAT (He et al., 2023a) lever- ages both time and frequency features for domain alignment, arguing that frequency features exhibit stronger domain in- variance. CauDiTS (Sun et al., 2024) approaches the prob- lem through causality, disentangling causal and non-causal patterns in time series, where causal patterns maintain do- main invariance. However, none of these methods explicitly model temporal state transitions or channel-wise shifts, nor do they provide an explainable outcome of the adaptation process, which are key contributions of TransPL.
Pseudo labeling constructs synthetic class labels (i.e. pseudo labels) for unlabeled target domain samples in unsupervised domain adaptation (UDA), where the labels serve as a pervision signal for training the model on target domain data. Existing pseudo labeling approaches can be classi- fied into several sub-types. confidence-basede methods such as Softmax (Lee et al., 2013) utilize prediction probabili- ties from source-trained classifiers; ATT (Saito et al., 2017) uses multiple classifiers to obtain pseudo labels through prediction agreement. Prototype-based methods like nearest class prototype (NCP) (Wang& & Breckon, 2020) leverage learned source class prototype representations. Another category includes clustering- -aaee techniques that rely on the latent representation of unlabeled target domains (Wang & Breckon, 2020). These methods have been further en- hanced through hybrid approaches that combine clustering with confidence-baase filtering to identify and remove un- reliable pseudo labels, as demonstrated in SHOT (Liang et al., 2020) and T2PI. (Liu et al., 2023a). However, these methodologies have mostly been developed for static data like images, and their application to time series (He et al., 2023b) suboptimal as they fail to capture two critical as- pects: the temporal dynamics inherent in sequential data and the multi-channel characteristics of time series. Unlike images, time series exhibit strong temporal dependencies and channel-wise shifts that require explicit modeling for ef- fective domain adaptation. Our TransPL bridges this gap for the first time by explicitly modeling both the temporal tran- sitions and thannel-wise shifts via vector quantized (VQ) codebooks and transition matrices.
After our submission, we discovered SSSS-TSA (Ahad et al., 2025) addresses channel-level variations using self- attention mechanisms to select relevant channels for align- ment. While we share similar motivations, SSSS-TSA dif- fers from ours by employing self-attention for channel selec- tion and implementing separable channel-level encoders and classifiers, where there is clear methodological distinction in how channels are selectively aligned.
2.3. Time Series Discretization
Methods like Symbolic approXimation (SAX) (Lin et al., 2003) transform continuous time series into symbolic se- quences by discretizing amplitude values into a finite al- phabet. However, the transformation typically relies on predefined quantization schemes that may not capture data- specific patterns. VQVAE (Vector Quantized Variational Auto Encoder) (Van Den Oord et al., 2017) is generative model that learns discrete representations (i.e. codes) of continuous data through codebook-based quantization ap- proach. VQVAE learns the discretization step directly from data, allowing for more adaptive and meaningful representa-
2.2. Unsupervised Domain Adaptation in Time Series
Due to the lack of semantics in time series, it is often known that labeling time series is costly compared to images and
2

---

TransPL: VQ-Code Transition Matrices for Pscudo-Labeling of Time Scries Unsupervised Domain Adaptation
tions of temporal patterns. In time series, VQVAE has been used for generation (Lee et al., 2023), self-supervised learn- ing (Gui et al., 2024), and for foundation models (Talukder et al., 2024). Here, TransPL is the first to leverage VQVAE for UDA in time series and to provide explainable insights through the use of code transition matrices.
raw time series data is impractical due its high dimen- sionality and continuous nature, which makes density esti- mation in the raw input space challenging. Therefore, we use a patch encoder Eg (i.e. Transformer) as the backbone to encode patches X E IR DxNNm into a latent representa- tion Z IR Dx N xdan, where ddim is the size of the latent. To simplify the notation the rest of this paper, we will focus on a single channel d where the latent patch sequence is given as Z = 1z..... [N We then employ VQ to map the patches into discrete codes, reducing the complexity while preserving temporal dynamics. This discretization enables modeling the joint distribution through tractable transition matrices from VQ codes. Here, the question is how to guide the VQ codes to capture generalized temporal patterns while maintaining reconstruction ability without being too fine-grained for tractable transition modeling.
3. Overview
In this section, we formalize the notations, and provide overview of TransPI. with an illustrative figure in Figure 1. Notations. Formally, we define the labeled source domain as S = (Xx,)) ~ P y ~ }..) where Px and Py are the instance and label distributions. Let X IR Pxr be a time series instance, where D and T denote the num- ber of channels (sensors) and sequence length, respectively. We employ the superscript d= d=1, ...: D to refer to each in- dividual channel X The unlabeled target domain T = [X[X- ~ }P is accessible during model training. Follow- ing the covariate shift assumption (Zhang et al., 2013), we assume P( = P while P * P.. Here, the label spaces p and PV are identical, with y E { [1,..... K}. and K denoting the total number of classes.
4.1. Coarse and Fine Codebook Training
To address this, we adopt a residual codebook learning strat- egy with two distinct codebooks: a coarse codebook C, = {ee)=s with a limited number of codes ne to capture pri- ay mary temporal patterns, and fine codebook Cy= (ey ) with a larger capacity (n. nny) to capture residual details, where C., ej E IR A codebook is a finite set of learnable vectors that serve as reference points for quantizing con- tinuous latent representations into discrete codes through euclidean distance assignments. The quantization process for a single patch token E
Overview. We first segment the time series into non- overlapping patches (i.e. tokens) of length m, where we ob- tain N = [ number of patches for each channel. As such, we can reshape the time series instance X E IR DxT into X E IRDD D Xxm and encode each patches into latent vec- tors using a patch encoder &g (i.e. Transformer). Patchifying time series enables each temporal segment to be mapped to discrete vector quantized (VQ) codes, which are later used for the construction of coarse code transition matrices, al- lowing us to represent temporal transitions and channel-wise alignment explicitly. Section 4 details the mapping of latent patches to discrete VQ codes and their utilization in con- structing three different types of transition matrices (TM): the class-wis, wise TM from the source domain, and channel- wise TM from both source and target domains. Section 5 describes how the class-wise wise TM is used to construct class- conditional likelihoods for the unlabeled target sequence, while the whannel-wise TMs are used for calculating chan- nel alignment scores using optimal transport (Flamary et al., 2021). These likelihoods and channel-wist wise alignment guide the generation of pseudo labels for the unlabeled target do- main, where the model is fine-tuned using the labeled source and pseudo-labeled target data for domain adaptation.
R follows:
き= arg min, (1(2(z) (2 12: where e, EC,
f f= arg min, [1(2(z)
(2e where ey EC,
where is first mapped to a coarse code and the residual (2 - f2 is quantized with a fine code. and f de- note the selected coarse and fine codebook indices, respec- tively, and lg is the L2 normalization which converts the Eu- clidean distance into cosine similarity assignment (Yu et al., 2021). After quantization, we perform regular VQVAE (Van Den Oord et al., 2017) training, where we optimize the VQ loss Lvg = crode+ The Loode optimizes the codebook and Lrea is used with a decoder Do (i.e. transformer) to reconstruct the original time series X.
Loode = || sg[z]] - e..12 + [g[l. 2//
+ 18/2 e.] e + ///gggee/ - -z -oa-er,) e,)
Free = X - (eee + e
4. Source Training
3 is commitment term which we 0.25 and sg is stop gradient operation. We also train classifier head using the [CLS] Rdai token that has been encoded using Ea, optimizing the cross-entropy loss Lee as the classification objective. The final loss function for source training is
The objective of source training is to model the joint P(X,y) from the source by constructing meaningful vector quantized (VQ) code sequences from the labeled source data. Directly modeling the joint distribution from
Lare = Lee + Lvg.
(1)
3

---

TransPL: VQ-Code Transition Matrices for Pscudo-Labeling of Time Scries Unsupervised Domain Adaptation
(A) Source Training
(C) Pseudo Label Construction
1. Original Time Series (SRC)
3. Coarse & Fine Codebook Training
Unlabeled
Channel-Wise Class Labels
3. Weighted
bar Lee + livo
(TRG)
Avg
"Class 1"
Ch.1
ww
MW
0.8
Ch.2
0.1
"Class 1"
Enc
VQ
p
Ch.3
0.9
Patched Time Series
a. Class-Conditional Likelihood
Channels (D)
A
Coarse Codebook
Fine Codebook
Quantized Token
99
P
2
Unlabeled Channel
Likellhond of Class
[0.95, 0.05]
Time (7)
Token
Residual
P B
ChannelWise Class Label
(B) Coarse Code Transition Matrices (TM)
Likellhood Class
b. Chignee-Alignment Score
0.7
0.5
Ch
Ch
Ch
0.3
High Alignment
Optimal Transport
Class
Class
TRG:
Ch
Ch 2
Ch
Ch
Cha
Low Alignment 0.1
Distance
Collect Coarse Codes to Construct TM
Class-Wise TM (SRC)
Channel-Wise TM (SRC & TRG)
High Alignment - 0.9
Coarse Code
Fine Code
[[CLS] Token SRC & TRG: Source, Target Domain
Figure 1: Overall scheme of TransPL. (A) Source Training: We first train the whole model architecture, iee,, encoder, decoder, two VQ codebooks (coarse and fine codebook), and classifier, using the labeled source domain data. [CLS] token is appended the input patches and used the input to the classifier. (B) Coarse Code Transition Matrices (TM): The trained encoder coarse codebook infer coarse codes from both target (unlabeled) and source (labeled) domains. These codes serve as states for constructing class-wise TM (from source) and channel-we -wiee TM (from both domains), (C) Pseudo Label Construction: For unlabeled target data, we compute conditioniii likelihoods per channel using class-wise TM obtain channel -iie class labels. These weighted by the similarity hetween and target channel-wise TMs, then averaged generate final pseudo labels.
Design method. The hierarchical structure of mapping to limited coarse codes followed by residual fine codes draws inspiration from classical time series additive decomposi- tion methods (Brockwell Davis, 2002), where time series can be decomposed into trend, seasonal, and residual. For simplicity, the coarse encodes the short-term trend of the patches and the fine maps the residual details. The coarse code can be thought of as capturing the essential time dynamics and is used for coarse code transition matrices, while the fine code solely used for stable VQVAE training. To validate the roles of the coarse and fine codes, we analyze their per- mutation entropy (PE), a measure of complexity (Bandt & Pompe, 2002). Figure 2 shows that the reconstructed coarse code has lower PE compared to fine codes in various time series tasks, aligning with our expectation that the coarse code captures the global trends, while the fine code encodes residual details. Table compares different codebook size combinations, showing that our design method main- tains strong reconstruction performance while having zero dead codes (i.e. codes that not being used), enabling tractable computation for transition matrices.
Permotation Entropo (P2)
8.7
Flle
PE:
PE:
Fine Cide
Fine Code 35
Fine Cade
adopt a two-level representation where
9.3
UCIHAR HHAR WISDM
PE: 0.87
0L:074
PE:
A. Average PE by Task
B. Codes Visualization
Figure 2: A. Average PE: The average permutation entropy (PE) score for reconstructed coarse and fine VQ codes. is measure of temporal complexity (Bandt Pompe, 2002). where lower PE indicates simpler pattern. Across all time series benchmarks (i.e. UCIHAR, HHAR, WISDM), the coarse code exhibits lower PF. compared to the fine code. B. Visualization: The reconstructed coarse and fine VQ codes shows that the coarse code has simplistic patterns (e.g. upward, downward trends), while the fine code has more complex patterns, Full results in Appendix B.
4.2. Coarse Code Transition Matrices (TMs)
After source training, we freeze all learnable parameters and infer the coarse codes from the training sets of both the source and target domains. We now view each coarse code sequence discrete Markov chain, where the codes

---

TransPL: VQ-Code Transition Matrices for Pscudo-Labeling of Time Series Unsupervised Domain Adaptation
Table I: Comparison of single VQVAE (top three rows) versus our residual coarse fine VQ codebook configurations (bottom rows) on HHAR task. Results are averages of 10 source-taret pairs.
and target. As such, we construct P P xDD for each channel d= ..,..,,.. in a channel-wise manner. Unlike the class-wise TM P the P.S. and P are constructed without considering the class labels. The channel-wise TM captures the transition patterns specific to each channel in both domains, later used for channel-wise alignment calculation in Section 5.
(1....... D} by constructing the TM
Course
Fine
MSE..
PL Ace
PL MF1 1
Dead Code (9t) 4
0.214
65.4
63.8
0.1
0.115
58.8
55.7
22.5
128
0.106
59.4
51.9
66.8
64
0.077
58.6
54.7
20.9
0.093
59.1
51.9
22.2
0.126
65.6
63.6
5. Target Adaptation
64
(.080
68.4
66.9
0.0
5.1. Pseudo Labeling
represent the states of the chain. Let 9t denote the state at time step t= [1, ... NJ. and C== [== {m be the set of ne possible coarse codes (states). The transition probabilities between states are estimated based on the observed code sequences in the training data, under the assumption that the probability of transitioning to a particular state depends only on the current state (i.e. 1-step Markov property). Formally, the transition probability from state to state is given by:
Strategy. We propose a pseudo-labeling approach that lever- ages transition matrices (TM) for domain adaptation. Given an unlabeled time series instance X from the target, we construct a pseudo label vector y y = [ūi...., Ut] where It. is the logits for class it and is calculated by:
Uk 1 D
L od
p p= p(k)
(3)
D(yt+1=clss=00) [c,) count(e;, ey)
cc:
The pseudo label can be seen as weighted aggregation of channel-wise class posteriors, where the posterior is formu- lated using Bayes' theorem (Bishop & Nasrabadi, 2006). The p( k) is the class conditional likelihood of ob- serving the coarse code sequence in channel d given the class-wise TM P and p(k) is the prior label distribution of label k in the target domain. The channel-wise class posteriors are weighted by the channel alignment score wa for all channels d [1,..., D]. Intuitively, class posteriors from channels that are shifted less are weighted more.
where count(e,, e,) is the number of occurrences of the transition from code c; to ej in the training sequences, and ce: is the total number of occurrences of code e,,
Using the inferred coarse codes, we construct three sets of coarse code transition matrices (TM): class-wise TM from the source domain PS_ and channel-wist PS, and P. from the source and target domains, respectively. Note that we can only construct the class-wise TM for the source, as we do not have access to the label information of the target.
Channel A Alignment via Optimal Transport When a chan- nel shift occurs between the source and target domains, the change is expected to manifest in the coarse code transition patterns, which can be captured by the channel-wise TMs. For notational simplicity, let P...): the transition probability vectors from code i to all other codes j = [I,..., no] in channel d of the source and target domains, respectively, with nt P(ū.) =>, P(,,) = 1. In practice, we add a small constant e to each element and re- normalize the rows to handle numerical instabilities. Here, simply measuring the difference between the two vectors based on measures such as the Euclidean distance does not take into account the code-wise semantics. For instance, coarse codes A and B might capture similar patterns. As such, the transitions A and A-B should be considered se- mantically similar, even though they correspond to different indices in the transition probability vectors.
Class-Wise TM (Source). Based on the covariate shift assumption P(y|X)$ P X)T, the temporal sequences from the same class should have similar coarse code tran- sition patterns between source and target, while sequences from different classes should have distinct transition pat- terns. As such, from the labeled source training data, we collect the coarse code sequences and construct the TM for each class and channel, leading to PS. E & Dxn,xxx where K is the number of classes, D is number of chan- nels, and ne is the number of coarse codes. Each class-wise TM P c1,k. where i E (1...., K), is used to calculate the channel-wise class-conditional likelihood p(X*ly [y = k) in Bayes' theorem for constructing pseudo-label, in the tar- get domain. Calculating the class-conditional likelihood is similar to how we perform the maximum likelihood esti- mation in Hidden Markov Models (Bishop & Nasrabadi, 2006). This likelihood measures the probability of observ- ing given coarse code sequence from channel d of X conditioned on the class label y k. based on the transition patterns observed from the source domain.
p P(a.) E R represent
To address this, we use optimal transport (Peyré et al., 2019) to measure the shift between the source and target transi- tion probabilities. Optimal transport finds a transportation plan 23 E R Xne that minimizes the cost of transport- ing ((..) into P ((.) where the cost is defined by a cost matrix M E TR. X that encodes the semantic distance be-
Channel- Wise TM (Source& & Target). Since P PPI, the marginal of the input data differs between the source
5

---

TransPL: VQ-Code Transition Matrices for Pscudo-Labeling of Time Series Unsupervised Domain Adaptation
tween the coarse codes. Formally, the optimal transport problem for code i is defined as:
Bayes' theorem when such information is given. Following the log computation in class conditional likelihood, the log prior is used: log p(k)/ where T is a temperature hyperpa- rameter that modulates the strength of the prior. Searching for an appropriate r was important in our analysis, as too strong T leads to degraded model performance by forcing the model to predict the dominant class.
7-- arg min (7 M) s.t. 11..1=1 = P(aa' ne = KMe NERReeMe
(4) where (:-)) denotes the Frobenius dot product, and 1 is all-ones vector. The constraints ensure that the marginal distributions of the transportation plan match the source and target transition probabilities. The cost matrix M(s.)) is the cosine distance between the coarse codes:
Putting all together. We compute the pseudo label for the target domain instance by: (1) computing the channel-wise class posteriors based on the likelihoods and label priors, and (2) weighting the channel-wise class posteriors based on the channel alignment scores that capture sensor shifts.
( 1 c //. ||e/llleelll
(5)
The intuition behind the cost matrix is that the cost is low when the transition happens between similar codes. This aligns with the idea that transitioning between semantically similar codes should be less costly than transitioning be- tween dissimilar codes. Once the transportation plan "f" is obtained, we can compute the channel alignment score wy:
5.2. Pseudo Label Training With Target Domain
After constructing the pseudo label vector ý for the target domain's 's training set, we use the arg max, ÿ as the label. For each mini-batch during training, we select the top Toop percent of samples based on their confidence scores, defined as max; yk. to form a reliable subset for model updates. We fine-tune all model parameters from the source model (i.e. encoder, decoder, classifier, and codebooks) and optimize the following objective similar to Lare in Equation (I):
nh wd= (-
2 / 0²
MI)
fhe
where (7,,) M) is the Earth mover's distance (Pele & Wer- man, 2009) between the source and target probability vec- tors. The exp(-) is the RBF kernel with a as the bandwidth hyperparameter, effectively converting the distance to an alignment score. The channel alignment score has an intu- itive meaning: place higher weights for channels that have shifted less, while placing smaller weights for channels that have undergone strong domain shift. This weighting scheme prioritizes class labels from more reliable channels.
Luzg = Acc + +22
(8)
The a and A2 are the weighting coefficients, which can be replaced with learnable parameters adopted from multi-task learning (Kendall et al., 2018) to avoid extensive search.
6. Experiments
We introduce the datasets, experiment setups, and compari- son baselines in our work. The details in Appendix C.
Class Conditional Likelihood The pI = k)) is the class conditional likelihood of observing coarse code se- quence of xd given class-wise TM for class & (Section 4.2). Assuming first-order Markov property, we calculate the likelihood of the sequence as the product of the individual transition probabilities [ p(s |st, y = k)). Here, St and 8 are the coarse codes at steps é and (+1 in the sequence xd. In practice, to ensure numerical stability, we compute the log- likelihood instead:
Datasets. We consider four time series datasets: UCI- HAR (Anguita et al., 2013), WISDM (Kwapisz et al., 2011), HHAR (Stisen et al., 2015), and PTB (Bousseljot et al., 1995). The first three tasks are human activity recognition tasks where we set each user as a single domain and select 10 pairs of source and target domains. The source-target pairs are exactly the same as the benchmark suite performed by AdaTime (Ragab et al., 2023). PTB is an electrocardio- gram (ECG) dataset, where we select each age group as domains and assess the adaptation performance between four different pairs of different age groups
1 N-1
log p( X k=
Σ
( (7)
Incorporating Prior. In UDA, the model does not have access to the label of the target distribution. As such, we set p(k), the prior label distribution of class a uniform distribution. However, the distribution of the label might be accessible as a form of weak supervision (e.g. self-report on the proportion of time a subject has spent on each exercise in HAR) and has been known as domain adaptation with weak supervision (Wilson et al., 2020). Following this, we can naturally incorprrate the label distribution as prior p(k) in
Experiments. We used the labeled source and unlabeled target's 's training set for training, and the labeled source do- main's 's test set as the validation set. We evaluated the per- formance of the adapted model on the target domain's 's test set (source risk setup (Ragab et al., 2023)). We utilized the same patch encoder from the works of (Gui et al., 2024) and re- re-implemented all baselines using the same encoder. We report the average accuracy and macro-Fi score (MF1) over the different domains, with full results in Appendix D.
6

---

TransPL: VQ-Code Transition Matrices for Pscudo-Labeling of Time Scries Unsupervised Domain Adaptation
Table 2: Adaptation Performance in Target. Mean accu- Best in bold,
7.2. Accuracy of Pseudo Labels
racy (Acc) and macro Fl (MF1) over 10 pairs. second best underlined. Full results in Appendix D.
We report the accuracy of the constructed pseudo label of TransPL in Table 3 over the unlabeled target domain's train- ing set, alongside other pscudo labeling methods. In prac- tice, the pseudo label's 's performance is not used or known during model training as we do not have access to the true labels of the target domain. However, this analysis provides valuable insights into the quality of our pseudo labels and their contribution to the overall adaptation performance. We first demonstrate that TransPI. is the best pseudo labeling method compared to existing pscudo label strategies such as SoftMax, NCP, SP, ATT, SHOT, and T2PL. The average performance gains are 6.1 % and 4.9% compared to the best results of all baselines. In addition, using the true label distribution for the prior p(k) as a weak supervision (WS) shows that the gains widen to 10.7% and 5.2% for accuracy and MF1, respectively. Also, we note that using WS leads to enhanced pseudo labeling performance in seven out of eight cases for TransPL, showcasing that our method effectively leverages prior knowledge when available while maintaining robust performance even without such information.
Dutuset
UCHHAR
WISDM
HHAR
PTB
Acc
MF1
Acc
MF1
Acc
MF1
Acc
MFI
No Adapt
57.0
53.6
59.8
49.1
55.7
52.0
50.5
56.9
DeepCoral
62.0
57.6
61.9
52.0
57.6
54.9
57.4
67.8
MMDA
60.8
54.0
60.1
52.0
58.7
55.6
60.0
70.1
CoDATS
62.7
58.5
63.7
48,3
61.4
59.4
56.1
67.6
SASA
57.2
51.4
60.9
60.3
56.5
62.4
73.8
RAINCOAT
58.6
61.1
47.3
63.0
58.6
61.1
59.8
41.2
SoftMax
62.4
57.4
61.8
52.7
62.5
59.4
62.3
70.7
NCP
59,4
53.9
56.7
50.0
51.5
45.6
60.6
67.7
SP
62.6
59.2
51.4
45.8
50.8
47.4
60.6
67.2
ATT
56.2
46.1
58.7
47.5
59.2
51.8
55.7
59.8
SHOT
67.8
64.3
62.2
54.6
64.8
63.2
61.6
66.9
T2PL
63.8
60.6
57.3
53.3
64.1
62.8
59.0
67.0
TransPI.
69.0
64.9
64.0
56.2
68.4
65.3
67.2
74.0
Baselines. We compared TransPL with several DA methods such as DeepCoral (Sun & Saenko, 2016), MMDA (Rahman et al., 2020), CoDATS (Wilson et al., 2020), SASA (Cai et al., 2021), RAINCOAT (He et al., 2023a), and pseudo labeling strategies such as Softmax (Lee et al., 2013), NCP (Wang& & Breckon, 2020), SP (Wang& Breckon, 2020), ATT (Saito al., 2017), SHOT (Liang al., 2020), and T2PL (Liu et al., 2023a).
Table 3: Pseudo-labeling accuracy in target training. Weak
supervision (WS) denotes the use of prior label information.
Dataset
UCIHAR
WISDM
HHAR
PTB
Acc
MF1
Acc
MF1
Aoc
MFI
Acc
MF1
Implementation. We selected the number of coarse and fine codes to n. =8 8, y = 64 for all tasks. The patch length was set to m = 15 for PTB, and the rest to m = 8. The detailed configurations and search ranges for TransPL and baselines are provided in Appendix E.
SoftMax
63.8
59.6
60.9
51.9
60.3
57.2
68.2
78.7
NCP
57.9
54.0
52.2
45.8
47.3
42.2
62.7
71.6
SP
57.4
54.5
49.9
46.2
48.0
46.6
59.8
68.5
ATT
55.7
45.7
58.8
46.5
50.4
58.9
64.0
SHOT
66.1
64.3
57.7
53.3
62.2
61.2
65.5
75.1
T2PL
62.9
60.8
56.3
53.5
61.3
60.7
65.5
75.1
ID-CNN
65.8
62.5
50.2
39.8
51.5
47.3
68.1
48.2
LSTM
62.2
58.6
42.3
29.1
46.8
42,8
64.4
46.9
7. Results
GRU
61.3
56.5
43.8
33.3
48.9
44.6
65.4
47.6
TramPL.
71.0
67.8
61.8
56.1
68.4
66.9
80.4
86.7
7.1. Performance on UDA
TranSP. (+WS)
74,2
68.7
53.0
89.3
In Table 2, we report the mean accuracy and mean macro Fl (MF1) of the target domain's 's test set across all baselines and datasets, with the full results in Appendix D. Following the evaluation protocol of AdaTime (Ragab et al., 2023), we maintain strict experimental consistency by utilizing identical source-target pairs (10 pairs for HAR tasks, four pairs for PTB) without any selective sampling. TransPL demonstrates the best adaptation performance across all four datasets, achieving large improvements over the non- adapted baseline with average gains of 1 11.4% in accuracy and 12.2% in MFI. The performance gain was obtained by explicitly modeling the temporal transitions and incor- porating channel-wise shifts. Notably, when compared to the strongest baseline SHOT, TransPL maintains consis- tent advantage of an average 3.0% in accuracy and 2.9% in MF1. These results are significant as they are achieved using a uniform label prior distribution; as demonstrated in Section 7.3, incorporating the true class distribution prior can lead to more substantial performance gains.
Use of Transition Matrix. TransPL. is a novel pseudo la- beling approach, where the joint distribution P(X, ((x y) of the source is modeled through the coarse code transition matrices (TM). The use of TM to model the joint distribu- tion of time series is beneficial for several reasons. First, the use of TM aggregates transition patterns across sequences, providing robustness against temporal variations and noise common in time series data. Second, TM enables the ex- plicit modeling of class-conditional patterns and channel- wise shifts that are unique characteristics in time series adaptation. To demonstrate, we compared our generative approach to the direct modeling of the coarse codes using discriminative approaches using models such as ID-CNN LSTM (Hochreiter, 1997), and GRU (Cho et al., 2014). Uti- lizing the same data as in TransPL, these sequential models show significantly sub-optimal pseudo labeling performance as in Table 3, failing to capture domain- domain-invariint invariant temporal dynamics present in the source domain.
7

---

TransPL: VQ-Code Transition Matrices for Pscudo-Labeling of Time Scries Unsupervised Domain Adaptation
7.3. Weakly Supervised UDA
target sequences, highlighting our method's invariance to amplitude shifts while preserving temporal dynamics. As such, unlike black-box classifiers or clustering-baseee ap- proaches, TransPL's 's pseudo labeling process provides trans- parent insights into the pseudo-labeling process.
We compared TransPL with CoDATS (Wilson et al., 2020) under the assumption that the true class label distribution of target training is known as form of weak supervision (WS). For instance, in human activity recognition, while individual sample labels are difficult to obtain, users can self-report their time allocation across different activities. CoDATS incorporates WS during model training by minimizing the Sellbackk-eibble (KL) divergence between the true label distribution and the expected target class predictions in each mini-batch. In contrast, TransPL leverages this distribution during the pseudo-labeling stage, employing it as a prior (k) in the Bayes formulation described in Equation (3).
Class
Closs 0.000
W
Class
Class 2: SOS
M&W
UAM
Class
()
Unlabeled Target Sequence (Class Label: 2)
MMW
Class 4: 0.000
a) Samples Class wise from Source Transition Matrix
Class Conditional
Likelihoods
Table 4: Comparing weak supervision (WS) performance be- tween CoDATS and TransPL.
Figure 3: Class conditional likelihood visualization in UCL Samples from the source are used to construct the class-wise tran- sition matrices (TMs). Then, these TMs are used to calculate the dass-conditions likelihoods of the unlabeled target sequence.
CoDATS
TransPL
Dataset
Metric
Base
+WS (Gain)
Base
+WS (Gain)
Acc MF1
62.7
62.3 (-0.4)
69.0
71.2 (+2.2)
UCIHAR
58.5
58.4 (-0.1)
64.9
67.1 (+2.2)
7.5. A Ablation Study
Ace
63.7
67.1 (+3.4)
64.0
71.3 (+7.3)
WISDM
MF1
48.3
50.8 (+2.6)
56.2
57.9 (+1.6)
We conducted ablation experiments in Table 5 to evaluate the joint usage of channel alignment (CA) weighting and prior label distribution as weak supervision (WS) in TransPL. The results demonstrate that both modules contribute to im- proved domain adaptation performance, whether applied individually or in combination. In seven out of eight cases, the best results were obtained when both modules were used together. Here, the performance gain from the use of CA in- dicates that it is beneficial to model the channel-wise shifts in multivariate time series for domain adaptation. Addition- ally, utilizing prior label distribution as WS enhances the model's adaptation capability. The findings confirm that CA and WS address complementary aspects of time series adaptation, making their joint usage beneficial.
Acc
61.4
60.8 (-0.6)
68.4
70.4 (+2.0)
HHAR
MF1
59.4
59.1 (-0.3)
65.3
67.3 (+2.0)
Ace
56.1
(-5.3)
67.2
72.4 (+5.2)
PTB
MF1
67.6
60.0 (-6.5)
74.0
77.3 (+3.3)
In Table 4, we show that utilizing WS is beneficial for TransPL in all datasets, while CoDATS shows mixed results. Notably, CoDATS exhibits performance degradation in UCIHAR, HHAR, and PTB tasks, suggesting that weak supervision can potentially hinder model performance by introducing prediction bias. In contrast, TransPI. achieves consistent performance improvements in both accuracy and MF1 across all tasks. These results highlight TransPL's 's robustness even in challenging scenarios where source and target domains exhibit different class distributions (Ragab et al., 2023), as observed in WISDM and PTB.
Table 5: Ablation of channel alignment (CA) and weak supervi-
sion (WS) modules in the adaptation performance.
UCIHAR
WISDM
HHAR
PTB
7.4. Class Conditional Likelihoods
CA
WS
Acc
MF1
Acc
MF1
Ace
MF1
Acc
MFI
The class-wise transition matrices (TMs) derived from TransPL provide interpretable insights into the robustness and discriminative power of our pseudo-labeling process. Figure 3 illustrates this through the analysis of class- conditional likelihoods for an unlabeled target sequence. Here, TransPL successfully identifies the true class (class 2) by assigning the highest likelihood, while also revealing meaningful similarities with class 0 through comparable temporal patterns. The zero likelihood assigned to class 4 further demonstrates the method's 's discriminative ability, as this class exhibits a distinctly different temporal pattern with static transitions between identical coarse codes. Most importantly, the TMs capture these temporal relationships despite significant amplitude variations between source and
x
x
68.0
63.5
62.3
51.0
63.2
59.5
68.3
73.3
V
x
69.0
64.9
64.0
56.2
68.4
65.3
67.2
74.0
X
/
68.6
63.8
69.2
55.2
62.3
58.8
72.2
77.9
/
71.2
67.1
71.3
57.9
70.4
67.3
72.4
77.3
7.6. Channel Alignment Analysis
We analyzed the effectiveness of our proposed channel align- ment (CA) distance measure by examining its representation space and its ability to capture source- target channel-win shifts. Figure 4 presents channel-wise visualization of source and target samples, revealing varying degrees of do- main shift across channels. Notably, channel three exhibits a more pronounced distributional shift between the source and target domains compared to channels one and two. By com-
8

---

TransPL: VQ-Code Transition Matrices for Pscudo-Labeling of Time Scries Unsupervised Domain Adaptation
paring our distance measure to clustering-based approaches such as prototype distance, we show that prototype-base paase methods fail to capture the channel-wise shifts, as they ag- gregate features across all samples and ignore the temporal dynamics inherent in time series. However, our CA module effectively captures the shift from the source to target by computing the average costs of transporting each code tran- sition vector between the source and target, demonstrating its ability address channel shifts in time series.
prove adaptation performance. Moreover, the transparent nature of our pseudo labeling provides interpretable insights at each stage, making it both powerful and explainable.
A Aeknowledgment
This work was supported by the Institute of Information communications Technology Plamning & Evaluation(IITPP grant funded by the Korea (WVeer (No.RS-2024
00508465) and Institute of Information & communications Technology Planning & (II) grant funded by the Korea (MVI) 20..R-2220--1201333 Arti- ficial Intelligence Graduate School Program(UNISS))
Source
x
Target
Source Prototype
Target Targe Prototype
1
Ch.a
C
The authors acknowledge Dr. Seokju Hahn and Dr. Yoontae Hwang for their insightful discussions that significantly contributed the development of this work. We also thank the anonymous reviewers for providing insightful feedback and going through our manuscript.
Distance Measures
Ch.t
Ch.2
Ch3
Rank
Prototype La Dsstnce
2.10
1.63
2.05
25
Earth Maver's Distance (ours)
0.08
0.14
0:33
Figure 4: Channel alignment (CA) analysis. We visualized the latent representation of each channels's [CLS] token and observe that the degree of shift differs between channels. Specifically, channel 3 shows higher degrees of shift between source and target compared to channel 1 and 2. We show that using prototype distances (as in clustering based approaches) lead to inaccurate distance measurement, while our earth mover's distance from the CA module provides well calibrated distance between channels.
Impact Statement
This paper presents work whose goal is to advance the field of unsupervised domain adaptation of time series. Previ- ous works have mostly focused simply enhancing the adaptation performance but have not provided explainable insights into "what") is being shifted in time series. Here, our TransPL. specifically addresses this problem by modeling the temporal transitions and channel-wise shifts in multi- variate time series through the use of coarse code transition matrices. We strongly believe that our approach of using the coarse code patterns provides novel insights into the time series community.
8. Limitation
We acknowledge the following limitations of our work. First, our work assigns lower weights to channels that are heavily shifted during the adaptation phase. However, only cer- tain channels may contain class-relevant information (Kim et al., 2024), and when class information is concentrated in channels experiencing significant domain shift, our method would assign lower weights to these channels, leading to degraded adaptation performance. Future works can in- corporate channel importance measures alongside ours, al- lowing for weighting that considers both channel shift and the importance of the channel for classification. Second, while we empirically observed that the coarse codes capture more general patterns and the fine codes capture more fine- grained details, this is not regularized mathematically. We may consider adding regularization terms to enforce such hierarchical relationships explicitly.
References
Ahad, N., Davenport, M. A., and Dyer, E. L. Time series domain adaptation via channel-selective representation alignment. Transactions on Machine Learning Research, 2025.
Anguita, D., Ghio, A., Oneto, L., Parra, X., Reyes- J. L., et al. public domain dataset for human activity recognition using smartphones. In Esann, volume 3, pp. 3, 2013.
Bandt, C. and Pompe, B. Permutation entropy: a natural complexity measure for time series. Physical review letters, 88(17):174102, 2002.
9. Conclusion
We propose TransPL, novel pseudo labeling method for time series domain adaptation, which incorporates coarse and fine vector quantized codes to model the temporal tran- sitions through VQ-code transition matrices (TMs). The TMs enable the explicit modeling of temporal transitions and channel-wise shifts in time series, enabling us to im-
Bishop, C. M. and Nasrabadi, N. M. Pattern recognition and machine learning, volume 4. Springer, 2006.
Bousseljot, R., Kreiseler, D.,, and Schnabel, A. Nutzung der siggalaaaaaatnn cardiodat der ptb über das internet. 1995.

---

TransPL: VQ-Code Transition Matrices for Pscudo-Labeling of Time Scries Unsupervised Domain Adaptation
Brockwell, P. J. and Davis, A. Introduction time seriey and forecasting. Springer, 2002.
Lee, D., Malacarne, S., and Aune, E. Vector quantized time series generation with bidirectional prior model. arXiv preprint arXiv:2303.04744 2023.
Cai, R., Chen, J., Li, Z., Chen, W. Zhang, K., Ye, J., Li, Z.,, Yang, X., and Zhang. Z. Time series domain adaptation via sparse associative structure alignment. In Proceed- ings of the AAAI Conference on Artificial Intelligence, volume 35, pp. 6859-6867, 2021.
Lee, D.-H. et al. Pseudo-label: The simple and efficient semi-supervised learning method for deep neural net- works. In Workshop on challenges in representation learning, ICML, volume 3, pp. 896. Atlanta, 2013.
Cho, K., Van Merriënboer, B., Gulcehre, C., Bahdanau, D., Bougares, F,, Schwenk, H., and Bengio, Y. Learn- ing phrase representations using rnn encoder-decoder for statistical machine translation. arXiv preprint arXiv: 1406. 1078, 2014.
Liang, J., Hu, D., and Feng, J. Do we really need to access the source data? source hypothesis transfer for unsuper- vised domain adaptation. In International conference on machine learning, pp. 6028 6039. PMLR, 2020.
Flamary, R., Courty, N., Gramfort, A., Alaya, M. Z., Bois- bunon, A., Chambon, S., Chapel, L.., Corenflos, A., Fa- tras, K., Fournier, N., et al. Pot: Python optimal trans- port. Journal of Machine Learning Research, 22(78):1-8, 2021.
Lin, J., Keogh, E., Lonardi, S., and Chiu, B. A symbolic rep- resentation of time series, with implications for streaming algorithms. In Proceedings of the Sth ACM SIGMOD workshop on Research issues in data mining and knowl- edge discovery, pp. 2- 11, 2003.
Ganin, Y., Ustinova, E., Ajakan, H., Germain, P., Larochelle, H., Laviolette, F., March, M., and Lempitsky, V. Domain- adversarial training of neural networks. Journal of ma- chine learning research, 17(59):1-35, 2016.
Liu, C.,, Wang, L., Lyu, L., Sun, C., Wang, X., and Zhu, Q. Deja vu: Continual model generalization for unseen domains. arXiv preprint arXiv:2301. 10418, 2023a.
Gui, H., Li, X., and Chen, X. Vector quantization pre- training for eeg time series with random projection and phase alignment. In International Conference on Machine Learning, pp. 16731-16755 PMLR, 2024.
Liu, C., Wang, L., Lyu, L., Sun, C., Wang, X., and Zhu, Q. Deja vu: Continual model generalization for unseen domains. In The Eleventh International Conference on Learning Representations, 2023b.
He, H.. Queen, O., Koker, T., Cuevas, C.,, Tsiligkaridis, T., and Zitnik, M. Domain adaptation for time series under feature and label shifts. In International Conference Machine Learning, pp. 1274--12774 PMLR, 2023a.
Parkka, J., Ermes, M., Antila, K., Van Gils, M., Manttari, A., and Nieminen, H. Estimating intensity of physical activity: a comparison of wearable accelerometer and gyro sensors and sensor locations. In 2007 29th an- nual international conference of the IEEE engineering in medicine and biology society, pp. 1511-1514. IEEE, 2007.
He, Q.-Q., Siu, S. W. I., and Si, Y.-W. Attentive recurrent adversarial domain adaptation with top-k pseudo-labeling for time series classification. Applied Intelligence, 53 110::1310-11319, 2023b.
Pele, O. and Werman, M. Fast and robust earth mover's distances. In 2009 IEEE 12th international conference on computer vision, pp. 460-467. IEEE, 2009.
Hochreiter, S. Long short-term memory. Neural Computa- tion MIT-Press, 1997.
Kendall, A., Gal, Y., and Cipolla, R. Multi-task learning using uncertainty to weigh losses for scene geometry and semantics. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 7482-7491, 2018.
Peyré, G., Cuturi, M., et al. Computational optimal trans- port: With applications to data science. Foundations and Trends in Machine Learning, 11(5-6)3355-60))) 2019.
Ragab, M., Eldele, E., Tan, W. L., Foo, C.-S., Chen, Z., Wu, M., Kwoh, C.-K., and Li, X. Adatime: A benchmarking suite for domain adaptation on time series data. ACM Transactions on Knowledge Discovery from Data, 17(8): 1-18, 2023.
Kim, J., Hahn, S.-J., Hwang, Y., Lee, J., and Lee, S. Cafo: Feature-centric explanation time series classification. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pp. 1372-1382, 2024.
Rahman, M. M., Fookes, C., Baktashmotlagh, M., and Srid- haran, S. On minimum discrepancy estimation for deep domain adaptation. Domain Adaptation for Visual Under- standing, pp. 81 81-94, 2020.
Kwapisz, J. R., Weiss, G. M., and Moore, S. A. Activ- ity recognition using cell phone accelerometers. ACM SigKDD Explorations Newsletter, 12(2):74-88 82, 2011.
10

---

TransPL: VQ-Code Transition Matrices for Pscudo-Labeling of Time Scries Unsupervised Domain Adaptation
Saito, K., Ushiku, Y., and Harada, T. Asymmetrie tri-
training for unsupervised domain adaptation. In Interna- tional conference machine learning, pp. 2988-2997.
PMLR. 2017.
Stísen, A., Blunck, H., Bhattacharya, S., Prentow, T. S., Kjærgaard, M. B., Dey, A., Sonne, T., and Jensen, M. M. Smart devices are different: Assessing and mitigatingmo- bile sensing heterogeneities for activity recognition. In Proceedings of the 13th ACM conference on embedded networked sensor systems, pp. 127-140, 2015.
Sun. B. and Saenko, K. Deep coral: Correlation alignment for deep domain adaptation. In Computer Vision-ECCV 2016 Workshops: Amsterdam, The Netherlands, October 8-10 and 15-16, 2016, Proceedings, Part III 14, pp. 443-
450. Springer, 2016.
Sun, S. et al. Caudits: Causal disentangled domain adap- tation of multivariate time series. In Forty-first Interna- tional Conference on Machine Learning, 2024.
Talukder, S., Yue, Y., and Gkioxari, G. Totem: Tokenized time series embeddings for general time series analysis. arXiv preprint arXiv:2402.16412 2024.
Van Den Oord, A., Vinyals, O.. et Neural discrete rep- resentation learning. Advances in neural information processing systems, 30, 2017.
Wang, Q. and Breckon, T. Unsupervised domain adaptation via structured prediction based selective beudo-labeling. In Proceedings of the AAAI conference artificial intel- ligence, volume 34, pp. 6243-6250 2020.
Wang. Y., Han, Y., Wang, H., and Zhang, Contrast every- thing: A hierarchical contrastive framework for medical time-series. Advances in Neural Information Processing Systems, 36, 2024.
Wilson, G., Doppa, R., and Cook, D. J. Multi-source deep domain adaptation with weak supervision for time-series sensor data. In Proceedings of the 26th ACM SIGKDD international conference knowledge discovery & data mining, pp.
2020.
Yu, J., Li. X., Koh, J. Y., Zhang, H., Pang. R., Qin, J., Ku, A., Xu, Y., Baldridge, J., and Wu, Y. Vector-quantized image modeling with improved vqgan. arXiv preprint arXiv:2/ 10.04600..42... 2021.
Zhang, K., Schölkopf, B., Muandet, K., and Wang. Z. Do- main adaptation under target and conditional shift. In International conference machine learning, pp. 819- 827. Pmlr, 2013.

---

TransPL: VQ-Code Transition Matrices for Pscudo-Labeling of Time Scries Unsupervised Domain Adaptation
A. Notations.
Symbol
Description
Dimension
X
Original time series instance
R
X
Original time series instance reshaped into patches
R Dx N...Xo xm
True label of time series instance
S
Source
T
Target
Px. Py
Time series instance and label distributions
D
Number channels (sensors)
Time sequence length
m
Size of patch
N
Total number of patch in a single time series sequence
dam
Dimension of latent representation
f
Number of coarse and fine codes
8, 64 IR gad
C.
Coarse codebook
C
Fine codebook
R dam Rdiio
R X
ec
Coarse and fine code vector
PS
Class-wise coarse code transition matrix from source Channel-wise coarse code transition matrix from source Channel-wise coarse code transition matrix from target
K x D Dxng Xn
Pš
Dxneke Xic
P
R Dxnx Xne
M
Cost matrix
R Ree
Table 6: Notation and Symbols
12

---

TransPL: VQ-Code Transition Matrices for Pscudo-Labeling of Time Scries Unsupervised Domain Adaptation
B. Coarse and Fine Codes
Cnarse
Coarse
Coarse
Coarse
Coarse
Coarse 5
Coarse
Coarse
Fine
Fine
Fine
Fine 3
Fine
Fine
Fine 6
Fine
Fine
Fine
Fine 10
Fine 11
Fine 12
Fine 13
Fine 14
Fine 15
6
Fine 16
Fine 17
Fine 18
Fine 19
Fine 20
Fiin 21
Fine 22
Fine 23
Fine 24
Fine 25
Fine 26
Fine 27
Fine
Fine 29
Fine 30
Fine 31
Fine
Fine
Fine 34
Fine 35
Fine
Fine
Fine 38
Fine
Fine
Fine
Fine
46
Fine
Fine
Fine 50
Fine 51
Fine
Fine
Fine 54
Fine
Figure 5: Visualization of the full coarse and fine codes in HHAR task. We visualized the trained coarse and fine codes from the
HIHR task 2 11. The top contains the 8 coarse codes, and the 64 fine codes. We observe that the fine codes capturing more grained detailed compared to coarse codes.
13

---

TransPL: VQ-Code Transition Matrices for Pscudo-Labeling of Time Scries Unsupervised Domain Adaptation
C. Experiment Details
Hardware and Software. We performed experiments on a single NVIDIA RTX A6000-48GB GPU. We used Python 3.10 and PyTorch 2.0.1. For the main experiment pipelines, we used PyTorch Lightning 2.1.2. All baselines were re-implemented within our frameworks.
Datasets. We used four datasets test our domain adaptation algorithm: UCIHAR, WISDM, HHAR, and PTB. The UCIHAR, WISDM, HHAR tasks are human activity recognition (HAR) datasets and are well-knoww benchmark datasets for domain adaptation in time series. We used the same datasets and splits provided in AdaTime (Ragab et al., 2023). PTB is an ECG dataset, where the task is to classify five different classes of diseases, However, more processed binary classification (Myocardial infarction vs Healthy Control) dataset was suggested by (Wang et al., 2024), and we used this dataset. The detailed distribution of classes and setup of domains are shown in Table 7.
Table 7: Distribution of Task. not used (N.U) age groups 20-30, 70-80, samples. We set age groups 30-40 as Domain I, 40-50 as Domain 2, 50-60 as Domain 3, and 60-70 as Domain 4.
as there were not enough balanced class
Age Group
Label
Patient Count
Domain
20-30
Healthy control
13
N.U
Healthy control
11
30-40
Myocardial infarction
Healthy control
6
40-50
2
Myocardial infarction
25
Healthy control Myocardial infarction
50-60
3
43
Healthy control
60-70
4
Myocardial infarction
70-80
Myocardial infarction
23
N.U
Healthy control
80-90
N.U
Myocardial infarction
Source and Domain Pairs. For UCIHAR, WISDM, and HHAR, used the exact same ten different splits provided in AdaTime (Ragab et al., 2023). For PTB, we utilized four different pairs of source and target, shown below.
UCIHAR: 2 11, 6 23, 13, 18, 16, 27,
27, 30 20.
WISDM: + 18, 20
30, 35 - 31, 17 + 23, 6 19, 11, +2, 26, 28 - 4, 23 32.
HHAR: + 6. + 6. 7,3 8, 5, + 0,6 3.0 2
PTB: + 1
Dataset
Task Type
Domains
Length
# Channels
# Class
UCIHAR
HAR
30
128
9
WISDM
HAR
36
128
3
6
HHAR
HAR
9
128
3
PTB
ECG
15
Table 8: Details of the datasets used our main experiments
D. Full Results
14

---

TransPL: VQ-Code Transition Matrices for Pscudo-Labeling of Time Scries Unsupervised Domain Adaptation
Table 9; UCIHAR Results Acc. Results across different cource-targe domain pairs.
Algorithm
30-+20
Averaag
Adapt
60.0
60.7
79.8
40.0
60.9
65.5
48.4
58.8
47.8
47.7
57.0
DeepCoral
63.2
78.8
67.3
59.3
61.1
75.2
59.3
60.0
61.1
52.3
62.0
MMDA
65.3
77.8
57.3
36.3
61.9
77.0
36.3
61.2
61.9
59.8
60.8
CoDATS
SASA
61.1
80.8
57.3
36.3
58.4
78.8
36.3
54.1
58.4
$7.0
57.2
RAINCOAT
SollMax
65.3
76.8
68.2
56.0
67.3
68.0
56.0
62.4
67.3
39.3
62.4
NCP
48.4
81.8
68.2
36.3
67.3
71.7
36.3
65.9
67.3
44.9
59.4
SP
51.6
64.6
62.8
51.6
71.8
64.6
50.5
62.6
ATT
80.0
70.7
51.8
30.8
49.6
81.4
30.8
56.5
49.6
53.3
56.2
SHOT
T2PL
65.3
72.7
72.7
57.1
69.9
63.7
57.1
69.4
69.9
36.4
63.8
TranSPL
75.8
84.8
67.3
59.3
66.4
89.4
59.3
75.3
66.4
61.7
69.0
Table 10: UCIHAR Results FI. Results across different source-target domain pairs.
Algorithm
30-+20
Average
Adapt
77.6
38.2
56.0
64.9
48.0
57.1
49.3
37.5
53.6
DeepCoral
55.7
55.5
76.1
35.1
65.7
72.2
57.4
55.6
59.1
43.8
57.6
MMDA
55.7
61.9
71.0
35.6
52.9
73.0
29.9
52.8
57.9
49.1
54.0
CoDATS
SASA
52.4
63.2
77.3
17.0
48.0
76.3
32.2
49.4
49.8
48.2
51.4
RAINCOAT
59.1
SoftMax
56.2
70.8
74.0
39.7
65.8
64.5
56.7
53.2
63.9
28.7
57.4
NCP
35.3
44.6
79.0
43.7
69.9
66.5
38.4
63.2
64.7
33.4
53.9
SP
48.5
62.2
78.4
51.3
60.4
59.3
50.6
72.9
60.4
48.7
59.2
ATT
77.4
36.4
61.3
28.5
41.0
71.4
23.6
46.9
39.4
35.2
46.1
SHOT
T2PL.
57.0
71.8
70.9
51.1
74.9
59.5
53.5
69.5
67.1
30.5
60.6
TranSL
70.4
63.1
82.3
35.9
64.6
88.1
56.2
72.7
63.5
$2.6
64.9
Table 11: WISDM Results Acc. Results across different source-targel domain pairs.
Algorithm
7-+18
5-+26
28
23
Average
No Adapt
80.2
48.3
62.1
31.6
73.2
83.3
27.5
59.8
DeepCoral
83.0
57.3
66.3
53.3
56.8
50.0
65.5
74.4
83.3
29.0
61.9
MMDA
70.8
19.4
59.0
71.7
75.8
42.1
73.6
73.2
54.5
60.9
60.
CoDATS
74.5
70.0
54.5
47.4
75.6
78.8
63.7
SASA
67.9
62.1
67.5
58.3
59.8
47.4
77.0
75.6
80.3
13.0
60,9
RAINCOAT
53.1
58.9
77.8
37.8
67.6
47.3
Sontaa
76.4
52.4
67.5
60.0
51.5
46.1
74.7
74.4
83.3
31.9
61.8
NCP
67.9
49.5
67.5
46.7
56.8
59.2
59.8
47.6
83.3
29.0
56.7
SP
55.7
44.7
59.0
35.0
55.3
61.8
48.3
46.1
84.8
23.2
51.4
ATT
82.1
49.5
49.4
75.0
39.4
44.7
71.3
73.2
87.9
14.5
58.7
71.7
83.3
62.2
T2PL
67.9
53.4
69.9
45.0
79.5
46.1
41.4
37.8
78.8
53.6
57.3
Ours
84.9
66.0
63.9
66.7
48.5
61.8
88.5
74.4
54.5
30.4
64.0
Table 12: WISDM Results F1. Results across differrnt source-targ target domain pairs.
Algorithu
7-+18
20->30
35-+31
17-+23
6-+19
2--11
33-+12
5-+26
28
23 23--32
Average
No Adapt
58.5
48.3
39.2
74.5
DeepCoral
66.3
50.9
56.5
32.5
47.8
63.3
56.3
39.7
75.5
31.5
52.0
MMDA
67.1
26.
54.3
47.2
69.5
51.4
61.4
39.3
62.5
41.2
52.0
CoDATS
50.3
42.5
54.7
48.3
SASA
32.4
47.3
61.1
35.4
50.6
38.9
67.2
41.5
73.6
7.7
45.6
RAINCOAT
SofiMax
66.5
47.5
60.4
40.1
45.2
59.4
59.4
39.7
76.8
32.2
52.7
NCP
43.8
24.6
51.3
65.7
31.6
83.6
50.0
SP
54.3
44.2
36.8
16.7
51.5
62.4
45.9
31.4
78.8
36.1
45.8
ATT
67.8
38.9
44.9
47.4
31.1
51.5
56.7
39.5
78.8
18.2
47.5
37.6
79.4
T2PL
65.8
52.2
63.7
31.5
72.6
57.3
43.6
20.8
82.5
43.4
53.3
Ours
68.9
66.1
58.3
44.9
39.8
63.3
80.9
39.6
64.3
36.5
56.2
15

---

TransPL: VQ-Code Transition Matrices for Pscudo-Labeling of Time Scries Unsupervised Domain Adaptation
Table 13: HHAR Results Ace, Results across different source source-target domain pairs.
Algorithm
0-
4-15
5
Average
No Adapt
37.3
56.9
45.1
63.0
63.1
47.5
73.3
63.5
55.4
51.8
55.7
DeepCoral
37.7
56.1
54.5
63.2
65.0
35.2
73.3
70.7
69.8
50.7
57.6
MMDA
38.3
55.3
57.2
53.0
57.3
47.3
80.2
76.0
61.1
61.3
58.7
CoDATS
35.9
58.7
SASA
44.1
52,9
$7.6
69.0
71.8
37.9
72.8
63.7
70.5
62.5
60.3
RAINCOAT
34.6
61.1
49.5
SoliMax
38.3
51.9
59.9
70.2
76.8
45.7
79.7
67.9
73.1
61.3
62.5
NCP
35.7
46.1
59.1
42.1
51.8
54.5
52.2
60.9
57.1
55.2
51.5
SP
30.5
44.7
44.8
57.4
48.1
47.2
55.5
59.7
61.5
50.8
ATT
36.3
52.1
51.6
77.4
68.3
47.5
63.6
76.0
59.5
59.6
59.2
SHOT
35.9
T2PL
37.9
64.7
55.3
73.3
89.4
37.9
75.2
77.4
63.7
66.5
64.1
Ours
39.5
73.1
60.5
72.7
75.4
52.3
77.1
89.2
80.3
64.2
68.4
Table 14: HHAR Results FI, Results across different source-targel domain pairs.
Algorithu
0-46
5-+0
Average
Adapt
34,0
49.2
40.1
63.4
57.4
38.7
72.8
56.3
47.3
52.0
DeepCoral
33.0
50.7
50.2
66.3
58.5
30.0
71.8
69.5
71.3
47.9
54.9
MMDA
35.9
48.2
51.1
54.7
50.8
36.4
80.8
75.1
63.0
60.1
55.6
CoDATS
32.3
SASA
41.4
45.7
52.5
68.6
64.1
28.7
71.4
61.8
69.8
60.9
$6.5
RAINCOAT
34.9
57.3
75.2
SoftMax
37.3
45.0
53.3
72.0
70.3
37.5
78.5
66.4
74.3
59.2
59.4
NCP
29.6
39.1
48.6
34.5
46.2
44.3
46.3
59.5
57.1
50.4
45.6
SP
29.8
40.6
56.6
36.3
52.2
40.8
42.9
54.1
61.8
59.2
47.4
ATT
27.5
43.2
40.4
74,8
57.4
34.5
54.8
72.2
56.4
56.4
51.8
86.9
70.7
T2PL.
37.3
59.1
51.7
73.8
89.9
33.8
74.6
76.3
66.7
64.9
62.8
Ours
37.3
72.5
53.9
72.1
68.1
43.0
74.5
89.5
80.4
61.8
65.3
Table 15: PTB Results Ace. Results across different sounce-target domain pairs.
Algorithm
Average
No Adapt
25.7
35.4
92.3
48.4
50.5
DeepCoral
47.5
55.2
89.7
37.4
57.4
MMDA
39.7
74.0
92.2
33.8
60.0
CoDATS
40.6
57.7
92.3
33.8
56.1
SASA
58.4
65.1
92.3
33.8
62.4
RAINCOAT
45.6
53,1
95.6
59.8
SoftMax
45.4
65.4
92.0
46.5
62.3
NCP
36.5
58.6
79.0
68.5
60.6
SP
36.4
58.6
74.8
72.8
60.6
ATT
86.7
7.8
91.7
36.6
55.7
SHOT
59.6
84.6
61.6
T2PL
35.5
59.0
87.8
53.9
59.0
Ours
51.9
72.7
94.4
49.7
67.2
Table 16: PTB Results MFL, Results across differentt source source-target target domain pairs.
Algorithm
Average
No Adapt
32.6
46.4
96.0
52.6
56.9
DeepCoral
59.2
68.5
94.5
48.8
67.8
MMDA
49.7
84.2
96.0
50.5
70.1
CoDATS
70.9
67.6
SASA
71.3
77.4
96.0
50.5
73.8
RAINCOAT
SoftMax
58.3
77.6
95.8
50.9
70.7
NCP
47.2
71.9
87.8
67.7
SP
47.1
71.9
84.9
64.8
67.2
ATT
92.9
0.1
95.6
50.4
59.8
72.8
66.9
T2PL
46.1
72.3
93.5
56.2
67.0
Ours
65.0
83.3
97.0
50.8
74,0
16

---

TransPL: VQ-Code Transition Matrices for Pscudo-Labeling of Time Scries Unsupervised Domain Adaptation
E. Baseslines and TransPL Setup
E.1. Baselines
For all Baselines, we used the official implementations or used the implementations from AdaTime (Ragab et al., 2023). For fair comparison, we utilized the same patch transformer encoder structure in our work. The batch size was set to for all works. We also conducted hyperparameter grid search for the learning rates between [0.001, 0.002, 0.0002, 0.0005]. reporting the learning rates with the best MF1 scores. Moreover, certain methods employ multiple loss functions for adaptation. As in our work, employed learnable parameter to automatically adjust the weights between these losses.
E.2. TransPL
To implement TransPI., used the patch transformer encoder used in (Gui et al., 2024) to encode time series patches. The patch representations were then quantized using coarse and fine codebooks. The coarse was first mapped to the patch representation, where the residuals were mapped to the fine codebooks. Here, we used codes for coarse and fine codebooks, respectively. The transition matrices are constructed using only the coarse codes, where the transitions are calculated using a vectorized approach. We also employed the K-Means initialization for the codebooks using the first mini-batch samples the source domain. We utilized the same encoder architecture for the decoder of VQVAE.
8 and n, 64 numbers of
Task
ddim
Batch
Max Epoch
Patch Length (m²
Tup
Source LR
Adaptation LR
UCIHAR
64
32
200
8
0.2
1,0
0.5
0.0005
0.0005
WISDM
128
32
200
8
0.1
2.0
0.2
0.0002
0.0005
HHAR
128
32
200
0.1
0.0002
0.0002
PTB
128
32
200
15
0.2
1.0
0.7
0.0005
0.0005
Table 17: TransPL Hyperparameter Configurations.
F. Different Patch Length
Table 18: Performance of Different Patch Lengths
UCIHAR
WISDM
HHAR
Length
Acc
MF1
Acc
MF1
Acc
MF1
69.0
64.5
64.2
52.6
64.7
60.7
8
69.0
64.9
64.0
56.2
68.4
65.3
m 32
65.4
60.7
64.7
56.6
64.5
60.0
67.1
63.2
56.5
49.1
55.0
51.5
Table 19: Performance of Different Patch Lengths in PTB
PTB
Length
Acc
MF1
m 5
69.9
75.5
10
63.2
68.1
m 15
67.2
74.0
m 30
68.7
76.5
17

---

TransPL: VQ-Code Transition Matrices for Pscudo-Labeling of Time Scries Unsupervised Domain Adaptation
G. Channel-level corruption
To further analyze our channel-wise alignment strategy, we conducted channel-level corruption experiments on the UCIHAR task across all source-target pairs. As TransPL assumes place lower weights on channels that have shifted strongly, we expect that our algorithm should place lower weights on channels where noise is added. From the UCIHAR task with ten source-targe target pairs, identified that the sixth channel (starting from zero index) consistently exhibited high values across most of these pairs. When we introduced increasing levels of noise (Gaussian) to this specific channel, we observed corresponding decrease in values, confirming the utility of our proposed channel-level adaptation.
Rank of Similarity Across Different Noise (UCIHAR)
Pair 0
Pair 1
Pair 2
3
Pair 3
4
Pair 4
Rank
5
Pair 5
Pair 6
6
Pair 7
Pair 8
Pair 9
8
10-2
10-1
Noise Value
Figure 6: Visualization of the ranks of wa for the UCIHAR task. Our results demonstrate that as noise magnitude increases in the sixth channel, its rank consistently decreases across all tested pairs, confirming that our channel alignment module successfully identifies channels that have gone through channel shift.
18


Reviews:
[{"review_id": "PNxqIOA3uD", "reviewer": "Reviewer_fkT4", "summary": "The authors propose a new method, TransPL,  for unsupervised time series adaptation. Unsupervised domain adaptation deals with settings where a model trained on source domain  data with available labels has to be adapted to perform well in target domain with shifted  data  without available labels. \n\nThe proposed method uses vector quantized variational auto encoder (VQAE) to get discrete latent code books for time series patches. This VAQE model is pretrained on source data. A classifier is also trained on top of these source encodings using the available source labels.  The learned discrete code books are used to obtain transition matrices which describe how a time series patterns switch.\nThe authors use this scheme to obtain transition matrices for each channel. \n The  computed transition matrices for the source and target domain channels are used in optimal transport distance to obtain domain discrepancy scores for each channel. This scheme ensures that the  computed optimal transport distance, and thus the resulting channel score, is lower for channels with large shifts between source and target domains. \nThese  channel scores are used as   weights for channel specific  posteriors for each  class. This  weighted (and normalized) sum across all channels of these channel specific posterior provides the posterior probability for the a particular class. This is repeated for all classes to obtain posterior score across all classes for the provided input. \nThese  posterior scores for a target data point can be used to obtain pseudo labels for unlabelled target domain data.\n\nHigh confidence pseudo labels in the target domain are used to to optimize the source model( VQAE encoder, decoder, codebooks and classifier on top of the encodings)\n\nThe proposed method is able to selectively down-weigh channels that have  a large discrepancy. It can also incorporate different label probabilities as priors when computing posterior probabilities. This allows the method to incorporate weak target supervision when target label distribution is available.\n\nExtended results on multiple domain adaptation datasets show that the proposed method improves performance on existing domain adaptation methods.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank Reviewer fkT4 for the thorough, insightful, and constructive feedback. We appreciate that the reviewer has found our work a novel contribution for UDA time series that has not been explored elsewhere. We also thank the reviewer for thinking through our problem definition with us. We have provided detailed responses to address each of its comments. \n\n**Q1. Training Cross-Entropy.** The cross-entropy is calculated using a [CLS] token appended to the input patches. After processing through the Encoder, this [CLS] token—having attended to all time series tokens via transformer—is used to train the classifier. We will add a guiding arrow in **Fig. 1** to clarify this flow. We also refer to Lines 194-196.\n\n**Q2. Class Conditional Likelihood.** After encoder training, we process unlabeled target time series to obtain discrete code sequences (e.g., A-B-A). We then calculate the likelihood of observing this sequence under each class-specific transition matrix from the source domain, similar to maximum likelihood estimation in Hidden Markov Models. For instance, for a given sequence A-B-A, the Class 1 Transition matrix may output higher likelihood, and the Class 2 Transition matrix may output low likelihood. This allows us to assign the most probable class label to each target sequence. We direct the reviewer to **Eq. 7** and **Fig.1** for additional clarification.\n\n**Q3. Correlations between Channels.** \n\nCurrently, we use the same codebook to model all sequences in a time series but construct channel-wise transition matrices to represent each channel. As such, we could presumably say that the shared codebook can capture correlations between channels. While we have also tried modeling each channel with separate codebooks, we empirically found that this did not lead to better pseudo-labeling results (It might be due to increased complexity; alternative design methods should be further looked into). \n\n**Q4. Transition Matrix Remains Similar.** This is also an interesting point. We believe that in such a scenario (e.g., DC shift), the transition patterns would greatly differ, as our codebook does not solely focus on the shapes of the time series pattern. If a large DC shift occurs, it would most likely return different time series signal values that should be reflected in the coarse code usage pattern. \n\n**Q5. Channel Importance.** We find this really interesting and appreciate this insightful point. The reviewer is correct that only certain channels may contain class-relevant information [1], and when class information is concentrated in channels experiencing significant domain shift, our method would assign lower weights to these channels due to the large EMD distance. This is a limitation we'll explicitly acknowledge in our revision. We plan to extend our approach in future work by incorporating channel importance measures alongside distribution shift metrics, allowing for weighting that considers both channel-shift and the importance of channel for classification.\n\n[1] CAFO: Feature-Centric Explanation on Time Series Classification (KDD'24)\n\n**R1. [TMLR paper]** We will include the provided reference. We also think it will strengthen our work!\n\n**W1. Limitation**. As the reviewer has noted in Q5, we believe that TransPL may not operate optimally in cases where the heavily shifted channel contains class-discriminative information, as our pseudo-labeling method would weigh less on such channels. We will incorporate this into our Limitation Section in the updated manuscript.\n\n **W2. Additional Analysis.** We appreciate the reviewer's valuable insight regarding channel alignment analysis. We propose the following experiment to address this concern:\n\n**Analyzing Channel-Level Corruption.** We plan to inject random noise into high-weight channels ($w_d $) in the adaptation scenario and measure adaptation performance by tracking the reduction in $w_d $ after noise injection. A reduction would demonstrate the model's ability to downweight corrupted channels. Would the reviewer consider this a suitable approach to provide more thorough evidence of our method's capability to identify and ignore channels with large distributional shifts?\n\nWe once again thank the reviewer for providing helpful feedback to improve our work. Please let us know if there are any additional uncertainties so that we can address them. Thank you.", "claims_and_evidence": "The claims made in the paper are mostly supported by convincing evidence.\n\nThe authors show that the proposed method results in improved performance over existing methods.\n\nThe ablation studies  show how their proposed method's ability to incorporate weak supervision and  adaptive channel alignment improve performance. These ablations provide clear and convincing evidence to support the stated claims.\n\n\nThe authors also provide ablation studies for the proposed channel adaptation layer, but visualizations on a single 3 dimension example are not fully convincing to back their claim the proposed scheme of capturing scheme and discarding channels with large shifts. This significance of these claims is also limited  by the  ablation results  in Table 5, where we see that the PTB dataset, with 15 channels, has its performance degraded when channel adaptation is used. Maybe this is a misunderstanding on my end, but for a dataset with large number of channels, the channel adaptation strategy should further improve performance.\n\nI would suggest a more thorough experimental analysis to verify that the proposed channel adaptive layer and discard channels with large shifts. This can be done through simulated examples on existing datasets where random channels are corrupted through noise.\n\n\nThe authors also claim that the proposed methods provides explainable insights for domain adaptation. This is slightly vague, and I can't seem to find direct experiments which back this claim.", "methods_and_evaluation_criteria": "The proposed method and evaluation criteria mostly  make sense. \nThe authors test on commonly used benchmarks for time series adaptation. They also provide a thorough comparison with existing unsupervised domain adaptation methods.\nThey also provide use commonly used metrics such as target domain AUC/F1 score to evaluate unsupervised domain adaptation performance \n\nThey also show how their proposed method improves pseudo labelling accuracy as compared to other baseline methods that also employ pseudo labelling. \n\nAdditional results are also provided which show how the performance degrades when their proposed approach of modeling both coarse and fine codes through VQAE is replaced by directly modeling codes through other encoders such as 1DCNN.", "theoretical_claims": "There are no theoretical claims made in this paper", "experimental_designs_or_analyses": "I have checked the experimental design and analysis results provided in Table 1 (that provides VQAE code performance interns of data reconstruction, and pseudo labelling accuracy).\n\nI also checked experimental design results for Table2 (adaptation performance on target), Table 3 (accuracy of pseudo labels), and Table 4 (weak supervision UDA), and ablation studies Table 5.\n\n\nThese experimental design make sense.", "relation_to_broader_scientific_literature": "The authors sufficiently place their paper in context of the broader scientific literature for domain adaptation and learning discrete latent codes.", "essential_references_not_discussed": "The authors mostly discuss all essential references.\nThey do claim that existing domain adaptation methods can not model channel level shifts.\n\nThere has been very recent work [1] that tackles channel level shift for unsupervised domain adaptation.\nThis paper seems to have been published pretty recently and perhaps before the ICML deadline, so ofcourse its totally understandable for the authors to not mention this originally.\n\nThough given how relevant this work is, mention [1] would strengthen the proposed work section.\n\n\n\n[1] Ahad, N., Davenport, M. A., & Dyer, E. L. Time Series Domain Adaptation via Channel-Selective Representation Alignment. Transactions on Machine Learning Research.", "other_strengths_and_weaknesses": "Strengths:\n\n- A promising  scheme of incorporating transition matrices for domain adaptation. This is very novel contribution which hasn't been explored within the context of unsupervised time series adaptation\n-  A scheme which allows to incorporate weak supervision\n- Thorough evaluation on datasets and comparison with numerous  to support claims made.\n\n\nWeakness:\n\n- There is not discussion on limitations of their proposed work. Unsupervised domain adaptation practically only works if many assumptions are met. [2] provides an overview of these assumptions for images, but the same assumptions can be extended to shifts for any types of domains.\n It makes sense to support their claim that code transition matrices are more invariant across changes (and can also hep identify and ignore channels with large shifts), but there certainly can be cases where the domain shift is large that transition matrices from incorrect classes are nearby.  There is no one domain adaptation method which is best for all scenarios. In some cases Frequency information might be more invariant,(like proposed by RAINCOAT), but in other scenarios transition matrices might be more invariant .\n- The analysis on channel alignment and how it affects performance in section 7.6 is weak and only considers one example of a 3 channel dataset. Considering how performance with channel alignment does not improve significantly on the  15 channel PTB dataset, I would suggest more through experiments to study how the proposed method effectively ignores channels with large shifts. This can be done through inducing channel level corruptions, and analyzing the proposed model's performance in terms of accuracy of target domain data , as well as the ability to ignore corrupted channels.\n\n\n\n[2] Gijs van Tulder and Marleen de Bruijne. Unpaired, unsupervised domaadaptation assumes your domains are\nalready similar. Medical Image Analysis.,  2023.", "other_comments_or_suggestions": "The paper is mostly well written and I wasn't able to find any  glaring typos", "questions_for_authors": "- How is the cross entropy layer classifier head trained? is traded on top of coarse codes? This was perhaps not clear from the text, or Figure 1 in its present form\n- How are class wise class conditional likelihoods obtained using class wise Transition matrices? This is perhaps not clear in the text in its present form\n- - There can be scenarios where code transitions should be computed across multiple channels as compared to once channel. Would these channel specific coarse codes capture correlations across channels which could be important to capture?\n- Can there be cases where there is a large shift between channels, but the  transition matrices are still relatively close for channels? E.g there might be a large DC shift in the channel, \n- The mutual information between channel content and class labels can vary across channels. There certainly can be cases where class information is mostly contained in only a few channels. how would the proposed method perform when there is a large corruption in such channels across source and target domains. Would the proposed scheme ignore such channels (as the transition metrics could be very different leading to lower $w_d$?) This is ofcourse totally fine, but this could be a limitation that needs to be made explicit for practitioners and readers.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "foG6doYTme", "reviewer": "Reviewer_H1Hj", "summary": "This paper introduces TransPL, a novel pseudo-labeling approach for unsupervised domain adaptation in time series data. The authors argue that traditional pseudo-labeling strategies fail to capture temporal patterns and channel-wise shifts between domains, leading to sub-optimal pseudo labels. To address this, TransPL leverages vector quantization to model the joint distribution of the source domain through code transition matrices. The method constructs class- and channel-wise transition matrices from the source domain and uses Bayes' rule to generate pseudo-labels for the target domain. The authors claim that TransPL outperforms state-of-the-art methods in terms of accuracy and F1 score, while also providing interpretable insights into the domain adaptation process.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely appreciate the reviewer’s thorough evaluation of our manuscript and the valuable feedback provided. We are pleased that the reviewer found our work to have strong experimental results and well-presented visualizations. Below, we have prepared a detailed response to address the reviewer’s concerns.\n\n**W1. Justification for VQVAE.** We respectfully disagree that VQVAE is merely a technical add-on—it is the cornerstone of our approach, which enables the density estimation of the source (**which is infeasible without VQVAE, Sec 4. Source Training**)\n\nVQVAE enables learning meaningful discrete representations of time series segments, which is essential for modeling the proposed temporal transitions in TransPL. To provide a very simplistic example, in a sequence like 1,2,5,6,1,2, VQVAE **learns** to map similar patches to discrete codes (1,2→\"A\", 5,6→\"B\"), creating a simplified and abstracted transition sequence A→B→A. Consequently, the use of transition matrices relies on these code transitions, and our proposed class-conditional likelihood generation for pseudo-labeling and the quantification of channel-wise shift rely on these transition matrices. As such, VQVAE is essential to our work. Other methods like SAX rely on predefined quantization schemes that may not capture data-specific patterns as in VQVAE. We would like to address the reviewer to Section 2.3 for detailed reasons behind our use of VQ.\n\n**W2. Design Principles** We respectfully note an oversight in this assessment. While the design may appear complex initially, each component serves a critical function in our framework. These elements work together to achieve our stated goal: effective time series pseudo-labeling that accounts for both temporal transitions and channel-wise shifts—the core motivations we established at the introduction.\n\n**(VQVAE)** - Please kindly refer to **W1**.\n\n**Optimal Transport (OT)** - TransPL requires comparing coarse code transition patterns between source and target domains while preserving semantic relationships. Unlike L1/L2 metrics that calculate absolute usage differences, **OT acknowledges semantic similarity between patches.** For example, if patches A and B encode similar information, transitions A→A and A→B should be considered similar. OT incorporates these semantics through a cost matrix defined by patch similarities, enabling a more meaningful comparison of transition patterns that respects the underlying data structure. \n\nBoth modules are necessary designs for constructing pseudo labels, and we believe that they are not overly complex. They are the most simplistic method for obtaining pseudo-labels that account for temporal transitions and channel-wise shifts. No other pseudo labels take these into account. \n\n**W3. Lack of Ablation for Coarse Code.** We direct the reviewer to **Table 1**, which contains our detailed ablation study on the use of coarse codes. The first three rows evaluate single codebook performance with varying sizes, while the last four rows compare different codebook size combinations for coarse and fine codes. These results demonstrate that our proposed design principle yields the best pseudo-labeling accuracy.\n\n**W4. Unclear Motivation.** We respectfully disagree that our motivation is unclear. As we have noted in our Introduction, **our motivation is to design a pseudo-label method that considers the temporality and channel-wise selective shifts that happen in time series adaptation**. No other pseudo label methods consider both problems nor incorporate these into the pseudo labeling process of time series. Other pseudo-labeling methods (SoftMax, NCP, T2PL) rely on the clustering ability, representation performance of the source classifier, and without any focus on time series characteristics, while our methodology focuses on the two most important aspects of time series (time and channel). We have shown in Table 2 that other method fails to obtain strong adaptation performance, and that pseudo label accuracy is low compared to ours in Table 3. We also show that channel-wise alignment distance is better captured through our proposed work. We believe that we have sufficiently addressed our motivation throughout the whole paper, and the experiments conducted are well justified to back our motivation. \n\nWe hope that we have addressed the concerns of the reviewers. If there is anything that is still unclear, please kindly let us know.", "claims_and_evidence": "The paper claims that traditional pseudo-labeling strategies fail to capture temporal patterns and channel-wise shifts, but it does not provide sufficient evidence or analysis to support this claim. The motivation for why existing methods fail is not well-justified, and the paper lacks a clear explanation of why the proposed method is better suited to address these issues.", "methods_and_evaluation_criteria": "The main concern in this part is the lack of Justification for VQVAE. Specifically, the paper does not provide a clear justification for why VQVAE is necessary or superior to other methods. The use of VQVAE feels like a technical add-on rather than a well-motivated choice, making it difficult to understand the true contribution of this component to the overall performance.", "theoretical_claims": "N.A.", "experimental_designs_or_analyses": "Lack of Ablation Studies on Coarse and Fine Codes: The paper introduces the concept of coarse and fine codes but does not provide ablation studies to show the individual impact of each. Without experiments that isolate the effects of coarse and fine codes, it is difficult to assess their respective contributions to the model's performance.", "relation_to_broader_scientific_literature": "Overly Complex Technical Framework: The paper combines multiple advanced techniques, including VQVAE, optimal transport, and pseudo-labeling, without clearly isolating the contribution of each component. This makes it challenging to determine which part of the framework is responsible for the performance gains, and whether the method is overly complex for the problem at hand.", "essential_references_not_discussed": "N.A.", "other_strengths_and_weaknesses": "Strong Points:  \n1.\t**Strong Experimental Results**: The paper demonstrates significant improvements in accuracy and F1 score across multiple time series benchmarks, outperforming existing state-of-the-art methods.  \n2.\t**Clear and Well-Presented Visualizations**: The paper includes well-designed figures and tables that effectively illustrate the method's performance and interpretability.  \n\nWeak Points:  \n1.\t**Lack of Justification for VQVAE**: The paper does not provide a clear justification for why VQVAE is necessary or superior to other methods. The use of VQVAE feels like a technical add-on rather than a well-motivated choice, making it difficult to understand the true contribution of this component to the overall performance.  \n2.\t**Overly Complex Technical Framework**: The paper combines multiple advanced techniques, including VQVAE, optimal transport, and pseudo-labeling, without clearly isolating the contribution of each component. This makes it challenging to determine which part of the framework is responsible for the performance gains, and whether the method is overly complex for the problem at hand.  \n3.\t**Lack of Ablation Studies on Coarse and Fine Codes**: The paper introduces the concept of coarse and fine codes but does not provide ablation studies to show the individual impact of each. Without experiments that isolate the effects of coarse and fine codes, it is difficult to assess their respective contributions to the model's performance.  \n4.\t**Unclear Motivation**: The paper claims that traditional pseudo-labeling strategies fail to capture temporal patterns and channel-wise shifts, but it does not provide sufficient evidence or analysis to support this claim. The motivation for why existing methods fail is not well-justified, and the paper lacks a clear explanation of why the proposed method is better suited to address these issues.", "other_comments_or_suggestions": "N.A.", "questions_for_authors": "N.A.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "iuUkzxOcZR", "reviewer": "Reviewer_n6fN", "summary": "The paper introduces **TransPL**, a novel unsupervised domain adaptation (UDA) strategy for time series classification. It addresses the key challenge of domain variability in time series data arising from **temporal transitions** and **sensor characteristics**. To tackle this, the method employs a **coarse-to-fine VQ structure** to construct class- and channel-wise transition matrices. Additionally, the integration of **transition matrices** and **channel alignment** enhances both adaptation performance and interpretability. Notably, TransPL can seamlessly extend to weakly supervised scenarios and outperform existing pseudo-labeling methods in UDA tasks.\n\n##  update after rebuttal\n\nThe authors explained the performance gaps between the results presented in the manuscript and those of prior work. This is due to their choice of interpretability over performance, which seems reasonable but also raises concern about whether such performance sacrifice is worthwhile. Overall, I think introducing the idea of vector quantization to time series adaptation is interesting and adjusted my score slightly.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We first and foremost thank the reviewer for the thorough review of our work. We greatly appreciate your services. Here, we have prepared a detailed explanation to address each of the reviewer's questions. \n\n**E1. Performance of Baseline Methods.** Thank you for pointing this out. The performance gap stems from our use of patch transformer versus the 1D-CNN backbone in previous works. For fair comparison, we standardized all baselines with the same transformer architecture. While transformers typically require larger datasets to outperform simpler models in time series applications [1], our choice was deliberate: patch transformers preserve the semantic meaning of individual time segments (patch) in latent space, making coarse code transition matrices interpretable. **As we are trying to model the temporal transition in time series, having meaningful and interpretable patch representation is necessary for our whole methodology**. Unfortunately, 1D-CNN representations lack this interpretability as it mixes all features in the latent space. We acknowledge this design choice prioritizes interpretability of the constructed pseudo labels at some cost to overall performance, and we would like to include this in our limitation. Thank you for addressing this point.\n\n[1] Are Transformers Effective for Time Series Forecasting? [AAAI 22]\n\n**E2. Applying to 1d-CNN backbones**. Thank you for the suggestion. We believe that using 1d-CNN models could lead to enhanced model performance. However, as mentioned in **E1**, our methodology relies on the use of patch representation to keep the semantics. One possible way is to jointly optimize the 1d-CNN model alongside the patch encoder, but this would increase the computation, and also, **we would not be able to solely focus on the performance gain that can be brought with our coarse code transition matrix modeling.** As the whole paper focuses on developing pseudo labeling strategies that reflect temporal transitions and the channel-wise shift, the use of patch transformer was necessary. \n\n**E3. Need for additional baselines.** Thank you for this valuable comment. We acknowledge that some of the baselines were missing (CauDiTS did not release their code), however, **we have compared our work to 12 other more relevant baselines**. These baselines include relevant works such as RainCOAT (UDA) and T2PL (pseudo-labeling), which help us understand the significance of TransPL. While adding additional baselines could be helpful, we courteously request the reviewer to have a look at the additional analysis we have performed, which is novel and both needed to support our claims in the paper. For instance, we showed class-conditional likelihoods to \n\n**C1. Time Complexity.** The dominant computational cost comes from counting code transitions across all source samples. With N_s source samples, N patches per sequence, and D channels, this requires O(N_s × D × N) operations. However, implementation is practical due to (1) efficient vectorization techniques (da_utilities/transition_matrix.py file) for counting transitions and (2) the extremely limited number of coarse codes (only 8). For the UCIHAR dataset (9 channels, 14 patches per sequence), the total transition matrix construction time takes only 9.954±0.478 seconds.\n\n**C2. Use of Transition Matrix**. The purpose of this section was to highlight the benefits of using transition matrices to construct pseudo labels instead of directly constructing classifiers (1d-CNN, GRU, LSTM) that could be used to predict the pseudo labels. These discriminative models were trained using the (source) coarse code sequences and were trained to predict source classes. However, we show that such discriminative approaches fall behind our use of the generative approach (modeling the conditional likelihoods using the transition matrix), validating the use of transition matrices. Based on the reviewer's suggestion, we will refine this section for better clarity in the updated manuscript.  \n\n**Q1,2.** We believe that we have addressed the questions in E1 and E2. \n\nWe hope we have addressed the reviewers' concerns. Please let us know if any points require further clarification.", "claims_and_evidence": "The author emphasizes the significance of characterizing temporal transitions in time series data and integrating selective sensor (channel) shifts in time series domain adaptation task, and illustrates this concept with an example from human activity recognition.", "methods_and_evaluation_criteria": "* TransPL models the joint distribution $P(X,y)$ of the labeled source domain by constructing code transition matrices, which are then employed to pseudo-label the unlabeled target training set using Bayes' rule. However, the validity of interpreting temporal dynamic transformations using Markov chains remains open to debate. \n\n* The paper evaluates TransPL on four widely used time series benchmarks, covering both human activity recognition (HAR) and electrocardiogram (ECG) classification.", "theoretical_claims": "The mathematical formulas in the paper seem correct, and the generation of pseudo-labels is based on methods from Bayesian inference and optimal transport.", "experimental_designs_or_analyses": "- Unjustified Performance Gaps with Baseline Methods: \n  The paper adopts the same domain pairs and source risk selection strategy as ADATime (a 1D-CNN-based method), yet reports substantially worse performance (e.g., CODATS accuracy of 39.6 vs. 72.67 on the HHAR dataset’s 0-to-6 task), despite using a stronger backbone (patch transformer). A performance drop of ~30 percentage points across multiple adaptation tasks is alarming, especially since ADATime and Raincoat (reproducible via open-source code) have demonstrated reliable results.\n\n  In short, why does the proposed method underperform ADATime and other reproducible baselines by such a large margin? \n\n- Contradiction Between Model Complexity and Effectiveness: The patch transformer architecture is more complex than the 1D-CNN used in ADATime, yet it achieves significantly lower accuracy. This contradicts the expectation that advanced architectures should enhance performance.\n\n\n    In short, can the proposed method improve performance when applied to simpler 1D-CNN backbones?\n\n- Outdated and Incomplete Baseline Comparisons:\n \n    The experiments exclude 2024 state-of-the-art methods, which weakens the paper’s effectiveness.", "relation_to_broader_scientific_literature": "TransPL extends previous work by integrating ideas from UDA, pseudo-labeling, vector quantization, and optimal transport. A key highlight of the paper is the construction and application of the transition matrices.", "essential_references_not_discussed": "The most recently developed methods on the topic are missing, e.g., \n\n[1] Dwlr: Domain adaptation under label shift for wearable sensor. IJCAI24.\n\n[2] Caudits: Causal disentangled domain adaptation of multivariate time series. ICML24.\n\n[3] Boosting Transferability and Discriminability for Time Series Domain Adaptation. NeurIPS24", "other_strengths_and_weaknesses": "* The proposed algorithm seems to exhibit considerable time complexity. Could the authors provide additional details?\n* In the experimental section, the subsection titled \"Use of Transition Matrix\" lacks clarity and is somewhat difficult to follow. A more detailed or structured explanation would improve its comprehensibility.", "other_comments_or_suggestions": "The authors adopt an innovative approach to generate pseudo-labels for time series data, which enhances their accuracy and supports more effective training of target domain data. However, when deriving pseudo-labels for a specific target domain sample, leveraging both the source domain’s transition matrix and the target sample’s transition matrix in the computation could potentially yield slightly more precise pseudo-labels.", "questions_for_authors": "* Why does the proposed method underperform ADATime and other reproducible baselines by such a large margin? \n\n* Can the proposed method improve performance when applied to simpler 1D-CNN backbones?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "KN9JKHo5Bv", "reviewer": "Reviewer_GrxU", "summary": "The paper presents TransPL, a novel unsupervised domain adaptation (UDA) method for time series data that improves pseudo-labeling by capturing temporal transitions and channel-wise shifts between domains. Traditional pseudo-labeling methods fail to model these patterns, leading to suboptimal labels. TransPL addresses this by constructing class- and channel-wise code transition matrices using vector quantization (VQ) of time series patches from the source domain and applying Bayes’ rule for adaptation to the target domain.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for thoroughly going through our manuscript, and providing valuable comments. We want to highlight points that were misunderstood and should be clarified. While we wish to thank you individually for each point, we are constrained by the length limit. Thank you for your understanding.\n\n**C1. Missing Ref.** ACON. We will add them to our updated manuscript. \n\n**C2. SFUDA.** This is a misunderstanding. Our TransPL is not source-free, as it utilizes the source training data alongside the pseudo-labeled target training data for adaptation, as noted in Line 162: *where the model is fine-tuned using the labeled source and pseudo-labeled target data for domain adaptation.* We note that our work can be extended to the SFUDA, if we only utilize the target data for adaptation, but we believe this is out of our scope where our current focus is on the UDA setup. However, based on the reviewer's insight, we found that this could be better clarified. As such, we added *The adaptation is complete by fine-tuning the model with both labeled source and the pseudo-labeled target training set* in Lines 321.\n\n**Q1. Weakly-Sup. UDA.** The term Weakly-Supervised means that the label distribution of the target domain is given as an additional source of information. Such scenarios are highly practical as users might not label all of their data but can self-report on the proportion of time they have spent on each exercise. This term was first used in time series by CoDATS [KDD'20] (we would like to address the reviewer to Lines 100-109 and Lines 353-355, where we have provided explanations and proper citations needed).\n\n**Q2. VQVAE.** The use of VQVAE is essential, and all the proposed works build on top of VQ. We are not aware of other architectures that could better replace VQVAE. Simply, a patch can now be represented as discrete codes. These discrete codes are then used for modeling the temporal transitions and channel-wise shifts, which are the main contributions of this work. Here, VQ enables the **mapping of each time series patch** into coarse code vectors. This makes the semantics of the time series intact, while making the transition matrices sensible.\n\n**Q3. Recon. Performance.** The reviewer is correct. Reconstruction is important for our use, as good reconstruction ensures meaningful code vectors to be constructed, which is critical for valid transition matrices. Constructing non-representative code vectors that can't represent the time series task at hand leads to meaningless transition matrices, leading to degraded pseudo label accuracy. In Table 1, we show that obtaining good reconstruction performance as well as making the transition meaningful (by limiting the # of coarse codes) are both essential to making accurate pseudo labels.\n\n**Q4. Recon. and Classification.** While there is no strict guarantee that the representations for classification and reconstruction are identical, we argue that they are well aligned for the following:\n\n1. **Empirical Evidence**: Our results show strong performance in both classification and reconstruction across multiple data, with no signs of overfitting to one task. The pseudo labels consistently achieve the best results, and both losses are well optimized, leading to stable outcomes.\n2. **Prior Works**: Prior works in time series [1,2] have successfully used VQVAE for both reconstruction and classification. Additionally, optimizing auxiliary tasks alongside reconstruction is a common practice in the broader literature [3].\n\n[1] TOTEM: TOkenized Time Series EMbeddings for General TS [TMLR'24]\n\n[2] VQ Pretraining for EEG TS with Random Projection and Phase Alignment [ICML'24]\n\n[3] DeWave: Discrete EEG Waves Encoding for Brain Dynamics [NeurIPS '23]\n\nQ5. While we have empirically observed that zero dead coarse code was achieved in all of our tasks, we acknowledge that this is a practical result. To practically ensure this, we have explicitly designed the coarse codes to have a limited number of codes (N=8; modeling the trend pattern) compared to the more large use of code size (N=256, 512), making sure that there is a higher chance of using all codes in the coarse codebook to map the trend pattern. However, we understand this is a practical outcome and would like to include it in the limitation section.\n\nQ6. EMD was necessary, as different codes may contain similar semantics. For instance, if code 1 and code 2 capture similar information, the transition between 1->1 and 1->2 should be deemed similar. Other metrics such as MSE cannot take this semantics into account (they treat 1 and 2 differently), while EMD can incorporate such information with the use of cost matrix M (defined as similarity in Eq 6). We direct the reviewer to the section \"Channel Alignment via Optimal Transport, where we have provided a detailed example and the motivation behind the use of EMD.\n\n**Q7. Eval. protocol.** We direct the reviewer to our response **E1 of Reviewer n6fN (3rd reviewer)**", "claims_and_evidence": "The author claims that the Permutation Entropy of UCIHAR, HHAR, and WISDM data sets can prove that fine VQ code is more complex than coarse VQ code. This can indeed be seen from the visual representation.", "methods_and_evaluation_criteria": "The experimental design and benchmark dataset are nearly consistent with the protocols of previous studies in this field.", "theoretical_claims": "This manuscript only uses the very basic Bayes’ rule.", "experimental_designs_or_analyses": "Yes, I found the experimental results to be unreasonable. (listed on questions)", "relation_to_broader_scientific_literature": "Since this method does not use both source and target domain data simultaneously, it may be more aligned with the field of “source-free unsupervised domain adaptation” (SFUDA).", "essential_references_not_discussed": "It is recommended to join ACON[1] in the future.\n \n[1] Liu, M., Chen, X., Shu, Y., Li, X., Guan, W., & Nie, L. (2024). Boosting Transferability and Discriminability for Time Series Domain Adaptation. Advances in Neural Information Processing Systems, 37, 100402-100427.", "other_strengths_and_weaknesses": "Strengths: \n(1) The paper introduces a creative adaptation of vector quantization (VQ) techniques to the UDA setting.\n(2) The integration of Bayesian inference with learned transition matrices offers a unique way to improve label reliability.\n\nWeaknesses: As questions", "other_comments_or_suggestions": "1. Typos:\nLine 171: “quantization”\n\n2. As mentioned above, since this method does not use both source and target domain data simultaneously, it may be more aligned with the field of SFUDA.", "questions_for_authors": "1.\tThe term weakly-supervised UDA is somewhat confusing. Please clarify its meaning (including in the abstract) to avoid misunderstandings. If this terminology has been used in prior research, please provide proper citations.\n2.\tThis pipeline does not necessarily require VQVAE and could potentially perform better with a Mixture of Experts approach. Could you explain why VQVAE is essential to this framework?\n3.\tSince VQVAE heavily relies on representation learning quality, the performance of the reconstruction task is a key factor influencing the domain adaptation task. Although Table 1 presents the MSE loss, could you provide further insights into the relationship between the reconstruction task and domain adaptation performance?\n4.\tHow can we justify that the representations learned for the classification task and the reconstruction task are similar rather than different? This could significantly impact how VQVAE learns representations. Given that this manuscript emphasizes interpretability, we would appreciate further clarification on this point.\n5.\tIt is unlikely that every dataset would achieve Zero Dead Code under the same codebook size. Could you explain how Zero Dead Code is ensured in this approach?\n6.\tWhy did you choose Earth Mover’s Distance?\n7.\tSince this manuscript follows the AdaTime evaluation protocol, which is the same as ACON [1], why do other methods (e.g., RAINCOAT, CoDATS, DeepCoral) perform significantly worse under the same dataset and scenario? Please provide a thorough explanation; otherwise, this discrepancy raises concerns about the validity of the manuscript’s findings.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper presents TransPL, a novel pseudo-labeling approach for unsupervised domain adaptation in time series data. To effectively capture temporal dynamics and channel-wise distribution shifts across domains, TransPL employs vector quantization to model the source domain's joint distribution via code transition matrices. Specifically, TransPL constructs class- and channel-wise transition matrices from the source data and applies Bayesian inference to generate high-quality pseudo-labels for the target domain. Experiments show that TransPL surpasses state-of-the-art methods in both accuracy and F1-score while offering interpretable insights into the domain adaptation process.

During the discussion, the rebuttal well addressed prior concerns regarding the justification for using VQVAE and optimal transport. The AC agrees with the two positive reviewers that while state-of-the-art (SOTA) performance and marginal improvements are worth noting, they should not be the primary focus—given that the authors introduce a novel and conceptually compelling idea to the field.
Decision: Accept (poster)