Spatially Resolved Temporal Networks: Online Unsupervised Representation Learning of High Frequency Time Series
Authors: Faris Faried Gulamali
Ashwin Shreekant Sawant
Ira Hofer
Matt Levin
Karandeep Singh
Benjamin S Glicksberg
Girish N Nadkarni
Venue: Submitted to ICLR 2023 (2023)
Keywords: High frequency time series
Representation Learning
Online Learning

Abstract: Univariate high-frequency time series are dominant data sources for many medical, economic and environmental applications. In many of these domains, the time series are tied to real-time changes in state. In the intensive care unit, for example, changes in an electrocardiogram signal can indicate a heart attack, and intracranial pressure waveforms can indicate whether a patient is developing decreased blood perfusion to the brain. However, most representation learning to resolve states is conducted in an offline, batch-dependent manner. In high frequency time-series, high intra-state and inter-sample variability makes offline, batch-dependent learning a relatively difficult task. Hence, we propose Spatial Resolved Temporal Networks (SpaRTeN), a novel composite deep learning model for online, unsupervised representation learning through a spatially constrained latent space. We simultaneously train two distinct blocks: a recurrent neural network ensemble $f_R$ that captures states in high frequency time series, and a spatial block $f_S$ that spatially resolves state changes from the predictions generated by $f_R$. The spatial block $f_S$ identifies the block in $f_R$ that best fits the current state of the time series, and the training procedure for $f_R$ optimizes that block. This procedure corresponds to a minimax framework. When $f_S$ and $f_R$ are deep neural networks, the entire system can be trained via back-propagation. Finally, we demonstrate the application of this framework to online forecasting and interpretable, zero-shot clustering. We compare and demonstrate that SpaRTeN outperforms spectral clustering and a Gaussian mixture model.

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CLINICALLY RELEVANT UNSUPERVISED ONLINE REP- RESENTATION LEARNING OF ICU WAVEFORMS
Anonymous authors
Paper under double-blind review
ABSTRACT
Univariate high-frequency time series with real-time state changes prominent in medical, economic and environmental applications. In the intensive care unit, for example, changes and intracranial pressure waveforms can indicate whether a patient is developing decreased blood perfusion to the brain during a stroke. However, most representation learning to resolve states is conducted in an of- fline, batch-dependent manner. In high frequency time-series, high intra-state and inter-sample variability makes offline, batch-dependent learning relatively dif- ficult task. Hence, we propose Spatial Resolved Temporal Networks (SpaRTeeN), a novel composite deep learning model for online, unsupervised representation learning through spatially constrained latent space. SpaRTeN maps waveforms to states, and learns time-dependent representations of each state. Our key con- tribution is that generate clinically relevant representations of each state for intracranial pressure waveforms.
INTRODUCTION
Univariate gighffrequency time series arise in several domains including economics, medicine, and environmental studies Thorsen-Meyer et al. (2020): Shakeel & Srivastava| (2021): Yao et al. (2019). High-frequency time series often exhibit different states. For example, patient suffering from stroke, an intracranial pressure (ICP) waveform normally flucturates somewhat. However, transi- tion a state where is persistently elevated may lead to blindness and other neurological problems Mollan et al. (2016). Early detection of this state transition may enable physicians to intervene ap- propriately for better outcome<[.wwyd et al. (2022).
Many algorithms like shapelets, hierarchical latent factor models, hidden Markov Model-like meth- ods, change point and anomaly detection techniques, and N-Beats are dedicated towards disen- tangling time series into their respective subcomponents Li et al. (2021); Grabocka al. (2015); Oreshkin et al. (2019a); Blazquez-
Conde (2022); Aminikhanghahi & Cook (2017); Van Den Oord & Vinyals (2017) but few are dedicated towards disentangling states within single time series Franceschi et al. (2019) or predicting future state transitions. For high-dimensional datasets, unsupervised methods like t-SNE, UMAP, and SOMs be used to project samples into lower di- mensions with spatial relationships Van der Maaten & Hinton (2008); McInnes et al. (2018). How- ever, in time series, dimensionality proportional series length. As result, state determination requires encoding time series into fixed-length vectors, followed by clustering algorithms like k- means. These methods can capture long-range dependencies but rely on con-differentiable function fitting.
Also, these methods are often offline, in that they learn from an entire training dataset at once, before being evaluated and deployed. This can be problematic, especially in the context of dataset shift or high inter-sample variability. Every time new batch of data is received, the entire model needs be retrained. figh-frrquency time series data like waveforms suitable for online learning, wherein a learner attempts to tackle some predictive task by learning a sequence of data in the order they received Hoi et al. (2021).
often encountered in scenarios more
Extraction of states or transitinniinnn from a fighffrequency time series requires online unsuper- vised representation learning, relatively understudied field. Fuzzy neural networks create a set of modifiable rules Luo et al. (2019). but successive rule changes makes state inference relatively volatile and inconclusive. Another example of the state-of-the-art time series forecasting method is

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temporal fusion transformers (TFTs), which provide interpretable risk prediction via attention mechanisms Lim et al. (2021); Kamal et al. This method combines feature attention with sequence attention to generate interpretable torecasts, and has shown great promise in time series forecasting.
We propose Spatial Resolved Temporal Networks (SpaRTeN), a composite differentiable unsuper- vised deep learning network to learn discrete spatial representation from high frequency time series via temporal ensemble learning. We show that our method outperforms TFTs with the same number of parameters in benchmarks of online learning tasks. We also note that TFTs be in- cluded within our method due to the flexibility of the composite model.
1.1
CONTRIBUTIONS
We introduce SpaRTEn, a new framework for online learning of spatial representations from high-frequency time series.
We demonstrate that introduction of a latent space improves rather than harms SpaRTEn's 's ability forecast and cluster high frequency data in real-time, compared to state of the art models.
We show that SpaRTeN can generate clinically meaningful representations medical in- tracranial pressure waveforms.
SPATIAL RESOLVED TEMPORAL NETWORKS
2.1 PROBLEM FORMULATION
For the purposes of time series forecasting, we examine the problem of simultaneously learning:
1. a function S mt - St, which maps time series æt of length {xt-k; Tt-k+1 xt), to discrete state 8t, and
2. a set of functions Rs. + Ôt which, for each state St. map the input time series of length i to a forecast time series ÿt {.++1. 2442.-...01. Ft-w of length equal to the prediction window
and R are optimized to maximize the probability of assigning the time series Iy to the most suitable function R(,) determined by objective function L:
max min (Zs(.,))))))
S Bi,)
where the expectation E.L()) taken over the set of all time series. This corresponds to the minmax framework described for GANs in Goodfellow al. (014)..
2.2 MODEL ARCHITECTURE AND THE FORWARD PASS
We implement the above with composite model architecture depicted in Figure I where S and R are depicted analogously named blocks. The height and width common the two blocks, represents the two dimensional discrete state space, which can also be considered to be the latent space for this model.
The S block implements convolutional filters (Appendix A.3 to map an input time series a to density over the discrete two dimensional space of states (green arrow 1). The R block consists of a spatially arranged ensemble of LSTT sub-networks, each of which makes forecast for the input 24 with prediction window wr (blue arrow 1). For each input Ty the sub-network in R corresponding to the greatest density output by S (green arrow 2) is used for generating the prediction Ột (blue arrows 2, 3).
We choose to place in two-dimensional discrete state-space (i,j), because it facilitates easy visualization of time series corresponding to individual states, which previous methods like SOM- VAE and TFT are unable currently do. We can parameterize the number of states by adjusting the width and height of the latent space, and The state space width and height are purer-pprrmeters that should be adjusted depending the priori assumptions of dataset complexity.
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Figure 1: Schematic representation of model architecture. Blue is forward propagation and green back- pack-propagation. Time series from the data space are forecast by the sub-networks in an R- block with a look-forward period of k. The dimensionality of the spatial representation is x b. Simultaneously, an S-Block predicts the most relevant sub-network for the time series. The predicted Under review as a conference paper at ICLR 2023
w w-lookforward
forecast
R-block
2
3
Inpul
Lines
2
S-block
S-block
R-block
Spatial Representation
P(y|x)
sub-network is used generate forecast and is then back-propagated via Equation ??.
2.3 LOss FUNCTIONS AND TRAINING WITH BACKPROPAGATION
When implemented as described here, the entire system can trained with backpropagation. Two distinct loss functions have to be accounted for, for the S and It blocks.
Sub-networks of R can have primary objective (Trobjective) of forecasting, classification or re- construction if we assign Ye to be the forecasting window, labeled class or It, respectively. For the examples in this paper, we consider the objective to be forecasting. To further impose struc- ture, introduce second objective inspired by contrastive loss and self-organizing maps, the distance distance-weighted contrastive loss (LDweL) (Appendix A.I). For a single sample, we define the loss function for be
(Yt LR Lobjective (yt Re, (x (Z); RR.,)
LDWEL (Ize; RR.,) R(x, Qx))
(1)
Rac
LDWCL(Rap R.) - log
(2)
ExnZ Ra.
|| 2||2
where Yt (I++1 Fe 2, .... Fr-w). the ground truth values from the time series, a is a learned
hyper-parameter parameter to modulate the relative effects of the two terms, z is state drawn from the set of all states Z, sim is a metric of similarity between Rg and Rs., such as normalized dot product or cosine-similarity.
LDweL forces similar states to closer and dissimilar states be separated, causing the wave- forms to cluster in the state space. During each forward propagation step, the predictions are gen- erated by each forecasting network the R-block. After the predictions are generated by each network in the A block, the distance-weighted contrastive loss is created by calculating the differ- ence the predictions between each of the network the R-block and network selected by the block, and weighting it by Euclidean distance of the network and the selected sub-network (blue leftwards arrow).
The S block has separate loss function L., contingent its objective, which is to predict the spatial state occupied by the next time step. can be conceptualized as the distance between S block prediction of the best state and the network in the R block with the lowest enror with respect to yt (green leftwards arrow): L, = [|5(xz)) arg min L(R,, (xx)))la
While an L, or L2 norm may better capture the information about the density the spatial net- works, in practice it may not provide sufficient gradient for learn well (Appendix A.3). Early

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in learning, when the sub-networks in the R-matrix perform poorly, S displays highly unstable dy- namics, which in turn hinders R-block learning. Rather than training S to directly maximize the spatial density, we can improve stability by treating the objective as classification problem and minimize the negative log likelihood (details in Appendix A.2).
The full training algorithm is provided in Algorithm 1.
2.4 ENSEMBLE WEIGHT SHARING
Inductive transfer learning leverages an inductive bias to improve performance on a target task and eliminates redundant learning of patterns in data structure Zhuang et al. (202I). To generate sub- networks with weights that represent distinct states rather than shared structure between states in the time series, we employ inductive transfer learning framework. This procedure increases the gap between the sub-network posteriors, which further enhances the contrastive learning aspect of the network. From an information theoretical perspective, the process of learning shared posterior can be thought of as lossless compression of the hidden states by encoding them into a shared embedding. In turn, non-unique learning of inteeindependent behavior only needs to take place once rather than x b times.
While mode collapse is a known problem, we find that the sharing of weights across the first few layers leads to robust performance as seen with the paradigm of transfer learning. This is quite unlike the mode collapse seen in the training of generative adversarial networks. Without the sharing of weights across the first few layers, we find that learning requires significantly more samples because the overall structure of the time series must be learned for each unit the f block, in addition to learning of the relevant state. In contrast, with weight sharing, we find that learning of the overall structure of time series can be done jointly, and the state separation can be learned by each sub- network.
In our implementation the SpaRTeN framework, this auxiliary network maps the hidden states of R. which is h x a x b embedding to low-dimensional embedding h', which is subsequently appended to a dense layer of each sub-network. This procedure ensures that the shared weights are differentiable during training. After back-propagation, weights are copied all sub-networks.
Algorithm Spatial Projection of Time Series with Temporal Ensembles
Require: (To....,.z) where T is the length of the time series. represents { vy } where is is the look-back period, and y represents the forecast (I.41.....2e where the forecast window. Assign width and height to the state space a, E Z=, Randomly initialize weights of the R and block: On, 0g ~ NO, 1). for m k: to m T w do
am + (Im-ki..... Im}
Um + (Im+l,..., Im+w3
(1,j) S(arm 0s)
(m.)) = R(,,)) mi OR)V(i: (0.a).j: (0,b))
Update Rii via gradient descent on LDweL (Ū (0m (1)) Vm)
Update S via gradient descent on (xS(m,), ), arg min (L(gm vm))
end for
2.5
RELATED WORK
2.5.1 TWIN NEURAL NETWORKS AND BOOSTRAP YOUR OWN LATENT SPACE
Twin neural networks and Bootstrap Your own Latent Space (BYOL) contain two more sub- networks He et al. (2018): Grill et al. (202)), and can learn semantic similarity between different samples. Subnetworks cast recurrent neural networks have been used learn and visualize time series similarities Pei et al. (2016). Like twin neural networks and BYOL, our framework employs contrastive loss with subnetworks. However, there are few key differences.
First, SpaRTeN learns relationships between states in an online, sequential manner rather than of- fline and batch-dependent. As result, SpaRTEn generates states that time-dependent, whereas
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implementations of BYOL are time-independent. When the learned network is time- iime-indeenndent, we may see a different state assigned to each sequential time point or punctuated changes in state rather than gradual evolution Fortuin et al. (2018). However, clinically relevant changes in state are usually time-dependent, and as such, SpaRTTe is expected to generate more interpretable pre- dictions. For example, a patient who is developing infection deteriorates over time until reaching a state of sepsis, rather than abruptly changing from a healthy to septic state.
Second, online learning captures relationships such stationary versus non-stationary time series that are not easily ascertained in time-agnostic state encodings. For example, in a stationary time series, we notice that after state has stabilized, the loss function for network belonging to that state slowly decreases. In non-stationary time series, patterns associated with the state start diverging from the expected pattern and the network loss gradually increases until it reaches threshold. At the threshold, a state transition occurs and new network is selected to represent that given state, implicitly allowing the detection of the state change. These relationships cannot be deciphered in time-step agnostic state-encodings.
2.5.2 TEMPORAL ENSEMBLES AND MIXTURE OF EXPERTS
Ensemble Learning refers to a family of techniques where multiple learners are trained to solve the same problem Zhou (2009). Ensemble methods construct multiple hypotheses from these base learner algorithms and join them to generate a prediction that generalizes much better than the in- dividual algorithms. Ensembles with base learner LSTMs have been used on financial time series forecasting to improve performance (Sun et al. (2018). Our framework forces base learners to occupy a Euclidean space, which can subsequently be used to generate interpretable representations. Other online unsupervised methods with time series have developed composite or adaptive model ap- proaches focused on anomaly detection followed by model adaptation Karaahmetoglu et al. (2020); Savitha et al. (2020). Having distinct sub-networks for each state allows for different models to uniquely represent distinct states.
The key advantage of utilizing the framework proposed in the paper over a mixture of experts is the idea of state separation, which allows visualization and explainability via representation. Utilizing the novel contrastive function to promote diversity in recurrent neural networks allows for state separation. This is particularly relevant in the medical setting, where state separation can allow for the identification of clinical states amenable to different diagnostic and therapeutic interventions. Learning these representations can allow physician to give drug an economist formulate a fiscal policy. We provide the specific example of the ICU measurements, where if an individual belongs state where increased pressure on the brain is identified, then an appropriately targeted intervention can be provided. Mixtures of expert models do not typically generate representations to interpret and therefore, have limited explainability state-dependent time-series analysis.
2.5.3 VAES AND TFTS FOR DISCRETE LATENT SPACES
Deep Learning Networks with discrete latent spaces have been utilized in the past with relatively high degrees of success. For example, VAEs can discretize the latent space with encoder-decoder setup, and has been more hcavily applied to interpreted disentangling of discrete representation learning Williams et al. (222I). Networks with attention such as temporal fusion transformers en- code a time series patterss into key-value dictionary, which can be thought of as another discrete latent space Lim et al. (02T).
SpaRTeN offers advantages over these methods. First, while VAEs and TFT generate representa- tion in the latent space, SpaRTEn clearly identifies the representation in the space of the time series. Generating representation in the same space as the time series allows for improved explainabil- ity, as we demonstrate in section 3.4 Second, VAFS are typically constrained to reconstruction or KL-divergence based loss and have yet to be implemented for forecasting. In contrast, SpaRTeN can be adapted to different tasks by choosing different loss functions for the Rt block. Third, our benchmarks as versatile ensemble, SpaRTEn can include these models networks in the R-B B-ooock. Fourth and finally, we benchmark against TFTs forecasting ability and show that SpaRTEn outper- forms.
One extension of VAEs with a spatially resolved latent space encodes time series in a organiiign map Fortuin et al. (2018) Self-organizing maps are an extension of discrete latent spaces that
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represents input space with fixed dimensionality discrete two-dimensional Euclidean space. Each node in the two dimensional map a single neuron, and the best matching neuron is adjusted towards imput. This model learns state transitions via Markov modeling the self-orgamizing map. We extend self-organizing maps differently, where nodes represent distinct subnetworks rather than decodable state, which allows distinet weights and architectures. Using separate block predict the node, we can eliminate the Markov chain used in SOM-VAES
3 APPLICATION
For our applications, we focus on three distinct tasks involving high frequency time series - online forecasting, zero-shot clustering and clinically significant representation learning.
3.1 ONLINE FORECASTING WITH SPARTEN
Online forecasting involves looking at window in time series and using that window to predict the next set of elements. For the R-Block, we minimize sMAPE (Symmetric Mean Absolute Percentage Error) the primary objective in forecasting task:
1 N
y y4
y/
sMAPE
19
where N is the number of examples used for training. sMAPE is metric that has been typically reported in the past with competitions like the M4 time series forecasting competition Makridakis al. 2018). For the S-Block, we utilize a standard cross-entropy loss for multi-class classification.
We benchmark against SOTA online forecasting models with convolutional approaches such as N- Beats Oreshkin al. (2019b) and attention based methods like Temporal Fusion Transformers Lim itt al. (2019) and Autoformers Wu et al. (202I). where SpaRTEn outperforms on three out of the four datasets (Table 1). Because these forecasting remains relatively unstable over these datasets, we only include RMSE calculated during which the S-block predictions were stable. Over large batches, we anticipate that other networks such as autoformers and TFTs that can capture long-term dependencies and recurrent patterns would outperform. However, these networks are not mutually exclusive with our ensemble method, and we utilize a base case of simple ruto-regressive networks to demonstrate that spatially constrained ensemble learning does not hurt performance.
Table I: RMSE of benchmarks on an online forecasting task
Datasets
Model
Electricity
Traffic
Stocks
Retail
LSTM
2.93
32.10
0.13
13.76
N-Beats
2.84
3.10
0.10
14.16
TFT
2.49
15.10
0.11
13.87
Autoformer
6.61
3.34
1.24
4.98
SpaRTEn 1.57
1.58
0.67
1.59
3.2 ZERO-SHOT CLUSTERING OF HIGH FREQUENCY TIME SERIES
Zero-shot clustering is unsupervised method that involves classifying the time series the first time is seen without information corresponding to label. We demonstrate that SpaRTeN can generate prototypical waveforms, that be utilized by K-Nearest Neighbors to perform ttate-of-the-art for zero-shot clustering methods. We benchmark on traditional clustering techniques such as KNN, Gaussian Mixture Modeling and Spectral Clustering.
In order to compare the distinct properties of each state and demonstrate the ability to cluster wave- forms within given state, we train SpaRTeN with latent state space of 3 x 3. We train KNN with & = 9 on the (3 x 3 = 9) distinct waveforms aggregated by state, and evaluate its ability to cluster all the waveforms the dataset using a silhouette score, which is widely used evaluate

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the goodness of a clustering technique. SpaRTEn outperforms all other methods used cluster time series on all four datasets.
Table 2: Silhouette score of benchmarks on an unsupervised clustering task
Datasets
Model
Electricity
Traffic
Stocks
Retail
Random
0.023
0.22
0,012
0.011
Spectral
0.005
0.09
0.005
0.002
GMM
0.024
0.12
0.011
0.010
SpaRTEn
0.028
0.24
0.026
0.027
3.3 ABLATION STUDIES
We run additional ablation experiments across these four datasets including increasing the size of the latent space, and eliminating the distance-weighted contrastive loss, which lead to deterioration on the clustering metric.
These ablation studies demonstrate that the S-block is necessary for adequate performance in online forecasting, which may be due to over-squashing in naive temporal models Alon & Yahav 2020 Other aspects of model are less important for this metric.
In contrast, all aspects of the model crucial to generating clusters. For example, eliminating the distance- distance-weighter weighted contrastive loss leads to a 15% decrease in silhouette score for UCI Electricity, a 29% decrease for UCI Traffic, and 53% decrease for Kaggle Retail. Although the online forecast- ing aspect of SpaRTen performed poorly in the Oxford stocks dataset, the clustering task beat the benchmarks. Eliminating the distance weiigttd contrastive loss led 51% decrease in silhouette score on this task. We hypothesize that adding a spatial loss improves sub-network diversity by increas- ing state separation, aiding downstream clustering tasks. We also find that an wee-parameterized the state-space can actually lead to self-regula eef-reeularization,, where the network learns to under-utilize the coordinate system given the complexity of the time series.
Table 3: Ablation study on benchmarked datasets
Dataset
Electricity
Traffic
Stocks
Retail
Ablation
RMSE
Silhouette
RMSE
Silhouette
RMSE
Silhouette
RMSE
Silhouette
S-block
2.93
X
32.10
0.13
X
13.76
10 x 10
2.58
0.019
1.58
0.15
0.57
0.005
1.61
0,001
DWCL
2.57
0.024
1.62
0.17
0.60
0.012
1.60
0.013
None 1.58
0.028
1.58
0.24
0.67
0.026
1.59
0.027
3.4 TIME BRAIN: CLINICALLY RELEVANT REPRESENTATION LEARNING
We demonstrate the practical application of SpaRTeN to intracranial pressure (ICP) waveforms from the MIMIC-IV dataset. ICP waveforms are suited for online learning because they provide high fre- quency time series with significant inter-individual variability. In neuro-critical care, time is brain Desai et al. (2019). Timely identification of ICP states may allow treating physicians to intervene and mitigate neurological injury.
We trained SpaRTeN on ICP waveforms across 400 time steps (Figure 2). optimizing hyper- parameters with a grid-search conducted over the state-space and learning rates for both the / and blocks, a, and the depth and width of the sub-networks. This resulted
distinct classes (Figure 2(c)). SpaRTeN outperformed spectral clustering, k-means applied random sampling and Gaussian mixture models as determined by the silhouette score, and this was robust to sample size (Figure b). Table 4)
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Row waveform data
Evalsution
10-
Scoted Intcoona Precsue (11r
8.0
Validate
Shooeh Score
KNN
SpaRTTeN
SC
1000
Visualize
Baseline
Hyperrectivee
Hyporeactive
Co chett
ZZZ
Scaled ICP grmn
0.0)
Decompensation
Management
Hemarrhage
Clinical
Interp
Hypotension
Hypertension
Instability
2.2
SpaRTeN
Clinical Relevance
Figure 2: Qualitatively and quantitatively evaluating model representations. Raw waveforms of Intra-cranial Pressure with high intra-sample variability. b) Bootstrapped (10x) results of silhou- ette score across different sized samples demonstrates that SpaRTeN outperforms other clustering methods. 95% Confidence intervals reported in the figure, but may be too small to see. c) Clusters generated by SpaRTeN represent distinct trends within the time series. d) Clinical interpretation of each of the waveforms.
The nine classes identified by SpaRTeN on are interpretable as clinical states (Figure 4()).
that the waveform is both stable and relatively constant. This is strong baseline for what non pathological waveforms should look like. At point (0, 1) we see increasing be part of an adaptive
At position 0),
oscillations in the pressure, but with smaller average change. This response to injurySvedung Wettervik et al.] (2020), where some of the compensatory mechanisms starting be hyper-reactive. In contrast, at point (0, 2). we see that the intraeranial pressure waveform has a U-shape, with a relatively slow dip and return to baseline. Such slow, hypo-reactive ICP waveforms have been associated with worse performance on the Glasgow Coma Scale Tian et al. (2013). measure of level of consciousness. A physician may try to shift patient's 's state from (0,2) (0. 1) order improve outcomes by increasing the tone of the sympathetic nervous system Schmidt et al. (2018).
In the second row represents acute dysregulation of ICP. At point (1, we see that the there are signs of instability, followed by acute drop in the intracranial pressure. Such a patient may ben- efit from an urgent CT scan. At point (1, 1) and (1, 2). we see that there is complete dysregulation of the brain's vasculature with dramatic decreases and increases in intracranial pressure, respec- tively. (1,2) may represent cerebral hemorrhage which causes a rapid increase in ICP. Physicians
manage this with various interventions surgeryCaceres Caceres & Goldstein (2012). (1, 1) shows
rapid decrease in intracranial pressure as might be expected following the placement of an external ventricular drain Kramer (202)).
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The bottom represents slower, more chronic decompensation than seen in the second row. (2, 0) and (2, 1) show slower decreases and increases ICP, respectively. While both these can manifest as headaches, diuretic drugs worsen the former but effectively treat the latter Luetzen et al. (2021). Finally, the pattern in (2,2) shows slower oscillations without much average change but may be early warning of progression one of the more acute states in the second row Oernbo et al. (2022).
Table 4: Silhouette Score of representations of Intracranial Pressure Waveforms
Sample Size
Model
10
25
100
400
Spectral
0.131 + 0.023
0.165 + 0.008
0.109 = 0.007
0.156
0.003
Random
0.366 + 0.018
0.275 = 0.007
0.252 = 0.005
0.276 = 0.002
GMM
0.341 + 0.019
0.345 + 0.005
0.329 + 0.004
0.344 0.003
SpaRTeN
0.415 + 0.020
0.422 + 0.006
0.385 + 0.005
0.405 + 0.002
To our knowledge, this is the first algorithm to use an online contrastive learning approach for time series classification. While it is known that discriminative region-based zero-shot learning in images can preserve context information Narayan et al. (202I), SpaRTeN representations quantitatively capture variations within the data, and qualitatively provide key clinical insights into waveform patterns.
POTENTIAL LIMITATIONS
SpaRTeN is novel min-max framework for decoding states, and has many of the same advantages and disadvantages as other min-max frameworks. Without sufficient gradient-based optimizations like smoothing and replacing density-based losses with negative log-likelihood losses, the gradients and states learned by SpaRTeN can be highly unstable (Appendix (A.2). Subsequently, a collapse in the gradients on one of the blocks can be highly detrimental other blocks.
Second, many datasets, especially in the ICU contain multi-modal sources of information. Currently, models like temporal fusion transforms can better account for multi-modal trends in time series and combine categorical with continuous variables. We anticipate further development of the SpaRTeN framework by including R-blocks that are capable of accounting for different variable types and data modalities may further enhance the ability of SpaRTeN to generate multi-nodal archetype waveforms, which can be subsequently used to qualitatively evaluate changing states in the clinical setting.
Third, we selected 2D geometry because it was computationally tractable in terms of the distance- weighted contrastive loss, and interpretable in the ICU setting, Ablation of the the contrastive loss leads to poorer representation learning and clustering. Future work could explore latent spaces and hyperbolic geometry.
5 CONCLUSIONS
We introduce a novel method called SpaRTeN (Spatially Resolved Temporal Networks) for discrete representations of time series via unsupervised learning and a forecasting objective. SpaRTeN stores models rather than samples in an embedding space, which allows for rapid interpretable learning of structured representations in high frequency time series. We show that it can be broadly applied to online forecasting and clustering. We anticipate that improvements in size, algorithmic and opti- mization details will only continue to further improve upon the SpaRTeN framework. Finally, we further intend to demonstrate the applicability of this model architecture to real-time, online clinical decision support in situations like the decoding states for patients in the ICU. Thus, the SpaRTeN framework can be generalized to different network blocks, optimization techniques and use cases. takes a key step towards the goal of generating individualized state representations with online learning. These analyses demonstrate that SpaRTEn is able to decipher clinically meaningful states. Moreover, utilizing these state analyses to better disentangle states can improve the understanding of clinical treatment and associated outcomes Samartsidis et al. 2018).
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REPRODUCIBILITY STATEMENT
All experiments were performed with PyTorch. The code for the algorithm is attached in the sup- plementary material.
7 ETHICS STATEMENT
Experiments with publicly available de-identified data from the MIMIC-III Waveform Database were conducted with IRB approval. All other datasets that we used also publicly available. This work is not expected to lead to negative societal implications.
REFERENCES
Uri Alon and Eran Yahav. On the bottleneck of graph neural networks and its practical implications. arXiv preprint arXiv:2006.05203 2020.
Samaneh Aminikhanghahi and Diane Cook. A survey of methods for time series change point detection, 2017.
Ane Blazquez-Gareia and Angel Conde. A review outlier/anomaly detection in time series data, 2022.
J Alfredo Caceres and Joshua N Goldstein. Intracranial hemorrhage. Emergency medicine clinics of North America, 30(3):771-794, 2012.
Shashvat M Desai, Marcelo Rocha, Tudor G Jovin, and Ashutosh P Jadhav. High variability in neuronal loss: time is brain, requantified. Stroke, 50(1):34-37, 2019.
Vincent Fortuin, Matthias Hüser, Francesco Locatello, Heiko Strathmann, and Gunnar Rätsch.
SOM-VAE: Interpretable discrete representation learning on time series. June 2018.
Yean-Yves Franceschi, Aymeric Dieuleveut, and Martin Jaggi. Unsupervised scalable representation learning for multivariate time series. January 2019.
Ian Goodfellow, Jean Pouget-Abadie, Mchdi Mirza, Bing Xu, David Warde-Farley. Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative ad adversarial nets. In Z Ghahramani, M Welling, C Cortes, N Lawrence, and Weinberger (eds.), Advances in Neural Information Processing Systems, volume 27. Curran Associates, Inc., 2014.
Josif Grabocka, Martin Wistuba, and Lars Schmidt-Thiens Scalable discovery of Time-Series shapelets. March 2015.
Bean-Bastien Grill, Florian Strub, Florent Altché, Corentin Tallec, Pierre Richemond, Elena Buchatskaya, Carl Doersch, Bernardo Avila Pires, Zhaohan Guo, Mohammad Gheshlaghi Azar, et al. Bootstrap your own latent-a new approach to self-supervised learning. Advances in neural information processing systems, 33:21271-21288 2020.
Hadsell, S Chopra, and LeCun. Dimensionality reduction by learning an invariant map- ping. In 2006 IEEE Computer Society Conference Computer Vision and Pattern Recognition (CVPR'06), volume 2, pp. 1735-1742, June 2006.
Anfeng He, Chong Luo, Xinmei Tian, and Wenjun Zeng. A twofold siamese network for real- time object tracking. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 4834 4843, 2018
Kaiming He, Haoqi Fan, Yuxin Wu, Saining Xie, and Ross Girshick. Momentum contrast for unsupervised visual representation learning. November 2019.
Steven C H Hoi, Doyen Sahoo, Jing Lu, and Peilin Zhao. Online learning: A comprehensive survey. Neurocomputing, 459:249-22 October 2021.
10

---

Under review as a conference paper at ICLR 2023
Sundreen Asad Kamal, Changchang Yin, Buyue Qian, and Ping Zhang. An interpretable risk pre- diction model for healthcare with pattern attention.
Oguzhan Karaahmetoglu, Fatih Ilhan, Ismail Balaban, and Suleyman Serdar Kozat. Unsupervised online anomaly detection on irregularly sampled or missing valued Time-Series data using LSTM networks. May 2020.
Andreas H Kramer. Critical iep in subarachnoid hemorrhage: how high and how long? Neurocritical Care, 34(3):114-715 2021.
Yuening Li, Zhengzhang Chen, Daochen Zha, Mengnan Du, Denghui Zhang, Haifeng Chen, and Xia Hu. Learning disentangled representations for time series. May 2021.
Bryan Lim, Sercan O. Arik, Nicolas Loeff, and Tomas Pfister. Temporal fusion transformers for interpretable multi-horizon time series forecasting, 2019. URL httpt:ttp////mm htttp:://axive http:///xxvvvo..//eeee 9122.9366
Bryan Lim, Sercan Ô Arık, Nicolas Loeff, and Tomas Pfister. Temporal fusion transformers for interpretable multi-horizon time series forecasting. Int. J. Forecast, 1744)1174--1764, October 2021.
Osian Llwyd, Jui-Lin Fan, and Martin Müller. Effect of drug interventions on cerebral hemodynam- ics in ischemic stroke patients. Journal of Cerebral Blood Flow & Metabblism, 42(3):471-485, 2022.
Niklas Luetzen, Philippe Dovi-Akue, Christian Fung, Juergen Beck, and Horst Urbach. Spontancous intracranial hypotension: diagnostic and therapeutic workup. Neuroradiology, 63(11):1765-1772, 2021.
Chao Luo, Chenhao Tan, Xingyuan Wang, and Yuanjie Zheng, An evolving recurrent interval type- intuitionistic fuzzy neural network for online learning and time series prediction. Appl. Soft Comput., 78:15 150-163, May 2019.
Spyros Makridakis, Evangelos Spiliotis, and Vassilios Assimakopoulos. The M4 competition: Re- sults, findings, conclusion and way forward. Int. J. Forecast., 34(4))802-800) October 2018.
Leland Mclnnes, John Healy, Nathaniel Saul, and Lukas Großberger. UMAP: Uniform manifold approximation and projection, 2018.
Susan P Mollan, Fizzah Ali, Ghaniah Hassan-Smith, Hannah Botfield, Deborah Friedman, and Alexandra J Sinclair. Evolving evidence in adult idiopathic intracranial hypertension: patho- physiology and management. Journal of Neurology, Neurosurgery & Psychiatry, 870))982-992 2016.
Sanath Narayan, Akshita Gupta, Salman Khan, Fahad Shahbaz Khan, Ling Shao, and Mubarak Shah. Discriminative region-based Multi-Label Zero-Shot learning. August 2021.
Eva K Oerbbo, Annette Steffensen, Pooya Razzaghi Khamesi, Trine L Berteeerressn, Dagne Barbuskaite, Frederik Vilhardt, Niklas J Gerkau, Katerina Tritsaris, Anja H Simonsen, Sara D Lolansen, et al. Membrane transporters control cerebrospinal fluid formation independently of conventional osmosis to modulate intracranial pressure. Fluids and Barriers of the CNS. 19(1): 1-25, 2022.
Boris N Oreshkin, Dmitri Carpov, Nicolas Chapados, and Yoshua Bengio. N-BEATS: Neural basis expansion analysis for interpretable time series forecasting. May 2019a.
Boris N. Oreshkin, Dmitri Carpov, Nicolas Chapados, and Yoshua Bengio. N-beats: Neural basis expansion analysis for interpretable time series forecasting, 2019b. URL https://axxix. org/ 1955. 10437
Wenjie Pei, David M Tax, and Laurens van der Maaten. Modeling time series similarity with siamese recurrent networks. March 2016.
11

---

Under review as a conference paper at ICLR 2023
Pantelis Samartsidis, Shaun R Seaman, Anne M Presanis, Matthew Hickman, and Daniela De An- gelis. Assessing the causal effect of binary interventions from observational panel data with few treated units. April 2018.
Ramasamy Savitha, Arulmurugan Ambikapathi, and Kanagasabai Rajaraman. Online RBM: Grow- ing restricted boltzmann machine on the fly for unsupervised representation. Appl. Soft Comput., 92:106278, July 2020.
Eric A Schmidt, Fabien Despas, Anne Pavy-Le Traon, Zofia Czosnyka, John D Pickard, Kamal Rahmouni, Atul Pathak, and Jean M Senard. Intracranial pressure is a determinant of sympathetic activity. Frontiers in physiology, 9:11, 2018.
Moonis Shakeel and Bhavana Srivastava. Stylized facts of high-frequency financial time series data. Global Bus. Rev., 22(2):550-564, April 2021.
Shaolong Sun, Yunjie Wei, and Shouyang Wang. AdaBoost-LSTM ensemble learning for financial time series forecasting, 2018.
Teodor Svedung Wettervik, Timothy Howells, Per Enblad, and Anders Lewén. Intracranial pres- sure variability: relation clinical outcome, intracranial pressure- voluuee index, cerebrovascular reactivity and blood pressure variability. Journal of clinical monitoring and computing, 34(4): 733-741, 2020.
Jans-Christian Thorsen-Meyer, Annelaura B Nielsen, Anna P Nielsen, Benjamin Skov Kaas- Hansen, Palle Toft, Jens Schierbeck, Thomas Strøm, Piotr Chmura, Mare Heimann, Lars Dyb- dahl, Lasse Spangsege, Patrick Hulsen, Kirstine Belling, Søren Brunak, and Anders Perner. Dy- namic and explainable machine learning prediction of mortality in patients the intensive care unit: retrospective study of high-frequency data in electronic patient records, 2020.
Ye Tian, Zengguang Wang, Ying Jia, Shengjie Li, Bin Wang, Shizhao Wang, Lin Sun, Jianning Zhang, Jieli Chen, and Rongcai Jiang. Intracranial pressure variability predicts short-term out- come after intracerebral hemorrhage: a retrospective study. Journal of the neurological sciences, 330(1-2):38 44, 2013.
Aaron Van Den Oord and Oriol Vinyals. Neural discrete representation learning.. 2017.
Laurens Van der Maaten and Geoffrey Hinton. Visualizing data using t-SNE. J. Mach. Learn. Res., 9(11), 2008.
Jennifer Williams, Yi Zhao, Erica Cooper, and Junichi Yamagishi. Learning disentangled phone and speaker representations in semi-supervised vq-vae paradigm. In ICASSP 2021 202/ IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 7053-7057, 2021. doi: 10.1 D0.1199/CAASPP9992222200000
Haixu Wu, Jiehui Xu, Jianmin Wang, and Mingsheng Long. Autoformer: Decomposition trans- formers with auto-correlation for long-tern series forecasting. Advances in Neural Information Processing Systems, 34:22419-22430, 2021.
Fangfang Yao, Jida Wang, Chao Wang, and Jean-François Crétaux. Constructing long-term high- frequency time series of global lake and reservoir areas using landsat imagery. Remote Sens. Environ., 232:111210 October 2019.
Zhi-Hua Zhou. Ensemble learning. Encyclopedia of biometrics, 1:270-273, 2009.
Fuzhen Zhuang, Zhiyuan Qi, Keyu Duan, Dongbo Xi, Yongchun Zhu, Hengshu Zhu, Hui Xiong, and Qing He. comprehensive survey on transfer learning. Proc. IEEE, 109(1):3376, January 2021.
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A APPENDIX
A.1 DISTANCE- SITANCE-WEIGHTED CONTRASTIVE LOSS
The general idea of contrastive loss is to preserve neighborhood relationships between data points by minimizing the distance between similar points and maximizing the distance between points of different classes Hadsell et al. (2066) The general form of the contrastive loss function the following:
(2 1y Mil d fol)) 1w: + vil cux(O,,-d(fo(x)).fee (5)
2
where I; and zjj two distinct samples, is function that maps -> R embedding of dimensionality k, d is distance metric, and is the distance to the margin. In multi-class classifi- cation problems, this be further extended as a classification problem with K categories He et al. 2019).
Lng = - log
(6)
E (ein(Soluxx
where (ia() (xx)) is metric of similarity between (x; and ((r, and is the normaliza- tion factor.
We can extend this forecasting where the positive example can be thought as the selected sub-network, whereas the negative examples are the irrelevant sub-networks. Finally, we add normalized distance metric, to ensure sub-networks that are closer in euclidean space have closer representations.
Rio
LowcL(Rr,: = -log
Ex (sim(Re x [[-
Des (2-1)++(y-))
We visualize this further in Figure 3
The overall computational cost is O(e(S, b) + (K - 1) c(J)), where c(f) ()) is the cost of forward propagating, and c(f, b) the cost of forward and back-propagating. and K the total number of blocks. Thus, computational cost scales with the number of sub-networks.
c.o
(a) Matrix Predictions
(c) Similarity Block
4:50
2018
(d) Loss Block
(b) Block Predictions
(d) Distance Block
Figure 3: Loss calculations for the R-matrix. (a) Is the caleulation of the R-matrix predictions for the next time step. (b) S-Block predicts the appropriate state for the next time step. (c) The similarity block calculates similarity between the chosen state prediction and the other states. (d) The distance block calculates the distance between each other state and the selected substates. The loss block is the dot product of the distance and similarity block. The loss block is summed to produce the final loss value
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A.2 ENCOURAGING SMOOTHNESS OVER TIME
The goal is to predict the development of a time series in an interpretable way. This means that we may have tradeoff between stable network dynamies and representation of a ground truth density. Learning a probabilistic model in a high-dimensional continuous space can be challenging, which necessitates the use of reductionist frameworks to improve interpretability.
Previous work in Markov chain modeling penalized state transitions via an additional smoothness term Fortuin al. (2018). Other methods have focused on incorporating quantile outputs maxi- mize the signal-tor comnalttonnoiee noise ratio Lim et al. (202I).
We find that by converting an L2-norm-baace loss function to cross-entropy loss, we can improve the stability of both the S-block representations, and by extension, the R-block ensemble:
[a.b)] Σ
Ls =
arg argmin(Ae arg.mn(RR,,aa)) - xo+1)² x logg((((z))
4
where 2 is a discrete two-dimensional space of integers in [a, b), the sum is over all the coordinates in the space, Rs,((2) is the prediction of the next time step by the network based on the previous time step, F is the next step. a represents soft-max function, and 5 ((x,) is the predicted state of the next time step. S fails provide strong initial gradients, in the case with Z--norm, then the instability the network prevents a single sub-network from learning the characteristics of a given state (Figure 4.. In turn, this causes the S-block to be increasingly volatile, which can turn further destabilize the R-block.
0132
My Mad wop
83
0.00
0005
Tran Step
Tomen Stepp
(a) La norn loss
(b) L--morm state
02-
-1.3
0.35
23
(c) NLL loss
(d) NLL state
Figure 4: Losses and associated states for L2- L2-norm and negative logelikelihood. (a) L2-norm loss significantly smaller and signal-to-noise ratio is smaller than (c) negative log likelihood (NLL) loss. The corresponding states calculated by the (b) L2 loss are more unstable than the states calculated by the (d) negative log likelihood S- b-olock.
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A.3 S-BLOCK ARCHITECTURE
The goal of the S-block is to translate a high-frequency time series into a spatial coordinate system with dimensionality of a, b. The flexibility of fully connected networks in conjunction with spatial constraints imposed by convolutional filters biases the network towards spatial representation of the temporal networks.
The S-block consists of four key layers, a ID-CNN, fully connected network layer with (a + 2) (b + 2) number of units, layer that reshapes the fully connected network block into an (a ( 2) x (b + 2) rectangle, followed by a 3 x 3 convolution with a stride length of 2, to produce an ultimate output layer of dimension ab (Figure
A discrete state space was chosen to improve the interpretability of the model sub-networks to produce meaningful results. However, future work may replace the discrete state space output with representation of a density distribution continuous vector space.
k
1xk
(x
(a+2) (b+2)
1
2
3
3
1
2
3
a+2
2
1
3
1D-CNN
FCN
reshape
2D-CNN
b+2
(a+2)
(b+2)
k
Figure 5: Network architecture the S-Block. The S-block consists of four key layers, a ID-CNN, fully connected network layer with (a 2) (6 + 2) number units, layer that reshapes the fully connected network block into an (a 2) x (b + rectangle, followed by a 3 x convolution with stride length of 2, to produce an ultimate output layer of dimension width length.
15


Reviews:
[{"review_id": "YkUu1ZyMNFN", "reviewer": "Reviewer_AkMC", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "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": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "", "main_review": "", "summary_of_the_paper": "In this paper, the authors propose a new time series forecasting model for univariate high-frequency time series. There two major components/blocks of the model: one block contains ensemble of base predictors/LSTM for time series forecasting and the second spatial block is trained using contrastive learning to find the best base predictor or LSTM. The whole model works like the minimax framework. Experiments on online forecasting and zero-shot clustering show efficacy of the proposed method.\n", "summary_of_the_review": "1. Regarding contrastive loss, we know that it works fine for images. Here the motivation and rationale of employing the distance-weighted contrastive loss DWCL for univariate time series forecasting is not clear to me. How are similar and dissimilar pairs selected in the training process?\n2. What is the benefit of using a two-dimensional discrete state-space in the S-block? For the purpose of selecting the best base predictor, one-dimensional state-space should be enough. Also in the training of the S-block, cross-entropy loss function is used which actually works fine with the one-dimensional state-space.\n3. In Sec. 3.3, why does ensemble weight sharing help for time series forecasting? If we wanna a diverse ensemble which can cover a broader state-space, should we limit the use of ensemble weight sharing which may lead to the mode collapse (common challenge in GAN).\n4. The S-block actually reminds me the attention mechanism which can also be used to select the optimal state/predictor. It would be interesting to see discussion on comparison of S-block and attention. For example, what are the advantages of S-block over attention and gating in the temporal fusion transformer (TFT).\n5. In practice, individual LSTM has limited forecasting power compared with state-of-the-art (SOTA) algorithms for time series forecasting. More analysis on how ensemble of LSTMs could achieve better prediction performance will help reader to understand the contribution and novelty of this work.\n6. Evaluations are limited and only done on two datasets which makes it less convincing. More experiments and comparisons with SOTA methods are encouraged", "strength_and_weaknesses": "Strength\nThe whole framework looks novel and incorporates recent advances in ML like contrastive learning for time series forecasting. \n\nWeakness\nMotivations and rationale behind the proposed model is not well explained. It is not very clear how these components interact and why all the components work in a synergetic way.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "VfZ5WQBXv", "reviewer": "Reviewer_9w1q", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "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": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "", "main_review": "", "summary_of_the_paper": "Spatial Resolved Temporal Networks (SpaRTeN) are described in this paper as a novel, composite deep learning model for online, unsupervised representation learning in a spatially constrained latent space. In the proposed approach, two distinct components are simultaneously learned: a recurrent neural network ensemble that captures states in high-frequency time series, as well as a spatial block that is able to spatially resolve state changes based on the predictions generated by the other network. Throughout, it is an interesting paper, and the proposed method yields several practical applications for a wide range of machine learning problems. Major concerns and minor comments are presented in the review section.", "summary_of_the_review": "a) The empirical studies do not provide convincing evidence. The proposed method can be applied to time series in a variety of applications, as indicated in the abstract. Consequently, it would be beneficial if authors benchmarked the proposed technique against several real-world datasets.\n\nb) The performance of the proposed method should be compared with similar state-of-the-art approaches. That would be interesting to compare the proposed method with some recent studies in Transformers, Energy-Based approaches, and Reinforcement Learnings.\n\nc) The figures and tables in this paper are ambiguous. As an example, what are the metrics in Table 1 (mean column) and Table 2? Furthermore, Figure 2 is blurry and difficult to read.\n\nd) In this paper, the notations are confusing. In regular papers, scalers are denoted by small letters; vectors are defined with small letters (highlighted in bold), and matrices are denoted by capital letters using bold. In this paper, they are a lot of conflicts. It is so hard to trace what is a set, a matrix, or even a distribution.\n\nf) There are some minor linguistic and typo problems in this paper.\n", "strength_and_weaknesses": "Please refer to the review section.\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "4qm5aBFqaG9", "reviewer": "Reviewer_8297", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 3, "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": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "", "main_review": "", "summary_of_the_paper": "The authors introduce a deep learning framework to analyze time series (identification of different states, detection of state transition, etc.). The framework presented in the paper is based on an ensemble network composed of LSTMs (each corresponding to a state) and a 1D CNN that allow to choose the best LSTM or state. The proposed technique has been applied for forecasting and clustering tasks on various time series data.", "summary_of_the_review": "The presentation of the proposed method lacks clarity, which makes it hard to understand their approach, how it differs from state-of-the-art. The results do not allow me to judge the usefulness of the proposed technique.", "strength_and_weaknesses": "Strengths:\n1.\tUse of different databases and applications (though does not see the clinical usefulness of the biomedical application, would have been interesting to assess on a classification problem (such as sepsis prediction for ICU data)\n2.\tThe authors performed an ablation to highlight the added-value of each part of their technique.\n3.\tSource code is provided for better reproducibility.\nWeaknesses:\n\n1.\tThe authors could have given more insight on the practical usefulness of their framework, for instance with the interpretation of clinical states with the ICP waveforms. Is the method clinically relevant given the low silhouette scores obtained? Could be interesting to visualize ECG forecasting. What more does SpaRTEn bring compared to the other methods, as it is hard to tell with sMAPE values only. Are the predicted ECGs still interpretable (clear delineation of P, QRS, T waves …)? I don’ t understand what it means to predict 20 ECG samples (what is the sampling frequency? Given the typical ECG sampling frequency, 20 samples would correspond to less than 100ms, so I fail to understand the clinical usefulness of predicting such a short window of ECG samples\n2.\tThe description of the proposed method lacks clarity. I would suggest present the methodology of the technique in a more structure way, clearly explaining how he training process is performed.\n3.\tI fail to understand the contrastive learning approach of the method. Do the authors suggest that the spatial representation is time independent? Could the authors compare their approach to a BYOL approach?  On top of that, one of the characteristics of biomedical times-series lies in their non-stationarity nature which would imply that the assumption of stable spatial representation does not hold. Could the author comment on that?\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}]

Author rebuttal:

Decision: Reject