Meta Guidance: Incorporating Inductive Biases into Deep Time Series Imputers
Authors: Jiacheng You
Xinyang Chen
Yu Sun
Weili Guan
Liqiang Nie
Venue: NeurIPS 2025 poster ()
Keywords: data imputation; time series; inductive bias; non-stationarity; periodicity
Primary area: other

Abstract: Missing values, frequently encountered in time series data, can significantly impair the effectiveness of analytical methods. While deep imputation models have emerged as the predominant approach due to their superior performance, explicitly incorporating inductive biases aligned with time-series characteristics offers substantial improvement potential. Taking advantage of non-stationarity and periodicity in time series, two domain-specific inductive biases are designed: (1) Non-Stationary Guidance, which operationalizes the proximity principle to address highly non-stationary series by emphasizing temporal neighbors, and (2) Periodic Guidance, which exploits periodicity patterns through learnable weight allocation across historical periods. Building upon these complementary mechanisms, the overall module, named Meta Guidance, dynamically fuses both guidances through data-adaptive weights learned from the specific input sample. Experiments on nine benchmark datasets demonstrate that integrating Meta Guidance into existing deep imputation architectures achieves an average 27.39\% reduction in imputation error compared to state-of-the-art baselines.

Meta Guidance: Incorporating Inductive Biases into Deep Time Series Imputers
Jiacheng You' Xinyang Chen lee Yu Sun? Weili Guan Liqiang Nie
School of Computer Science and Technology. Harbin Institute of Technology (Shenzhen) Coollege of Computer Science, DISSec, Nankai University School of Information Science and Technology, Harbin Institute of Technology (Shenzhen) mieliqiang)@@mail. @gmail. com
{jiachengyouhiiz chenxinyang95, niel mieliqiang) sunyu@nankai. cn, guanweil 1i@hit. edu.cn en
Abstract
Missing values, frequently encountered in time series data, significantly im- pair the effectiveness of analytical methods. While deep imputation models have emerged the predominant approach due their superior performance, explic- itly incorporating inductive biases aligned with time-series characteristics offers substantial improvement potential. Taking advantage of non-stationarity and pe- riodicity in time series, two domain-speciie Non-Stationary Guidance, which operationalizes the proximity principle address highly non-stationary series by emphasizing temporal neighbors, and (2) Periodic Guidance, which exploits periodicity patterns through learnable weight allocation across historical periods. Building upon these complementary mechanisms, the overall module, named Meta Guidance, dynamically fuses both guidances through data-adaptive weights learned from the specific input sample. Experiments on nine benchmark datasets demonstrate that integrating Meta Guidance into existing deep imputation architectures achieves an average 27. 27.39% reduction in imputation error compared to state-of-the-ard baselines.
inductive biases are designed: (1)
Introduction
Multivariate time series data ubiquitous in domains ranging from finance healthcare. However, real-world deployments commonly exhibit missing values [32 43 caused by sensor malfunctions, communication disruptions, or incomplete data acquisition. Such missingness undermines data integrity and impedes downstream applications [II), establishing accurate imputation as a critical prerequisite for robust modeling and analysis.
Traditional imputation methods 24 13 have demonstrated competence in time series completion. The deep learning revolution has further advanced imputation techniques (5] capitalizing their ability to model nonlinear dependencies. Recent innovations in diffusion models [4 and transformer architectures [41 & have emerged state-of-the-art imputers. However, current approaches always adopt end-to-end learning to implicitly infer temporal patterns, largely overlooking the strategic integration of domain-specific inductive biases known enhance imputation. This motivates our core research problem: Can deep time series imputers achieve superior performance by incorporating domain- -seciifc inductive biases rather than relying exclusively on data-driven pattern discovery?
In this paper, we introduce an intuitive and interpretable approach for embedding inductive biases into deep time series imputation models. Real- world time series often exhibit non-stationary trends [14] and periodicity (9] To capture these properties, we design two interpretable guidance matrices: Non- Stationary Guidance (NSG) and Periodic Guidance (PG). In the NSG matrices. the "proximity principle" is employed, wherein heightened importance is assigned to values in close proximity to the
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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missing value. In the PG matrices, increased importance is assigned to values located at one or more period lengths away from the missing value. Recognizing that different segments of time series data vary in their dominant characteristics, we develop Meta Guidance (MG) a learnable mechanism that adaptively fuses NSG and PG based on specific input. When injected into advanced deep architectures (TCN, diffusion, and Transformer), MG consistently improves performance, yieldiin 27.39% average error reduction across nine datasets.
Our main contributions are summarized as follows:
By exploiting the non-stationarity and periodicity properties of time series data, two inductive biases for time series imputations are proposed and explicitly encoded through two interpretable structures. Among them, NSG captures local temporal continuity via the proximity principle, while PG models periodic dependencies by emphasizing values at fixed temporal intervals.
MG, lightweight and model madel-agnostic module that adaptively learns the importance of NSG and PG based on the characteristics of the specific input are proposed. MG can be seamlessly integrated into diverse deep imputation architectures, enhancing their flexibility and enabling dynamic adaptation to varying temporal dynamics.
We integrate MG into advanced deep imputation models and evaluate its performance nine real- world datasets, achieving an average error reduction of 27.39%. The proposed method consistently enhances imputation accuracy and achieves state-of-the-ar results, demonstrating its generality, effectiveness, and broad applicability.
2
Related Work
2.1 Statistical based imputation
Statistical methods are widely used for time series data imputation. A fundamental strategy is using the mean or median value of time series data for imputation [1. Since most time series data usually do not present sudden changes, researchers [12) propose to utilize k nearest neighbors to impute missing values of the incomplete tuple. In addition, regression models 1 are considered for time series imputation as well, since they can capture intertemporal and intratemporal dependencies within the sequences. Auto Regressive (AR) (1 and ARIMA [31] use the observed values at previous time points to predict missing data in the univariate time series. Furthermore, to obtain more accurate fillings, MICE 2 iteratively creates multiple fillings for obtaining the final imputation.
In general, although statistical methods are explainable and easy to use, they usually rely on strong assumptions and cannot effectively capture complex temporal dependencies in real-world time series.
2.2 Deep Learning based imputation
Deep learning models are inherently good at capturing complex and non-linear relationships among data. RNN-based models are more common earlier works. GRU-D (5), a variant of the gated recurrent unit (GRU), is proposed to address missing data in time series classification tasks. Soon after, BRITS 4 imputes missing values using a bidirectional recurrent dynamical system, without specific assumptions. In the case of M-RNN (45,, it imputes missing values based on hidden states derived from bidirectional RNNs. Since the generation ability is naturally suited to the imputation task, generative models are then widely used in filling missing values. E2GAN (20) incorporates generator based on GRUI within an auto-encoder framework. For spatiotemporal sequence imputation, NAOMI [8 introduces a non-autoregressive model to comprise a bidirectional encoder and a multiresolution decoder. With diffusion models gaining popularity, CSDI (34) emerges, which is conditional based diffusion model designed for time-series imputation. Advancing temporal variations into the two-dimensional
further, TimesNet [41] expands the examination space, while considering the presence of multiple periodicity in time series data. NRTSI [30], an approach for time-series imputation that treats time series as a collection of time-data pairs. SAITS [8] conducts simultaneous reconstruction and imputation by employing weighted combination of two diagonally masked self-attention blocks. PSW-I 39 leverages optimal transport with spectral regularization impute time-series data under temporal and distributional shifts.
Although the aforesaid methods optimize the process of imputing time-series data in various aspects, they do not explicitly encode the characteristies of non-stationarity and periodicity inductive bias

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for time series imputation. This oversight leaves significant room for improvement when dealing with missing data that exhibits complex non-stationarity and periodicity.
2.3 Time series characteristics
Time series usually exhibit complex characteristics, with non-stationarity being one of them. Tradi- tional statistical methods generally stabilize data through decomposition differencing [.] Adaptive Norm [27 employs a method known as z-score normalization to normalize sampled data segments.
DAIN 28 trains a nonlinear neural network to adaptively stabilize the dataset. RevIN [TS] performs a normalization and a reverse normalization before and after the model [37], to bring the distributions of various time segments closer together. Periodicity another important characteristic of time series, To identify the periodicity in complex time series, cyclical or seasonal components are decomposed from the time series. Classical time series decomposition methods, such as XI1 (d, iteratively apply moving averages to decompose the time series into multiple components. Fast Fourier Transform (FFT) [23] identifies the potential periodicity by efficiently transforming time series data from the time domain to the frequency domain.
While the existing methods are primarily designed to mitigate non-stationarity capture periodicity for specific tasks other than imputation, we propose an imputation-oriented inductive bias that jointly models both properties.
3 Method
Problem Formulation Given collection of multivariate time series X = (...) E Rx with 7 timestamps and C channels (attributes). The imputation task is to impute the missing values in X. Formally, observation mask is defined as M =mITT,CC) RxxC where m 0 if Tt. is missing, and Mr,e if ot is observed.
3.1 The Impact of Non-stationarity and Periodicity in Time-series Imputation
Time series often exhibit complex dynam- ies characterized by varying degrees of non- stationarity and periodicity, which motivates us to design inductive biases that adapt to these properties. To design an effective approach that incorporates these properties, we first investigate how non-stationarity and periodicity manifest in real-world time series data.
Non-slationry
Parook
Sppy
Specifically, we adopt the Augmented Dickey- Fuller (ADF) test statistic [10] quantitatively assess the degree of stationarity, where higher ADF statistic indicates stronger non-stationarity. As illustrated in Figure T(a) we present rep- resentative non-station time series segment from the HD dataset, with ADF statistic of 1.958. In such sequences, the trend component is difficult to infer from distant historical observations. This motivates a natural inductive bias: the imputation model should prioritize temporally local information when handling non-stationary data.
(a) Examples in HD
(b) Examples Weather
Figure (a) An example in HD Dataset which shows a higher degree of non-stationarity. (b) An example in Weather Dataset which shows a higher degree of periodicity.
In contrast, periodicity offers more straightforward inductive prior. As shown in Figure [[b]] for missing value, observations located at regular intervals (i.e., one or more period lengths apart) are more likely to be similar. This property suggests that periodic dependencies can be exploited by assigning greater importance to such temporally aligned points during imputation.
Overall Framework Based on the above intuition, our approach consists of three major steps: (1) Learning Non-Stationary Guidance to inject inductive bias considering non-stationarity into imputation model; (2) Learning Periodic Guidance to inject inductive bias taking advantage of the properties of periodicity into the imputation model; (3) Learning Meta Guidance by learning to weigh Non-Station Stationary Guidance matrices and Periodic Guidance matrices using meta weighting network.
3

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Missing values
G
PDF (0.1)
Non-stationary Guidance
m
Multipiicstion
Projector
Meta Guidance
Interpolation
Projector
Projector
Perl
Periodic Guidance
Periodic Guidance
m11
G
Pt
Poriadic Guidannc
1
Pork
FFT
Periodic
Guidence
Figure 2: Three steps to learn Meta Guidance: (1) Learning Non-Stationary Guidance, represented in the orange area. (2) Learning Periodic Guidance, represented in the green area. (3) Learning weigh two guidances considering the properties of input data via meta weighting network. Appendix H presents visualized examples of NSG and PG constructions.
Meta Guidance can automatically adjust the weight of types of inductive bias based on the degree of non-stationarity and periodicity in specific time series data through meta weighting approach.
3.2 Learning Non-Stationary Guidance
As aforementioned, -ta-Soati Guidance (NSG) can be designed following the insight that the imputation model should focus more on the values near the missing data rather than the values far from the missing data. Our aim is to learn Non-Stationary Guidance matrix GNS (o } R Since channel independence is proven to work well in time-series analysis on both linear models (46), CNNs [47, and transformers [26]. we design GS in a Channel-indepenee
style, i.c. g is only related the value of m = [e .mT,e]- The core insight in designing NSG is "proximity principle", i.e., values near the missing value can give a guidance on filling the missing value, and the
smaller the distance, the stronger the guidance. To achieve this goal, the elements in NSG defined as follows:
NS 91.c
Σ
(bi)
NS 1(1 -
1mmist, 0),
(1)
where (1) is the probability density of standard normal distribution No 1) when the variable is i. r is hyperparameter to determine the distance within which neighbors can provide guidance for missing values. NS is a scaling scalar channel which can dynamically adjust the strength of guidance and is learned by two-layer Multi-Layer Perceptron (MLP). The symbol 1 (-) denotes the indicator function. The existence missing data impedes the capability of networks to learn the inherent properties of the data slice, thus we adopt vanilla linear interpolation to the missing data:
Interpolation(X M),
then > can be learned via MLP:
log NS MLP (x
where x"_ = [at_er ..., ,
The usage of logarithm to ensure that 7 is non-negative, and Channel-wise scaling scalar can make the guidance adapt to different channels with varying degrees of non-stationarity. The architecture GSS encourages imputation algorithms to prioritize local contextual patterns surrounding missing data entries.

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3.3 Learning Periodic Guidance
In stationary time series, the periodic component typically dominates over the trend component, making it essential to incorporate periodicity-aware inductive bias into the imputation process. As discussed in Section 3.1 values separated by regular -odevvll-typiccllyy one or more period lengths-teit tend to exhibit higher similarity. Therefore, for time series exhibiting strong periodicity, the imputation model should assign greater attention to observations occurring at periodic offsets from the missing timestamps. To enable this, we first estimate the dominant period lengths for each channel of the input sequence. We adopt Fast Fourier Transform (FFT) to analyze each channel of time series data in the frequency domain,
a Amp (FFT (x,)))
(4)
where FFT(.) and Amp(.) denote the FFT and the calculation of amplitude values, a,e indicate the amplitude of each frequency in channel c. Then we select the top-k amplitude values and obtain the most significant frequencies:
( fk,e)
arg Topk (a.c)-
(5)
61,-,(1,-
We can get the corresponding period lengths as follows:
T
Pt.c
fi,c
(6)
Similar to Non-Stationary Guidance, we design Periodic Guidance (PG) in channel-independen style. For the period length corresponding 1-th significant frequencies, the elements of PG is defined as follows:
Per. 9t.
Per. Perd 1(1 S Σ (0)) 7e
Pto + +1S))
0),
where Per.1 is a scaling sealar in channel e which dynamically adjust the strength of guidance and is learned by a two-layer Multi-Layer Perceptron (MIP):
Per. = MLP Ji,e)
The usage of logarithm is to ensure that 7/ Per. is non-negative, and channel-wis. scaling scalar can make the guidance adapt different channels with different degrees of periodicity. The selected frequencies fı.e are also fed into the MLP as extra information.
For each frequency ft.c channel c, we can obtain PG vector Perd according Equation The 8 overall PG vector in channel e can be fused depending on how significant each frequency is, which can be measured by the amplitude at, of each frequency ft.e, as in Equation
Per
aie
8
Per.
(9)
1=1
apr.
3.4 Learning Meta Guidance for Imputation
Effectively obtaining conclusive guidance utilizing NSG and PG remains challenge, particularly when addressing the varied degrees of non-stationarity and periodicity present in different time-series data. To tackle this challenge, we propose Meta Guidance (MG), which automatically learns the weight of NSG and PG in different time-series slices. Similar to the design of the scaling scalars in Equation and Equation
g we design the weighting scalar X in a channel-independee style:
Pery d = MLP (x B.,e g.,
(10)
where g., [91.er 22
PT.c] is the channel-wise guidance, the activation function in the final layer of MLP Sigmoid ensure that A [0, 1]. Then we can get the channel-wise MG:
g
Meta Ae g + (1 X²) g.
Per
(11)
Finally we can get a MG matrix consisting e channel-wise MG vectors:
G
Meta Metal
[g g.c
5

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3.5 Injecting Meta Guidance on Transformer
Meta Guidance assigns importance weights different time points during the imputation of miss- ing values and can be seamlessly integrated into advanced deep learning architectures, such as Transformer-basee based models. To illustrate the integration process, we use the vanilla Transformer as a representative example. Detailed descriptions of how MG is incorporated into other model architectures are provided in Appendix A
Injecting MG into Embedding In trans- former, X first embedded into feature rep- resentation:
Oulputs
4,a
De-Nomelizaatinn
E Iipput Embedding (X) P.
(12)
where P is positional encoding. An intuitive idea is to use Meta to provide extra informa- tion in representation. G Meta is first embedded by an embedding layer:
Linear
Encoder
Positional Encoding
E Meta Embedding (G 6
(13)
where Meta @ X means the Hadamard prod- uct of Meta Guidance Meta and input X. The adoption of Hadamard product because it can achieve the goal of assigning importance weight each data point Zt.e. Then we use concatena- tion to fusion the two representations:
Guidance Embedding
Input Embedding
14.0
Normalizatinn
Guidance Generator
E Inputt Meta]
(14)
E, instead of Elpput is then feed forward the next block.
Inputs
Figure 3:
The overall framework of injecting Meta Guidance the Transformer. Compared to the vanilla Transformer, it includes additional components: the Guidance Generator, the Guid- ance Embedding module. Normalization and De- normalization modules.
Injecting MG into Normalization Normal- ization techniques are essential for deep learn- ing architectures, and instance normalization [37 is proven effective for time-series analysis. Inspired by that, the advanced normalization method, RevIN [15, normalizes the input to the model with learnable parameters, aligning the distribution of each sequence, and applies an inverse transformation (de-nom (ice-ormalization) assign an importance weight to each data point. We apply this idea to modify the learning process of the normalization module. Specifically, calculated weighted mean and weighted variance using Meta Guidance as the specific weight:
the model's output. As aforementioned, Meta Guidance can
Σt (gh =I,e)) Me Σl Pt.c
of
Eim (#t,e mc)²
Meta gi.e
1. Tt,c
(II.c - pe) (15)
Σ St.
Meta
Oe
Also, in the de- de-normalization module, we inverse transform the output of the model H. using the same mean and variance in each channel c:
Úr.c Oe It.c + Pe:
(16)
where It.. is the prediction of the base model, and Òc.c is the prediction processed by ne-oomaalzation module.
4 Experiments
In this section, we incorporate our framework into several advanced deep imputers and compare them with state-of-the-art time series imputation methods. The results indicate that the perfor- mance of all methods improves by incorporating our framework. Our codes are available at

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Table I: Summary of datasets, where a larger ADF indicates greater non-stationarity.
Dataset
HD
Electricity/
Traffic
Weather
ETTh1
ETTh2
ETTml
ETTm2
TCPC
C
5
321
862
21
7
7
7
7
8
T
3,020
26,304
17,544
52,696
17,420
17,420
69,680
69,680
52,416
ADF
1.958
-8.444
-15.021
-26.681
-5.908
-4.136
-14.984
-5.663
-22.199
4.1
Experimental Setup
Datasets Nine real-world IoT datasets are used in experiments. Table shows the main statistics
of each dataset. (1) HD is subset of the DJIA 30 Stock Time Series Dataset [7]. which collects
daily stock trading information of HD company over 12 years, exhibiting high non-stationarity. (2)
Weather 44 comprises 21 weather indicators with data recorded every 10 minutes in 2020. (3)
Electricity (36 collects hourly electricity consumption data of 321 customers from 2012 to 2014. (4)
Traffic [29 describes road occupancy rates and contains hourly sensor data of San Francisco freeways from 2015 to 2016. (5) ETT [48) consists of two hourly datasets (ETTh) and two 15-minute datasets (ETTm)) Each of them includes load characteristics of seven types of oil and power transformers from July 2016 to July 2018. (6) TCPC (Tetuan City power consumption) [33 which is collected in
a rrom estimate occupancy, featuring temperature, light, sound, CO2, and PIR sensors.
Baselines We integrate our framework into Transformer 38), CSDI 34 TimesNet 41), SAITS (1, and iTransformer (17), since they yield the state-of-the-art performance in most cases and the process of integrating Meta Guidance into them is fundamentally similar. Regarding other methods, such M-RNN 45)
44 BRITS 4. TIDER (16), ImputeFormer 255, ModernTCN GAIN
[19], and PSW-I 39 we utilize them as baselines for comparison. Due to space constraints, we
report results for subset of advanced baselines and representative datasets in the main paper. The full experimental results can be found in Table 10 and of of Appendix G
Implementation Details We follow the configuration and parameters of TimesNet [41], using the same dataset partitioning method, missing pattern, and imputation window length. Specifically, for methods requiring training, testing, and validation sets, we split them in a 7:2:1 ratio; otherwise, use an 8:2 ratio for training and testing. Missing values are injected using the Missing Completely At Random (MCAR) mechanism, which is adopted in most existing studies. Other missing mechanisms are considered in Appendix D For methods requiring an imputation window, we set the window length to 96. Transformer-base based methods use consistent set of parameters based the dataset, matching the settings in TimesNet. Experiments were conducted on system with 8 NVIDIA RTX 4090 GPUs (24GB VRAM each), a 128-core AMD EPYC 7513 CPU, and 503GB RAM. All reported results are averaged over three independent runs. The standard deviations of the full experiments are provided in Appendix C
4.2 Comparative Experiments
We investigate the imputation performance of different methods on real datasets with varying missing rates, and the corresponding results are presented in Table 2 We observe that the optimal methods across all datasets are those incorporating our framework. For instance, regarding the MAE metric, the Meta Guidance framework leads to an average improvement of 43. 43.76%, 26.49%. 9, 17.91% %, 9.88%, 25.82%, 34.61% % for the methods on HD, Weather, Electricity, Traffic, ETT and TCPC datasets, respectively. Such results demonstrate that Meta Guidance an effective lightweight framework applicable to wide range of deep learning imputation models, significantly enhancing their imputation performance.
We observe that traditional imputation methods struggle on highly non con-stationary datasets such as HD. In contrast, methods augmented with our MG framework exhibit notably larger performance gains on non-stationary datasets compared to stationary ones. This is attributed to the fact that -ta-toatio time series exhibit evolving statistical properties and shifting joint distributions, which can mislead data-driven models. Notably, both our method and other recent advances substantially outperform earlier baselines on the HD dataset, demonstrating MG's effectiveness in mitigating non-stationarity. Moreover, MG also yields consistent improvements stationary datasets with strong periodicity,
7

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Table 2: Imputation results over real datasets with different missing rates. The notation "+MG" signifies that the method incorporates our MG framework. "Promotion" denotes the average reduction in MAE for the corresponding dataset. We evaluate our approach across 9 datasets and compare it
with 12 baseline methods. See Table IC and for full results.
datasct
HD
Weather
Electricity
Traffic
ETTml
TCPC
metric
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
10%
0.112
0.188
0.088
0.182
0.276
0.379
0.233
0.441
0.177
0.257
0.177
0.248
Transforner
25%
0.119
0.234
0.095
0.196
0.284
0.394
0.231
0.453
0.213
0.308
0.233
0.328
40%
0.134
0.247
0.101
0.204
0.291
0.407
0.233
0.466
0.238
0.344
0.276
0.382
Transformer +MG
10%
0.046
0.082
0.049
0.159
0.180
0.261
0.198
0.388
0.108
0.169
0.069
0.118
25%
0.050
0.095
0.052
0.168
0.191
0.276
0.203
0.397
0.134
0.207
0.086
0.145
40%
0.057
0.105
0.058
0.176
0.200
0.289
0.217
0.422
0.153
0.235
0.103
0.169
10%
0.096
0.163
0.022
0.151
0.115
0.188
0.126
0.356
0.069
0.124
0.019
0.057
CSDI
25%
0.166
0.285
0.024
0.159
0.119
0.195
0.113
0.333
0.076
0.136
0.021
0.068
40%
0.151
0.265
0.027
0.172
0.6
0.205
0.123
0,358
0.085
0.151
0.024
0.074
CSDI
10%
0.040
0.107
0.019
0.127
0.102
0.163
0.104
0.263
0.065
0.110
0.018
0.054
+MG
25%
0.041
0.107
0.022
0.139
0.113
0.180
0.097
0.264
0.073
0.126
0.021
0.062
40%
0.042
0.103
0.024
0.152
0.122
0.195
0.110
0.301
0,082
0.142
0.023
0.068
10%
0.050
0.085
0.048
0.159
0.201
0.293
0.237
0.474
0.111
0.172
0.059
0.106
TimesNet
25%
0.055
0.096
0.055
0.170
0.208
0.302
0.243
0.477
0.128
0.200
0.076
0.131
40%
0.058
0.105
0.063
0.180
0.216
0.312
0.253
0.489
0.145
0.225
0.092
0.154
TimesNet
10%
0.050
0.085
0.046
0.158
0.194
0.280
0.231
0.463
0.095
0.150
0.045
0.088
+MG
25%
0.052
0.094
0.054
0.169
0.201
0.292
0.238
0.471
0.111
0.176
0.059
0.111
40%
0.057
0,103
0.064
0.182
0.209
0.303
0.246
0.482
0,126
0,200
0.070
0.128
10%
0.078
0. 1666
0.044
0.166
0.314
0.448
0.228
0.493
0.196
0.314
0.060
0.109
SAITS
25%
0.095
0.202
0.052
0.179
0.321
0.455
0.238
0.510
0.242
0.411
0.073
0.133
40%
0.113
0.214
0.080
0,202
0.344
0.482
0.274
0.548
0,362
0.568
0.096
0.166
SAITS
10%
0.037
0.081
0.032
0.161
0.197
0.286
0.194
0.401
0,105
0.164
0.032
0.069
+MG
25%
0.044
0.097
0.037
0.177
0.209
0.301
0,209
0.421
0,115
0.186
0.040
0.093
40%
0.055
0.111
0.046
0.182
0.234
0.332
0.244
0.462
0.148
0.234
0.057
0.121
10%
0.107
0.153
0.081
0.193
0.184
0.262
0.198
0.390
0.155
0.236
0.087
0.136
iTransformer
25%
0.114
0.190
0.103
0.214
0,213
0.298
0,230
0.433
0.181
0.269
0.111
0.164
40%
0.131
0.226
0.122
0.234
0.237
0.329
0.257
0.474
0.207
0.303
0.122
0.181
iTransformer +MG
10%
0.075
0.109
0.055
0.176
0.166
0.241
0.185
0.375
0.128
0.205
0.052
0.103
25%
0.071
0.110
0.055
0.185
0.186
0.267
0.208
0,411
0,142
0.226
0.064
0.119
40%
0.073
0.118
0.060
0.192
0.205
0.293
0.231
0.448
0.156
0.244
0.076
0.138
Promotion
1 %
1 26.449 %
1 17.91 %
9.88 %
1 25.82%
34.61 %
such as Electricity, by guiding models to better capture periodic patterns. We further present the performance of MG under different missing patterns in Appendix D
2249
222
C304
0240
Transfomeer MG
Timeatat MGG
SAITHMG
CSD
425
25
0254
16
20
16
20
6372
16
20
(a) Transformer+MG
(b) TeteMGG
(c) SAITS+MG
(d) CSDI+MG
Figure 4: Varying the hyperparameter value of ls over ETTh1 dataset with 10% missing values.
4.3 Analysis
Hyperparameter k The hyperparameter is controls the maximum number of frequencies selected during period extraction. We explore the impact of different k values on model performance. As shown in Figure both too small and too large values of result in decreased imputation performance. A small k fails to capture enough frequency information, leading to ineffective Periodic Guidance. Conversely, a large introduces noise frequencies that do not aid imputation, potentially distracting the model. The optimal value of k varies across models, depending on their ability to perceive frequency and period.
Hyperparameter r The hyperparameter r controls the neighborhood range for providing guidance to missing values. As shown in Figure 5 model performance becomes stable when > 3, since the Guidance Generator applies a standard normal distribution centered on missing values. Beyond this range, additional neighbors contribute negligible weights, making larger r values redundant.
8

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422
C386
Timeoeel-M
SATS-MG
323
(a) Transformer+MG
(b) MG
(c) SAITS+MG
(d) CSDI+MG
Figure 5: Varying the hyperparameter value of r over ETThl dataset with 10% missing values.
Conversely, too small an r truncates the distribution, distorting the Guidance and causing unstable results. To ensure both stability and efficiency, we set r = 3 by default.
Table 3: Imputation results obtained by applying different methods to Transformer.
HD
Electricity
Weather
TCPC
G NS
Per
G Meta
10%
25%
40%
10%
25%
40%
10%
25%
40%
10%
25%
40%
MAE
0.112
0.119
0.134
0.276
0.284
0.291
0.088
0.095
0.101
0.177
0.233
0.276
RMSE
0.188
0.234
0.247
0.379
0.394
0.407
0.182
0.196
0.204
0.248
0.328
0.382
MAE
0.047
0.052
0.058
0.182
0.194
0,202
0.053
0.056
0.064
0.076
0.112
0.115
RMSE
0.083
0.096
0.107
0.262
0.279
0.292
0.161
0.172
0.182
0.131
0.176
0.178
MAE
0.051
0.056
0.062
0.186
0.208
0,208
0.0S1
0.055
0.061
0.072
0.093
0.104
RMSE
0.088
0.099
0.112
0.267
0.288
0.298
0.160
0.174
0.179
0.127
0.159
0.175
MAE
0.046
0.050
0.057
0.180
0.191
0.200
0.049
0.052
0.058
0.069
0.086
0.103
RMSE
0.082
0.095 0.105
0.261
0.276
0.289
0.159
0.168
0.176
0.118
0.148
0.169
Ratio A To statistically validate the behavior patterns of Meta Guidance across datasets with varying characteristics, we com- pute the average À for Transformer and SAITS across different datasets, which represents the proportion of Statitatton Guidance within Meta Guidance. The results, shown in Fig- ure 6, indicate that datasets with higher non-stationarity exhibit higher X, reflecting the dominance of Non- Non-Stationary Guid- ance. Conversely, stable datasets with strong periodicity show lower A. This demonstrates that our method can automati- cally adapt to different dataset characteristics, making Meta Guidance broadly applicable.
HD Electricity Weather
ET711
ETT2
1.0
0.2
0.0
Transformer+
Figure 6: Average À values.
Ablation Study To further investigate the impact of individual components of our framework, we conduct ablation studies on the Transformer. The experiment results are presented in Table 3 As shown, the variant without any component represents the vanilla Transformer. The variant with only G NS or G indicates the use of the Meta Guidance framework, but only Non-Stationary Guidance or Periodic Guidance is used in calculating Meta Guidance. Having G Meta signifies the use of the complete Meta Guidance framework. We observe that, compared to the vanilla Transformer, both Non-Stationary Guidance and Periodic Guidance can boost the performance of the original model. This indicates that inductive bias for non-stationarity and periodicity boost time series imputation. Our method effectively addresses both aspects, reducing the adverse effects of complex temporal properties imputation.
Time Complexity We conduct a time consumption evaluation on the HD dataset. The training time for one epoch of the vanilla Transformer and the Transformer with Meta Guidance are 2.6 seconds and 2.9 seconds, respectively. The extra time overhead is acceptable. Additional analysis of time complexity is provided in Appendix
5 Conclusion
In this paper, we propose two inductive biases for time-series imputation: -on-Stationary Guidance for non-stationary series and Periodic Guidance for periodic series. Meta Guidance is derived by learning to weigh these two guidance matrices based on the input data's characteristies. As a lightweight framework, Meta Guidance can be integrated into deep imputation models to significantly improve their performance. Experiments on nine real-world datasets demonstrate its versatility and effectiveness.

---

Acknowledgements
This work was supported by the National Natural Science Foundation of China (62306085, 62302241, 62476071, U23B2055, U24A20328), Shenzhen College Stability Support Plan 1XXWD2003113011112900
CCF-ALIMAMA TECH Kangaroo Fund (CCF-ALIMAMA OF 2025001), Guangdong Basic and Applied Basic Research Foundation (2055A1515011732 and Shen- zhen Science and Technology Program (KQTDD22407299022555066 ZDSYS2023062609 2200000023000020000003333)3333)
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12

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A Methods for applying Meta Guidance to other models
A.1 TGme
The overall structure of TimesNet is very similar to that of the Transformer, making it casy to apply the MG (Meta Guidance) method without needing any changes. The only aspect that needs attention is TimesNet's 's proprietary Meta Guidance approach, we have to switch out this built-in module for the Meta Guidance version.
arimalizationDDenoomllaaaa
module. To align with the
A.2 iTransformer+MG
The architecture of I'Transfommer is also similar to that of the Transformer. The only notable difference dimension permutation operation applied during the input embedding stage. To seamlessly integrate MG into I'ransffrmer, it is sufficient to apply the same dimension permutation to the MG sequence.
A.3 SAITS+MG
SAITS also based on the Transformer architecture, yet it distinguishes itself by incorporating a Tran-frrasformer configuration. Specifically, the primary Transformer specifically engineered to enhance the imputation of missing data, whereas the secondary Transformer is optimized to more accurately fit the observed data. Our Meta Guidance framework is meticulously tailored augment the imputation process and is, therefore, exclusively integrated into the first Transformer, preserving the original functionality of the second Transformer intact. The integration methodology employed parallels that of the Transformer+MG approach.
A.4 CSDI+MG
Distinct from preceding models, CSDI leverages conditional diffusion model framework, presenting a structural deviation from the Transformer architecture. This foundational difference notwithstanding. the deep learning underpinnings of the diffusion model permit streamlined adaptation of the MGG methodology for CSDI+MG implementation, necessitating minimal adjustments:
1) Throughout the training phase, CSDI employs the actual values missing data points to generate noisy target. It is imperative, therefore, within the Guidance Generator and the normalization process, to preserve the original values of missing data in x rather than defaulting them
For these missing values, Meta Guidance is assigned value of 1. Subsequent to the generation of the noisy target, these missing values are nullified (set to O) to preclude the model from accessing extra information pertaining the missing data.
2) In addition the conditional observation, CSDI introduces auxiliary condition termed "Side information", encompassing Time Embedding, Feature Embedding, and the condi- tional mask. The matrix produced by Guidance Embedding is integrated this juncture, amalgamated with the initial Side information, and subsequently employed as conditional input to the diffusion model.
3) The training loss for the diffusion model is computed based on the variance from random noise, diverging from the Transformer's approach of contrasting the imputed missing values against their actual counterparts. This distinction necessitates the exclusion of the De-normalization transformation from the training output. The Normalization module exclusively retained during the training process. Conversely, in the evaluation and testing phases, when the diffusion model generates the imputed sequence, the comprehensive Normalization/De wewaan/DeeDnenntttiiiiioo module is reinstated.
13

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B Additional Experiments on the Hyperparameters k and T
To further validate the stability and robustness of Meta Guidance (MG), we conduct an extended investigation into its sensitivity with respect to key hyperparameters under different missing- rate conditions. Specifically, we focus on two important hyperparameters, l and r. These hyperparameters jointly influence the receptive field and the inductive bias of MG. Evaluating their effects helps us understand how the model behaves when these configurations vary.
We systematically examine the performance of MG-enhanced models across a wide range of k and r values. As shown in Tables 4-7, the results reveal that the MG module consistently achieves stable performance across different settings. The variance among configurations is marginal, indicating that our method largely insensitive hyperparameter choices and can be applied without extensive tuning. This property further highlights MG's practical robustness and adaptability when deployed in diverse real-world time-series applications.
Table 4: Varying the hyperparameter value of k over ETTh1 dataset with 25% missing values.
25% missing rate
k=1
k=4
k=8
k=12
k=16
k=20
Transformer+MG
0.299
0.299
0.307
0.319
0.299
0.299
MG
0.288
0.288
0.288
0.288
0.288
0.288
SAITS+MG
0.282
0.280
0,280
0.279
0.279
0.280
CSDI+MG
0.213
0.210
0.212
0.213
0.212
0.215
Table 5: Varying the hyperparameter value of k over ETTh1 dataset with 40% missing values.
40% missing rate
k=1
k-4
k=8
k=12
k=16
k=20
MG
0.347
0.347
0.346
0.346
0.346
0.346
Mi
0.319
0.319
0.319
0.319
0.319
0.320
SAITS+MG
0.355
0.358
0.358
0.358
0.356
0.358
CSDI+MG 0.266
0.269
0.268
0.265
0.264
0.263
Table 6: Varying the hyperparameter value of r over ETTh dataset with 25% missing values.
25% missing rate
r=1
r=2
r=3
r=4
r=5
MG
0.338
0.299
0.301
0.317
0.307
MG
0.288
0.288
0.288
0.288
0.288
SAITS+MG 0.279
0.279
0.280
0.283
0.280
CSDI+MG 0.209
0.215
0.207
0.212
0.215
Table 7: Varying the hyperparameter value of r over ETTh1 dataset with 40% missing values.
40% missing rate
r=1
r=2
r=3
r=4
r=5
Mransforme++GG
0.348
0.347
0.346
0.346
0.346
Mi
0.321
0.320
0.319
0.319
0.319
SAITS+MG
0.356
0.356
0.357
0.356
0.356
CSDI+MG
0.267
0.265
0.266
0.266
0.266
14

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C Details on the standard deviation
Standard deviation measures how much data deviates from the mean, reflecting the variability or consistency of dataset larger values indicate greater dispersion, while smaller values suggest tighter clustering around the mean. In our experiments, all results are averaged over three independent runs. Table 8 reports the corresponding standard deviations.
Table 8: Details on the standard deviation of methods that incorporate the Meta Guidance framework.
stdev
HD
Weather
|Electricity
Traffic
ETThi
ETTh2
ETTml
ETTm2
TCPC
M-RNN
0.1794
0.0164
0.0011
0.0021
0.0351
0.0555
0.0357
0.0564
0.0263
GAIN
0.0249
0.0764
0.0026
0.0016
0.0995
0.0663
0.0355
0.0399
0.0662
BRITS
0.0486
0.0022
0.0014
0.0019
0.0085
0.0080
0.0108
0.0060
0.0030
TIDER
0.0170
0.0789
0.0241
0.0290
0.01
0.0095
0.0207
0.0136
0.0074
Imputeformer
0.0170
0.0789
0.0241
0.0290
0.0110
0.0095
0.0207
0.0136
0.0136
ModernTCN
0.0170
0.0789
0.0241
0.0290
0.01
0.0095
0.0207
0.0136
0.0136
PSW-I
0.0079
0.0208
0.0002
0.0007
0.0015
0.0008
0.0005
0.0003
0.0003
Transformer
0.0479
0.0040
0.0009
0,0014
0.0031
0.0032
0.0033
0.0031
0.0060
SAITS
0.1325
0.0028
0.0019
0.0029
0.0240
0.0155
0.0093
0.0164
0.0028
TimesNet
0.0021
0.0023
0.0013
0.0013
0.0050
0.0013
0.0012
0.0006
0.0014
Transformer
0.0093
0.0022
0.0005
0.0006
0.0057
0.0024
0.0013
0.0005
0.0023
CSDI
0.0038
0.0017
0.0015
0,0018
0.0021
0.0018
0.0023
0.0011
0.0016
Transfomer+MG
0.0022
0.0018
0.0004
0.0033
0.0050
0,0012
0.0010
0.0007
0,0010
SAITS+MG
0.0023
0.0022
0.0007
0.0021
0.0059
0.0018
0.0044
0.0006
0.0007
TimesNet+MG
0.0019
0,0027
0.0027
0.0024
0.0038
0.0012
0.0010
0.0006
0.0017
Mr
0.0020
0,0022
0.0004
0,0007
0.0058
0.0010
0.0007
0.0002
0.0014
CSDI+MG
0.0025
0.0010
0.0008
0.0016
0.0022
0.0008
0.0017
0.0005
0.0012
D Missing Pattern Analysis
We consider another two missing data injection mechanisms, i.e., Missing At Random (MAR) 42
and Missing Not At Random (MNAR) [35], following the existing study (22]. Figure shows the experimental results returned by various methods with different missing mechanisms. We observe that the performance of various methods fluctuates slightly under different missing mechanisms, but the methods incorporating Meta Guidance still achieve significant performance improvements. This demonstrates the applicability of Meta Guidance across various types of missing data.
GAIN
Transfomee
Transfomer+MGG
MRNN
TimesNet
TimesNet- MG
BRITS
1.0
TIDER
CSDI
CSDI+ MG
RMSE
0.6
0.4
0.2
MCAR
MAR
MNAR
Figure 7: Varying the missing mechanism over ETThl dataset with 10% missing values.
15

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E
Showcase
To highlight the effect of Meta Guidance (MG), present imputation showcases on the ETTml dataset with 40% missing data (Figure 8). The vanilla Transformer suffers from short-term periodic fluctuations that deviate from the ground truth, whereas incorporating MG effectively suppresses these artifacts and yields more accurate results. Even strong models like TimesNet benefit from MG, which enhances performance by guiding attention toward informative neighboring values and mitigating unrealistic deviations during imputation.
Transformer
Transformer+
Imputation
Imputation
0.8
GroundTruth
0.00
GroundTruth
-10
-1.0
-12
-12
-1.2
-1.3
-1.3
+1.
-1.
100
100
120
140
TimesNet
TimesNet+Me
-0.7
Imputation
-0.7
Imputation
-0.8
Gruu
-0.8
GroundTruth
1.0-
1.0
-1.2
-1.2
-1.4
-1.5
-1.5
20
40
100
120
140
80
100
120
Figure 8: Visualization of ETTml imputation results given by models under the 40% mask ratio setting. The black lines stand for the ground truth and the orange lines stand for predicted values.
F Time Complexity Analysis
Since the construction of NSG and PG follows linear process, the overall time complexity of MG can be expressed O(Tr) + O(Td). where T represents the dataset length, is an MG hyperparameter (as defined Equation of Section 3.1 typically set to around 3, and denotes the dimensionality of the MLP hidden layer, set to 12 in our experiments. Here, O(Tr) accounts for the complexity of constructing the raw NSG and PG sequences, while O corresponds to complexity of the Projector's 's linear layer. Given that both and d fixed hyperparameters, the additional computational complexity introduced by MG simplifies to O(T), making its overhead negligible.
To further validate the computational efficiency of MG, we conducted additional experiments using the SOTA methods (CSDI vs. CSDI+MG) datasets with more time steps and channels, and the Table 9 shows the training time per iteration across datasets. The results show that our method introduces even less time overhead on larger datasets, approximately 3%, which is acceptable.
Table 9: Runtime per iteration (in seconds) across different datasets.
time cost (s)
Weather
ETTh1
Electricity
Traffic
CSDI
0.0363
0.0261
0.7561
1.4512
CSDI+MG
0.0397 (+9.3%)
0.0288
(+10.1%)
0.7783 (+2.9%)
1.4820 (+2.1%)
16

---

G Full experimental results
In this section, we present the full experimental results, which include all baseline methods. As shown in Table TO and 11 the methods incorporating Meta Guidance outperform all baselines. In particular, CSDI, due to its excellent intrinsic qualities, demonstrates superior performance across most datasets after integrating our framework. Compared to the original methods, the performance of those incorporating Meta Guidance shows significant improvement. Overall, methods incorporating Meta Guidance exhibit marked performance boost over the original approaches.
Table 10: MAE imputation results on real-world datasets under varying missing rates. The notation
"+MG" signifies that the method incorporates our Meta Guidance framework.
HD
Weather
Electricity|
Traffic
ETThl
ETTh2
ETTml
ETTm2
TCPC
10%
0.727
0.291
0.355
0.286
0.627
0.621
0.639
0,584
0.712
M-RNN
25%
0.831
0.341
0.368
0.302
0.672
0.638
0.672
0.616
0.722
40%
0.904
0.382
0.381
0.321
0.702
0.659
0.702
0.643
0.742
10%
0.209
0.268
0.257
0.180
0.596
0.610
0.558
0.598
0.701
GAIN
25%
0.222
0.303
0.257
0.189
0,567
0.600
0,593
0.610
0.689
40%
0,239
0.310
0,261
0.196
0.680
0.652
0.615
0.614
0.775
10%
0, 1.19
0.045
0.249
0.216
0.249
0.147
0,109
0.090
0.067
BRITS
25%
0.232
0.059
0.267
0.226
0,291
0.171
0,147
0.119
0.107
40%
0.279
0.077
0.292
0.244
0.339
0.202
0,183
0.152
0.164
10%
0.185
0.368
0.568
0.523
0.471
0.472
0.548
0,541
0.634
TIDER
25%
0,224
0.378
0.575
0.539
0.527
0.518
0.593
0.576
0.640
40%
0.331
0.401
0.558
0.557
0.621
0.590
0.635
0.611
0.679
10%
0,748
0.086
0.408
0.373
0.437
0.209
0,259
0.125
0.146
Imputeforner
25%
0.829
0.090
0.424
0.368
0.455
0.232
0,281
0.136
0.155
40%
0.904
0.103
0,459
0.419
0.495
0,280
0,318
0.158
0.173
10%
0,080
0.049
0.169
0.180
0.147
0.093
0.091
0.053
0.034
ModernTCN
25%
0.076
0.062
0.192
0.206
0,161
0.097
0.099
0.057
0.035
40%
0.079
0.060
0,203
0.227
0.181
0.103
0.109
0.063
0.04
10%
0.074
0.056
0.192
0.266
0.195
0.125
0,108
0.074
0.034
PSW-I
25%
0.077
0.059
0.213
0.260
0.206
0.130
0,113
0.078
0.039
40%
0.084
0.063
0,243
0.285
0,225
0.140
0.121
0.083
0.046
10%
0,112
0.088
0.276
0.233
0.236
0.179
0.177
0.150
0.177
Transformer
25%
0.119
0.095
0.284
0.231
0.276
0.203
0.213
0.166
0.233
40%
0.14
0.101
0.291
0.233
0.306
0.225
0.238
0.181
0.276
10%
0.078
0.044
0.314
0.228
0.273
0.222
0.196
0.129
0.060
SAITS
25%
0.095
0.052
0.321
0.238
0.333
0.258
0.242
0.161
0.073
40%
0.113
0.080
0.344
0.274
0.415
0.333
0.362
0.253
0.096
10%
0.050
0.048
0.201
0.237
0.174
0.091
0.111
0.059
0.059
TimesNet
25%
0.055
0.055
0.208
0.243
0.211
0.107
0,128
0.070
0.076
40%
0.058
0.063
0.216
0,253
0,236
0.122
0.145
0.078
0.092
10%
0.147
0.081
0.184
0.198
0,221
0.142
0,155
0.101
0.087
Transformer
25%
0.234
0.103
0.213
0.230
0.258
0.
0.181
0.124
0.111
40%
0.340
0.122
0.237
0.257
0.291
0.184
0.207
0.144
0.122
10%
0.096
0.022
0.115
0.126
0.103
0.049
0.069
0.031
0.019
CSDI
25%
0,166
0.024
0.119
0.113
0,118
0.058
0.076
0.036
0.021
40%
0.151
0.027
0.126
0.123
0.143
0.068
0.085
0.041
0.024
Transformer +MG
10%
0.046
0.049
0.180
0.198
0.169
0.089
0.108
0.058
0.069
25%
0.050
0.052
0.191
0.203
0.208
0.108
0.134
0.073
0.086
40%
0.057
0.058
0,200
0.217
0.237
0.126
0.153
0.081
0.103
SAITS
10%
0.037
0.032
0.197
0.194
0.146
0.075
0,105
0.043
0.032
+MG
25%
0.044
0.037
0.209
0.209
0.178
0.091
0.115
0.037
0.040
40%
0.055
0.046
0.234
0.244
0.227
0.116
0.148
0.067
0.057
TimesNet +MG
10%
0.050
0.046
0.194
0.231
0.161
0.085
0.095
0.053
0.045
25%
0.052
0.054
0.201
0.238
0.192
0.100
0.111
0.062
0.059
40%
0.057
0.064
0,209
0,246
0.217
0.114
0.126
0.071
0.070
iTranforrmer +MG
10%
0.075
0.055
0.166
0.185
0,194
0.112
0,128
0.067
0.052
25%
0.071
0.055
0.186
0.208
0.214
0.120
0,142
0.076
0.064
40%
0.073
0.060
0.205
0.231
0.234
0.130
0.156
0.084
0.076
CSDI
10%
0.040
0.019
0.102
0.104
0.100
0.045
0.065
0.027
0.019
25%
0,041
0.022
0.113
0.097
0.114
0.054
0.073
0.033
0.021
+MG
40%
0.042
0.024
0.122
0.110
0.136
0.062
0.082
0.038
0.024
17

---

Table 11: RMSE imputation results on real-world datasets under varying missing rates. The notation "+MG" signifies that the method incorporates our Meta Guidance framework.
HD
Weather
Electricity|
Traffic
ETThl
ETTh2
ETTml
ETTm2
TCPC
10%
0.821
0.468
0.490
0.527
0.826
0.779
0.839
0.737
0.763
M-RNN
25%
0.936
0.514
0,504
0.542
0.883
0.801
0.884
0.774
0.777
40%
1.019
0.555
0.519
0.564
0.920
0.824
0.920
0.803
0.805
10%
0.424
0.716
0.396
0.361
0.829
0.846
0.789
0.823
0.884
GAIN
25%
0.418
0.677
0.392
0.383
0.821
0.849
0.826
0.850
0.925
40%
0.483
0.683
0,396
0.403
0,969
0.917
0.855
0.873
1.024
10%
0.235
0.162
0.357
0,463
0.372
0.210
0,180
0.134
0.121
BRITS
25%
0.283
0.179
0.375
0.478
0.425
0.240
0.229
0.170
0.168
40%
0.333
0.197
0,405
0.504
0.488
0.279
0.271
0.212
0.237
10%
0.393
0.753
0.731
0.783
0.710
0.702
0.777
0,765
0.609
TIDER
25%
0.445
0.760
0.738
0.795
0.768
0,748
0.829
0.805
0.611
40%
0.536
0.767
0.721
0.815
0.860
0.821
0,875
0.843
0.656
10%
0,185
0.195
0.370
0.488
0.412
0.211
0,202
0.120
0.158
Imputeforner
25%
0.193
0.213
0.388
0.502
0.446
0.238
0.239
0.136
0.171
40%
0.205
0.229
0,430
0,589
0,512
0.266
0.295
0,160
0.195
10%
0.119
0.167
0.241
0.336
0.226
0.132
0,144
0.082
0.070
TCN
25%
0,119
0.184
0.272
0.382
0.248
0.138
0.159
0.088
0.077
40%
0.126
0.180
0.290
0.420
0.277
0.146
0.176
0.097
0.090
10%
0,235
0.324
0.291
0.499
0.293
0.192
0,183
0.122
0.092
PSW-I
25%
0.255
0.334
0.325
0.504
0.315
0.199
0.192
0.129
0.107
40%
0.270
0.344
0.373
0.551
0,346
0.216
0.205
0.140
0.119
10%
0.188
0.182
0.379
0,441
0,333
0.242
0,257
0.202
0.248
Transformer
25%
0.234
0. 1.1966
0.394
0.453
0.386
0.273
0.308
0.223
0.328
40%
0.247
0.204
0.407
0.466
0.428
0.302
0.344
0.242
0.382
10%
0. 1616
0.166
0.448
0.493
0.417
0.299
0.314
0.178
0.109
SAITS
25%
0.202
0.179
0.455
0.510
0,530
0.340
0.411
0.220
0.133
40%
0.214
0.202
0.482
0.548
0.633
0.433
0.568
0.335
0.166
10%
0.085
0.159
0.293
0.474
0.262
0.129
0.172
0.090
0.106
TimesNet
25%
0.096
0.170
0.302
0.477
0.31
0.150
0.200
0.102
0.131
40%
0,105
0.180
0.312
0.489
0.346
0.171
0.225
0.113
0.154
10%
0.193
0.193
0.262
0.390
0.325
0.199
0.236
0.143
0.136
iTransorner
25%
0,300
0.214
0.298
0.433
0.368
0.227
0.269
0.173
0.164
40%
0.426
0.234
0.329
0.474
0.41
0.253
0.303
0.200
0.181
10%
0.163
0.151
0.188
0.356
0.187
0.085
0.124
0.065
0.057
CSDI
25%
0.285
0.159
0.195
0.333
0.206
0.096
0.136
0.072
0.068
40%
0.265
0.172
0.205
0.358
0.242
0.110
0.151
0.079
0.074
Transformer
10%
0.082
0.155
0.261
0.388
0.255
0.130
0,169
0.089
0.118
+MG
25%
0.095
0.168
0.276
0.397
0.308
0.155
0.207
0.7
0.145
40%
0.105
0.176
0.289
0.422
0.350
0.181
0.235
0.117
0.169
SAITS
10%
0,081
0.161
0,286
0.401
0.226
0.113
0,164
0.072
0.069
+MG
25%
0.097
0.177
0.301
0.421
0.279
0.138
0,186
0.084
0.093
40%
0.111
0.182
0.332
0.462
0.354
0.174
0.234
1.5
0.121
TimesNet +MG
10%
0.085
0.158
0.280
0.463
0.244
0.122
0,150
0.083
0.088
25%
0,094
0.169
0,292
0.471
0.287
0.142
0.176
0.094
0.111
40%
0.103
0.182
0.303
0,482
0.321
0.162
0.200
0.106
0.128
iTranfformer +MG
10%
0.109
0.176
0.241
0.375
0,292
0.157
0.205
0.099
0.103
25%
0.110
0.185
0.267
0.411
0.318
0,
0.226
0.111
0.1
40%
0.118
0.192
0,293
0.448
0,344
0.183
0.244
0.122
0.138
CSDI
10%
0.107
0.127
0.163
0.263
0.177
0.078
0.110
0.056
0.054
25%
0.107
0.139
0.180
0.264
0.194
0.093
0.126
0.064
0.062
+MG
40%
0.103
0.152
0.195
0.301
0.228
0.103
0.142
0.074
0.068
18

---

H
Visualization of NSG and PG construction
N5C
PC
MBG
Samples
0.0
2..
099
5 6
9
10
20
40
60
80
100
Time pornts
Thmme paints
NSG Construction
(b) PG Construction
Figure 9: Visualizations of NSG and PG construction.
Figure (a) presents an illustrative example NSG construction. In this example, the 4th and 7th points in the time series are missing. Given a hyperparameter setting of = 3, each missing points will influence three nearest neighbors, weighted by Gaussian function v/(1). Specifically, if the 4th position is missing, the 3rd position receives a weight of (1),, the 2nd position (2)2,, and the 1st position (3). following the same pattern for other missing points. After applying this weighting scheme to all missing points, the resulting sequence constitutes the NSG.
Figure 9b) presents illustrative example of PG construction. The construction of PG follows a similar approach to NSG. In this example, the original time series has a period of T 10, with missing values at the 40th and 70th positions. In PG, the influence of (i)) propagates with step size of T. Specifically, if the 40th position is missing, the 30th position receives weight of (1), the 20th position (2), and the 10th position (3). following the same pattern for other missing points. After applying this weighting scheme to all missing points, the resulting sequence constitutes the PG.
I Limitation
Due to its construction, Meta Guidance can only be integrated into deep lcarning methods and cannot be used with statistical and mathematical imputation methods. However, considering that Meta Guidance can significantly improve the performance of deep learning methods, even achieving state-of-the-art results, this limitation is acceptable.
J Broader Impacts
Our work provides a more robust and accurate method for imputing missing values by integrating novel framework Meta Guidance with existing deep learning architectures, crucial for data analysis in various domains. Furthermore, by addressing the challenges of non-stationarity and periodicity in time series data, this research be instructive for future research in machine learning and data science, fostering the development of more sophisticated and adaptable imputation methods. Therefore, our paper mainly focuses on scientific research and has no obvious negative social impact.
19

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Reviews:
[{"review_id": "x30SNHKedE", "reviewer": "Reviewer_NQxZ", "summary": "In this submission, authors introduce Meta Guidance (MG), a novel technique designed to enhance multivariate time series imputation tasks. The authors present three key contributions that constitute MG: first, a guidance mechanism for non-stationarity that utilizes measurements from timesteps close to the missing data point; second, a guidance mechanism for periodicity that employs measurements from timesteps N periods away from the missing point; and third, a method to combine both guidance approaches by determining which to favor based on dataset characteristics, as controlled by a parameter lambda. Notably, this proposal is channel-independent and can be applied to various existing architectures such as Transformers or Diffusion models. \n\nThe effectiveness of MG has been evaluated across nine common multivariate time series datasets against multiple baselines.", "questions": "### Similarity to Existing Solutions\nThe PeriodGuidance (PG) approach appears similar to existing solutions where deep learning imputation methods typically leverage learned patterns in the dataset. While I understand the proposal of PG is different, I would appreciate confirmation on how it distinctly differs from current methods.\n\n### Performance Analysis\nThe paper should provide more intuition or explanation regarding why Meta Guidance (MG) shows limited benefit for TimesNet/CSDI models. The performance difference is relatively small (~0.00X) compared to other models across most datasets, which warrants further discussion.\n\n### Hyperparameter Investigation\nRegarding the hyperparameter $r$, it might be more appropriate to have separate investigations for Non-Stationary Guidance (NSG) and Periodic Guidance (PG). The assumption that the same $r$ value should be used for both guidances is not immediately obvious and could benefit from justification or separate analysis.\n\n### Clarification Needed\nThe sentence on line 275 (\"Notably, both our method and other recent advances substantially outperform earlier baselines on the HD dataset, demonstrating MG's effectiveness in mitigating non-stationarity\") seems contradictory to line 271. I believe this refers to Table 10 with additional baselines, but this should be clarified to avoid confusion. (how other advances demonstrate MG effectiveness?)\n\n### Ablation Study Improvements\nFor the ablation study in Table 3, the last row should include checkmarks for both $G^{NS}$ and $G^{Per}$. The $G^{Meta}$ column could be removed since it represents $\\lambda \\times G^{NS} + (1 - \\lambda) \\times G^{Per}$. \nActually, it would be more suitable to replace column $G^{Meta}$ with a $\\lambda$ column. The first row of the ablation study would include only $G^{NS}$, the second only $G^{Per}$, a third one will sum them without using $\\lambda$ and the last one would sum them using $\\lambda$ (all items checked to showcase $G^{Meta}$). This would emphasize the impact of $G^{Meta}$ as a whole and better demonstrate the impact of $\\lambda$ compare to the section on the lambda ratio with detailed lambda value (which could be  moved to the appendix if necessary).\n\n### Suggested Improvements regarding Parameter Impact Analysis\nThe impact of $k$ for selecting top frequencies should be evaluated on highly cyclical datasets like weather or traffic, rather than ETTh1. Figure 6 suggests that weather dataset use more $G^{Per}$ (lambda < 0.5), making it more suitable for this analysis. But to avoid overgeneralization, it would be preferable to test $k$ on multiple datasets with varying seasonality, including highly seasonal datasets (weather, traffic) and less seasonal ones (ETTh1 or others).\n\nSimilarly, the impact of $r$ for proximity selection should be analyzed on highly non-stationary datasets like HD to better understand its effect. This analysis should also include less non-stationary datasets (ETTh1 or others) to provide a comprehensive view.\nAnd if $r$ is investigated for both guidance, the chosen dataset should reflect each guidance.\n\n### Clarity Enhancements\n * The double bar notation (1) should be explicitly identified as the indicator function for clarity. \n * Figure 2 would benefit from adding $X'_{:,c}$ notation. Besides, the pink and yellow blocks in this figure should be replaced with their respective notations ($g^{NS}$, $g^{Per,l}$, $g^{Per}$) to avoid confusion (reader might see the block as a place where additional operations are being performed).\n * The acronym MCAR on line 255 should be introduced with its full form (\"Missing Completely At Random\") and potentially include a reference for readers unfamiliar with the term.\n * Figure 8 should clearly identify the missing points to better illustrate the impact of imputation.\n\n### Proofreading\nThe text on line 208 requires revision for clarity and correctness.", "limitations": "### Limitations and Suggestions for Improvement\nThe submission would significantly benefit from incorporating a synthetic dataset where trend and frequency components are controlled. This addition would provide a clearer demonstration of MetaGuidance's benefits, particularly in visualizing the shifts in lambda values under different conditions. While this might not be feasible for the camera-ready version, it's important to acknowledge this point and suggest it as future work.\n\nA more comprehensive evaluation using controlled missingness with various missing data ratios and patterns would strengthen the study. The current focus on a maximum missing ratio of 40% and primarily Missing Completely At Random (MCAR) patterns may not sufficiently demonstrate the method's robustness. In large datasets with MCAR, consecutive missing data points might be rare, potentially making linear interpolation methods appear more effective than they would be in more challenging scenarios.\n\nTo provide a more thorough analysis, the authors should consider adding baseline comparisons and testing higher missing ratios. Specifically, comparing MetaGuidance components with established imputation methods would help validate the claims:\n * Comparing Non-Stationary Guidance (NSG) against linear interpolation or k-nearest neighbors (kNN) imputation\n * Comparing Periodic Guidance (PG) against seasonal historical averages\nThese comparisons would better illustrate how the proposed methods provide more informative data for imputation and validate claims about handling complex temporal dependencies.\n\nThe evaluation would also benefit from incorporating more diverse missing data patterns beyond MCAR. As noted by Niu et al. [https://epubs.siam.org/doi/pdf/10.1137/1.9781611977653.ch37], controlled environments with clearly defined missing patterns enable better interpretation of results and clearer understanding of when a proposal performs well or poorly. The analysis should consider not just individual missing data points but also consecutive missing timesteps, both synchronized and unsynchronized across different channels (which close to reality). For multivariate time series datasets, it's particularly important to examine how imputation can leverage relationships learned between channels.\n\n### Reproducibility Concerns\nReproducibility is currently limited due to several factors:\n * The Git repository is not available (expired), preventing verification of the implementation. \n * Crucial experimental details are missing, including:\n     * The number of diffusion steps used for CSDI\n     * Sequence and prediction lengths employed\n     * Specific prediction configurations (M2M, M2U)\n\nFor the latter, while default parameters might have been used, explicitly stating this would eliminate any ambiguity and enhance reproducibility.\n\n### Conclusion\nGiven the current state of the submission, I have selected a borderline accept. However, I would be inclined to increase the score to accept if several of the points mentioned in the questions and limitations sections are adequately addressed during the rebuttal and reflected in an updated version of the paper. I understand that not all suggestions can be implemented immediately, particularly those regarding different missing data patterns or tests on controlled datasets. Nevertheless, many other points can be discussed or incorporated to strengthen the submission.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "### Strengths\n * Presents a well-designed and clearly understandable architecture\n * Conducts extensive experimentation across multiple datasets and scenarios\n * Offers an interesting proposal that has strong potential to become an important baseline in the field\n * Demonstrates compatibility with various existing architectures (Transformers, Diffusion models)\n\n### Weaknesses\n * Focuses primarily on individual missing data points, which may not fully represent real-world scenarios with consecutive or patterned missing data\n * Uses datasets that may not be best suited for studying the impact of hyperparameters, potentially limiting the insights gained\n * Lacks sufficient analysis of lambda's impact in the ablation study, which is crucial for understanding the method's behavior\n * Git repository is not available, hindering verification and reproduction of results\n * Without prior knowledge of existing baselines, it can be challenging to fully appreciate the contributions (though page limitations make exhaustive comparisons difficult)\n * Would benefit from evaluation on synthetic datasets with controlled trends and frequencies\n * Lacks component-wise comparisons with simpler baselines\n * Could provide more detailed analysis of how different parameter settings affect performance across various dataset characteristics", "was_revised": true, "final_justification": "The valuable additional information presented during the rebuttal process - including the simple baselines comparison, analysis of lambda's impact, hyper-parameter study, examination of the relationship between top-k selection and results, discussion of potential distortions, and comparison with detrending methods - should be properly incorporated into the main paper. If space constraints make this difficult, these elements could be clearly referenced in the main text with detailed discussions included in the appendix. This comprehensive integration would provide readers with a more complete and accurate understanding of the proposal's current status and capabilities.\n\nGiven that these additional results and experiments effectively address the majority of my initial concerns, and assuming the authors will successfully update their submission to reflect these important points, I am increasing my evaluation score to accept.", "rebuttal": "# Response to Reviewer NQxZ\nWe sincerely thank you for the thorough and insightful review and for recommending a borderline accept. Unless explicitly noted, all new results will be included in the camera-ready version and the public code release.\n\n### **W1 & L2 & L4: Broader Scope to missing pattern**\n\n**In Appendix D, we have explored the missing patterns other than MCAR**, includingMissing At Random (MAR) and Missing Not At Random (MNAR). To further investigate the performance of MG under time-varying missing patterns, we conduct additional experiments with a dynamically changing missing rate. Specifically, the missing probability of a data point is modeled as a time-dependent function, with the missing rate oscillating between 0.1 and 0.4 over time.\n\n$p(i) = 0.25 + 0.15 \\cdot \\sin\\left(\\frac{2\\pi i}{100}\\right)$ .\n\n||HD|ETTh1|Weather|TCPC\n-|-|-|-|-\nTransformer|0.035|0.184|0.061|0.094\nTransformer+MG|0.009|0.109|0.037|0.024\nTimesNet|0.010|0.121|0.040|0.028\nTimesNet+MG|0.008|0.095|0.038|0.013\n\nWe additionally conducted experiments under a consecutive missing setting. Specifically, we randomly removed continuous segments of length 10 until the overall missing rate reached 10%. The experimental results are presented below.\n\n||HD|ETTh1|Weather|TCPC\n-|-|-|-|-\nTransformer|0.112|0.325|0.072|0.303 \nTransformer+MG|0.016|0.245|0.041|0.189 \n\n\nThe results show that MG continues to significantly improve model performance, even in the presence of complex, time-varying missing patterns.\n\n### **W2 & W8 & Q6: Dataset suitability for hyper-parameter study**\n\nThank you for your suggestion. Following your advice, we conducted additional hyperparameter experiments with k on the Weather and Traffic datasets, and with r on the HD dataset. The results are as follows:\n\nk|1|4|8|12|16|20\n-|-|-|-|-|-|-\nWeather|0.048|0.050|0.048|0.051|0.048|0.055\nTraffic|0.198|0.201|0.204|0.198|0.200|0.197\n\n\nr|1|2|3|4|5\n-|-|-|-|-|-\nHD|0.0443|0.0442|0.0442|0.0441|0.0442 \n\nAs presented in the table, the performance remains relatively stable across different values of hyperparameters $k$ and $r$, highlighting the robustness of our approach. This indicates that our method requires minimal hyperparameter tuning in real-world deployments.\n\n\n\n### **W3 & Q4: Insufficient analysis of $\\lambda$'s impact**\n\nIn response to your suggestion, we introduced an additional variant in the ablation study (Section 4.3), denoted as \"MG w\\o $\\lambda$\", where NSG and PG are combined by directly averaging their outputs instead of using the weighting factor $\\lambda$. The results, presented in the table below, show a performance drop without $\\lambda$, underscoring the necessity of the weighted summation.\n\n||HD|Weather|TCPC|\n-|-|-|-|\nvanilla|0.112|0.088|0.177|\nonly NSG|0.047|0.053|0.076|\nonly PG|0.051|0.051|0.072|\nMG w\\o $\\lambda$|0.048|0.056|0.071|\nMG|0.046|0.049|0.069|\n\n### **W4 & L5: Code repository**\n**The anonymous code repository has been made publicly available** and can be accessed through the link provided in Section 4.\n\n\n### **W5: Context for Baselines**\nWe recognize that readers unfamiliar with time-series imputation may need clearer baseline context; in the revision we will add a concise \"baseline\" table to make our contributions easier to situate.\n\n### **W6 & L1: Need evaluation on synthetic data**\n\nWe designed a preliminary synthetic dataset composed of a trend component and multiple periodic components, formulated as follows.\n\n$$\nf(t)=0.01\\ t\n      +1.5\\ \\sin(0.002\\,t)\n      +2.0\\ \\sin\\left(\\frac{2\\pi t}{50}+\\frac{\\pi}{6}\\right)\n      +1.2\\ \\sin\\left(\\frac{2\\pi t}{120}+\\frac{\\pi}{4}\\right)\n      +0.8\\ \\sin\\left(\\frac{2\\pi t}{300}+\\frac{\\pi}{2}\\right)\n      +\\varepsilon_t \\qquad\n\\varepsilon_t\\sim\\mathcal{N}\\left(0,\\ 0.3^{2}\\right)\n$$\n\nWe sampled 1,000 points from this signal to construct the dataset. Experimental results demonstrate that our MG module consistently improves baseline performance, even on data with manually controlled trends and periodicities. We leave a more comprehensive investigation of MG's behavior on synthetic data for future work.\n\nmiss ratio|0.1|0.25|0.4\n-|-|-|-\nTransformer|0.0525|0.0659|0.0884 \nTransformer+MG|0.0176|0.0248|0.0428 \nTimesNet|0.0105|0.0112|0.0113 \nTimesNet+MG|0.0089|0.0095|0.0097 \n\n### **W7 & L3: Missing comparisons with simple baselines**\n\nFollowing your suggestions in the *Limitations and Suggestions* section, we incorporated three additional baselines: Linear Interpolation, KNN Imputation and Seasonal Historical Averages. The experimental results are shown below. While Linear Interpolation achieves surprisingly strong performance on certain datasets, our MG module consistently outperforms all baselines, further demonstrating its effectiveness.\n\n\n||Electricity|ETTh1|ETTm1|\n-|-|-|-|\nTransformer|0.276|0.236|0.177|\nLinear|0.182|0.204|0.119|\nKNN|0.748|0.604|0.574|\nSeasonal|0.818|0.769|0.770 \nTransformer+MG|0.180|0.169|0.108|\n\n\n\n\n### **Q1: Similarity to Existing Solutions**\n\nPeriod Guidance (PG) represents a fundamental departure from existing imputation methods. Whereas conventional deep learning imputers treat seasonality as an implicit pattern to be rediscovered and re-encoded within model weights through training, PG explicitly extracts dominant periods using a lightweight FFT-based peak detection module and feeds them back as **zero-parameter guidance. This \"hint\" can be seamlessly integrated into any backbone model and toggled on or off without retraining.** To the best of our knowledge, no prior imputation method offers such detachable, plug-and-play seasonal guidance. If relevant work exists, we would sincerely appreciate the citation and will gladly acknowledge it in the final manuscript.\n\n### **Q2: Why MG brings only marginal gains to TimesNet / CSDI**\n\nAlthough the raw differences look modest—e.g., CSDI at 0.027 vs CSDI+MG at 0.024 may only be a 0.003 improvement—this translates to an **11.1 % relative error reduction**, and MG delivers an **average 15.6 % improvement across all CSDI datasets**. For TimesNet, its built-in FFT already captures much of the periodic signal, leaving less headroom; even so, MG still yields a **notable 11.9 % boost on ETTm1**. In short, the perceived \"limited benefit\" stems from low baseline errors, but on a percentage basis MG provides consistent, meaningful gains.\n\n### **Q3: About hyperparameters $r$**\n\nThe normal distribution function used to generate NSG and PG is the standard normal distribution, characterized by a mean of 0 and a variance of 1. Since 99.7% of a standard normal distribution lies within [-3, 3], setting r = 3 effectively captures nearly all informative neighbors. In practice, larger values yield no measurable improvement. Using a shared radius helps minimize the hyperparameter budget and ensures consistency across datasets.\n\n### **Q4:  Clarifying the wording around Lines 271-275**\n\nWe agree the current phrasing is ambiguous. Line 275 was intended to summarise Table 10, which compares three groups: (i) earlier baselines (e.g., Transformer), (ii) recent advances (e.g., CSDI, SAITS), and (iii) our MG-enhanced models. Both groups (ii) and (iii) outperform the older baselines on the highly non-stationary HD dataset—but only group (iii) contains MG, so the sentence conflates two separate observations. In the camera-ready version we will replace it with:\n\n    \"Table 10 shows that (a) recent architectures already reduce HD error relative to older baselines, and (b) adding MG yields a further 15-25% reduction, highlighting MG's specific contribution to non-stationarity mitigation.\"\n\nThis revision explicitly separates the effects of modern backbones from the additional gains brought by MG, eliminating the contradiction.\n\n### **Additional Clarification about Q7 & Q8 & L5**\n\nWe confirm that every wording adjustment highlighted by the reviewer will be incorporated into the camera-ready version. Moreover, all baselines in our experiments were executed with their original default hyper-parameters as released in the corresponding papers or official repositories. No extra tuning was applied, ensuring that the observed performance gains arise exclusively from the proposed Meta Guidance mechanism."}, {"review_id": "mumFImr9GC", "reviewer": "Reviewer_i1nN", "summary": "The paper addresses the imputation task for time series that exhibit non-stationarity and periodicity behavior. In particular, the authors propose two modules, namely Non-Stationary Guidance (NSG) and Periodic Guidance (PG), to extend existing deep learning (DL) models in handling the aforementioned challenges and leveraging the non-stationarity and periodicity characteristics of the time series. Finally, a Meta Guidance (MG) module is introduced. The MG module learns to balance the matrix representations learned by NSG and PG, and to appropriately weight the time series within the deep learning architectures.\n\nIn the experiments, the authors integrate the MG module into 5 state-of-the-art models, they evaluate them on 9 real-world datasets. The models+MG show improved performance across all scenarios. The authors also present various ablation studies.", "questions": "1) What is exactly the MLP loss used in the different modules? Is it a reconstruction loss wrt the vanilla imputation? If so, can the authors motivate better this strategy, and alternatives.\n2) The results are averaged over three independent runs. Does it mean the models are trained 3 times? Or the imputation is done three times, using different random seeds / initialisation? \n3) I understand the added computation time for the MG module is reasonable, for a single epoch. However, we have additional embeddings, does a model requires more epochs to converge / achieve the optimal performance? Are the base models and models+MG trained the same number of epochs/ amount of time?\n4) What if we apply a simple pre-processing (like de-trending or differentiation) instead of meta guidance? What about the performance in this case?", "limitations": "Yes. However, the authors could extend the limitation section.", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- The idea is novel, and the performance of the MG module are quite interesting.\n- The paper is well written and easy to follow, although some details could be improved or explained more  (see below).\n\nWeaknesses:\nMajor:\n- There is no comparison againsts other approaches handling non stationarity and periodicity. Like simple pre-processing approaches, or deep learning solutions.  \n- In the modules,  \"ψ(i) is the probability density of standard normal distribution N(0,1)\" , centered at the current time step and used to compute the guidance matrices; and the hyperparameter \"r\" controls the neighborhood points. I wonder whether this hyperparameter could instead be learned, or better, whether the model could learn the most appropriate distribution (e.g., the standard deviation of N(0, sigma2)) for each channel, rather than relying on hyperparameters. The authors provide some ablation studies, but further exploration would be useful.\n- All the proposed modules are channel-independent. While the deep learning architecture may still capture inter-channel dependencies, I believe that the embeddings produced by the MG module could mislead the imputation process (of the DL models) for some multivariate datasets. I would like to see more discussion of this potential limitation.\n- Some well-known datasets with missing data are not included. For example, the Air Quality (PM2.5) dataset (which may have periodicity behavior); and PhysioNet. Both are used benchmarks in CSDI. \n\nMinor and Typos:\n- The repository link is expired; it would be helpful to provide an active one.\n- Figure 1 could be improved in quality. The meaning of the yellow dots and pink squares is not explained, their interpretation is left to the reader. Also, the figure style is quite different from the others in the paper.\n- Although basic, it would be useful to define the MAE and RMSE acronyms, and briefly justify why these metrics. For example, why not use the Continuous Ranked Probability Score (CRPS)?\n- The use of bold metrics in Table 11 is unclear. \n- Table 8, which includes standard deviations, is confusing to me. Which experiments are the values referring to?", "was_revised": true, "final_justification": "The paper proposes an approach to handle missing values in time series. The MG module is interesting, yet I have some concerns about its overhead as (for some datasets) a simple detrending has a very close performance to it.", "rebuttal": "# Response to Reviewer i1nN\nWe sincerely thank you for the detailed and constructive feedback. Unless explicitly noted, all new results will be included in the camera-ready version and the public code release.\n\n### **W1 & Q4: Missing comparisons with simple baselines**\n\nFollowing Q4's recommendation, we added a simple pre-processing baseline (de-trending) and an additional deep-learning baseline (Non-Stationary Transformer [1]). The experimental results are shown below, and the results show that our Transformer+MG approach consistently outperforms them, achieving the best overall performance.\n\n[1] \"Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting\", NeurIPS\n\n||ETTh1|ETTm1\n-|-|-\nTransformer|0.236|0.177 \nTransformer+detrending|0.197|0.130 \nNS Transformer|0.185|0.129 \nTransformer+MG|0.169|0.108 \n\n\n### **W2: Making r and sigma learnable**\n\nTo further investigate this issue, we conducted additional experiments in which the hyperparameter r and the standard deviation of the normal distribution were treated as learnable parameters. The results are presented in the table below.\n\n||HD|Weather|TCPC\n-|-|-|-\nvanilla MG|0.044|0.049|0.069 \nlearnable r|0.045|0.056|0.072 \nlearnable sigma|0.045|0.050|0.069 \n\nThese results reinforce our decision to keep a simple fixed radius, which delivers the strongest accuracy with minimal complexity; nonetheless, the learnable options remain available in the public code for users who wish to experiment on other data regimes.\n\n### **W3:  Could channel-independent guidance mislead multivariate imputation?**\n\nOur design intentionally keeps NSG/PG channel-specific so that each variable receives the most relevant temporal neighbours, while the backbone (e.g., Transformer or Diffusion) still performs full cross-channel mixing through self-attention or shared latent states. To test whether this separation harms correlated variables, we conducted an additional experiment in which the MG from all channels are averaged and then applied to all channels:\n\n||HD|Weather|TCPC|ETTh1\n-|-|-|-|-\nTransformer|0.112|0.088|0.177|0.236 \n+MG (channel-independent)|0.046|0.049|0.069|0.169 \n+MG (channel-aware)|0.067|0.055|0.082|0.175 \n\nOur new experiments confirm that the channel-independent MG does not impair—and in fact enhances—multivariate imputation. Keeping each variable's guidance separate lets the backbone attend to genuine inter-channel relations without conflating the distinct temporal dynamics of individual series, thereby delivering the strongest and most efficient performance.\n\n### **W4:  Experiments on the additional dataset**\n\nWe conduct additional experiments on the PhysioNet and PM25 dataset, and the method with MG also achieve excellent results. Below are the MSE results of the experiments under different missing rates:\n\nPhysioNet|10%|25%|40%\n-|-|-|-\nTransformer|0.640|0.684|0.692\nTransformer+MG|0.582|0.638|0.639\nTimesNet|0.633|0.659|0.665\nTimesNet+MG|0.561|0.577|0.606\n\nPM25|10%|25%|40%\n-|-|-|-\nTransformer|0.125|0.129|0.139 \nTransformer+MG|0.078|0.091|0.104 \nTimesNet|0.102|0.108|0.116 \nTimesNet+MG|0.082|0.092|0.103 \n\n### **W5:  Minor and Typos**\n\nThank you for the detailed presentation-quality remarks. \n- The anonymous code repository has been made publicly available.\n- Figure 1 will be redrawn in higher resolution and consistent styling; a legend will clarify that yellow dots denote the current missing point and pink squares mark the reference points located at the same value positions (periodic neighbours).\n- We will define MAE (Mean Absolute Error) and RMSE (Root Mean Square Error) on first use and note that they are the prevailing point-estimate metrics in imputation research; CRPS targets probabilistic forecasts, which are beyond our scope.\n- The caption of Table 11 will state that boldface marks the best score in each column.\n- For Table 8 we will clarify that each entry is the standard deviation over three independent training runs for the corresponding experiment reported in Table 10 and 11. \n\nAll of these revisions will appear in the camera-ready version.\n\n\n### **Q1:  Explanation of the \"loss\" in MLP**\n\nThe two-layer MLP inside each guidance module does not introduce an additional, standalone loss term. Its parameters are trained end-to-end with the backbone via the same imputation objective (MSE on masked values). We follow the common meta-learning rationale: by propagating gradients only through the main task, the MLP learns the neighbour weights that best serve the ultimate imputation goal, instead of optimising a surrogate signal that may mis-align with overall error. Furthermore, for each missing entry we know the true value we must recover, but we do not know the \"correct\" neighbour weights that should be assigned by the MLP.\n\n### **Q2:  Meaning of \"three independent runs\"**\n\nWe fully retrain each model three times under identical hyper-parameter settings but with different random seeds (affecting weight initialisation, data shuffling, and mask generation). The reported values are the mean of these three complete runs.\n\n### **Q3:  Do the extra MG embeddings require more training epochs?**\nNo—models with MG are trained for exactly the same number of epochs as the original backbones and reach their optimal validation error within that schedule."}, {"review_id": "9hmmtbhpYH", "reviewer": "Reviewer_sQEU", "summary": "The authors introduce a novel method that enhances deep learning for time-series imputation. It achieves this by integrating inductive biases for both non-stationary and periodic characteristics, dynamically weighted by a Meta Guidance mechanism. This approach is highly adaptable, designed to augment existing imputation methods, and is shown to improve their performance across diverse real-world time-series datasets with various missing data types (MAR, MNAR, MCAR) and rates.", "questions": "- The construction of the non-stationary guidance, periodicity guidance, and meta-guidance vectors remains unclear. Visualizing these guidance vectors would greatly enhance understanding of when and why the imputation process prioritizes non-stationary or periodic signals. Can the authors elaborate on this?\n\n- A concern arises regarding potential overfitting of the gamma parameters in Equations (3) and (8) to the training set. How do the authors address this and demonstrate that the parameters are well chosen in augmented imputation methods?\n\n\n- While the authors have provided an extensive ablation study, they primarily focused on showing the effect of including or excluding certain components. The authors do not adequately explain when and why non-stationary guidance and periodic guidance are beneficial, nor do they connect these benefits to specific characteristics of the evaluated time-series datasets. A plot illustrating the method's performance against key time-series statistics would significantly strengthen this aspect.\n\n-  The authors demonstrate the method's effectiveness across multiple real-world time-series datasets and various missingness scenarios (e.g., MAR, MNAR, MCAR) and missing rates. However, these static missingness patterns fail to capture the dynamic nature of real-world missing data, where missingness is often influenced by temporal dependencies. This raises questions about why augmenting the proposed method helps and when it is most effective. Hence, a more thorough investigation of its behavior under dynamic temporal variations is recommended. Specifically, the authors could explore: \n(i) How the meta-guidance mechanism responds to changing temporal characteristics.\n(ii) How the method performs when missingness is generated based on temporal dependencies, rather than static patterns.\n\n- While the authors highlight contributions in non-stationary/periodic modeling and meta guidance, the related work section fails to adequately position their approach. The discussion of stationary imputation and general time-series characteristics is too broad, hindering a clear understanding of the proposed method's novelty.\n\n- As mentioned in the Weakness, important multiple imputation methods for time-series data are missing.\n\n- It would be valuable to incorporate experiments illustrating that the imputed values produced by the proposed method maintain high predictive and/or discriminative power.", "limitations": "Yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strength: \n- The proposed method is compatible with existing time-series imputation techniques and offers a promising avenue for performance enhancement through augmentation. \n- The MG mechanism is highly adaptive and can be applied to other existing imputation methods.\n- The performance improvements are both consistent and significant across various experiments.\n- This work offers a meaningful departure by providing compatibility with existing time-series imputation techniques (which have primarily concentrated on developing novel architectures and objective functions, often incorporating diverse inductive biases, frequency and trend-seasonality decomposition) and offering a promising avenue for performance enhancement through augmenting high-level information of the given time-series.\n\nWeakness:\n- While the authors mentioned that the current time-series imputation methods do not concurrently consider the characteristics of non-stationarity and periodicity in time series, many recent related works use inductive bias to put localized influence [A, B] or both trend and seasonality [C] for time-series imputation.\n- The proposed framework is highly adaptive. But, its adaptability to multiple imputation methods (such as [A, B, C] and many more) is missing. \n\n\nReferences: \n\n[A] M. Choi and C. Lee, \"Conditional Information Bottleneck Approach for Time Series Imputation,\" ICLR 2024.\n\n[B] V. Fortuin et al, \"GP-VAE: Deep Probabilistic Time Series Imputation.\" AISTATS 2020.\n\n[C] X. Yang et al., \"Frequency-aware Generative Models for Multivariate Time Series Imputation,\" NeurIPS 2024.", "was_revised": true, "final_justification": "After rebuttal: I have updated my score to a \"borderline accept\".", "rebuttal": "# Response to Reviewer sQEU\nWe sincerely thank you for the thoughtful, detailed review. Below we respond point-by-point, following the order of your comments. All new analyses, figures and baselines are included in the updated appendix and will be integrated into the camera-ready version.\n\n### **W1: Clarifying MG's distinct contribution**\nThank you for raising this point. In the methods you cite, periodicity or non-stationarity is built into the model itself: TimeCIB [1] incorporates a kernel term directly in its information-bottleneck loss, GP-VAE [2] places a Gaussian-process prior on the latent trajectory, and FGTI [3] learns separate latent variables for trend and seasonality. These method encode periodicity or non-stationarity as integral parts of the model architecture or training objective, rather than as detachable inductive hints.\n\nBy contrast, Meta Guidance remains entirely external to the backbone. Our non-stationary and periodic maps are delivered only as lightweight guidences, and a learnable gate $\\lambda$ lets the model decide how much to trust each guidence. Nothing in the backbone or loss is changed, so MG acts as a detachable inductive bias that can be plugged into CIB, GP-VAE, FGTI, or almost any other deep-learning imputer. In the revised experiments we include these methods as baselines and show that simply adding MG to a vanilla Transformer reliably surpasses their performance.\n\n\n[1] \"Conditional information bottleneck approach for time series imputation.\", ICLR.\n\n[2] \"Gp-vae: Deep probabilistic time series imputation.\", AISTATS.\n\n[3] \"Frequency-aware generative models for multivariate time series imputation.\", NeurIPS.\n\n\n### **W2 & Q6: Additional baseline methods**\nWe conduct additional experiments on three relevant methods [1,2,3], and the results show that our Transformer+MG approach consistently outperforms them, achieving the best overall performance. Below are the MSE results of the experiments under 10% missing rates:\n\nMSE|HD|ETTh1|Weather\n-|-|-|-\nTimeCIB|0.302|0.199|0.107\nGP-VAE|0.644|0.504|0.163\nFGTI|0.165|0.125|0.031\nTransformer+MG (Ours)|0.007|0.065|0.025\n\n\n\n\n### **Q1: Visualization of NSG and PG construction**\nThank you for the suggestion. A full, step-by-step walkthrough already appears in Appendix H, accompanied by new figures that both illustrate how NSG and PG are built and show the final guidance maps after construction.\n\nWe realise this figure is easy to miss, so we will add a forward-reference from the main text in the camera-ready version.\n\n### **Q2: Discussion on $\\gamma$ parameters overfitting**\n\nTo check whether the scaling factors $\\gamma$ in Equations (3) and (8) simply memorise the training data, we ran an additional experiment. The table below reports (i) the Augmented Dickey–Fuller statistic (ADF: larger ⇒ more non-stationary) and (ii) the values learned for $\\gamma$ on three representative datasets:\n\ndataset|HD|ETTh1|TCPC\n-|-|-|-\nADF|1.958|-5.908|-22.199\n$\\gamma^{NS}$|1.069|1.076|1.021\n$\\gamma^{Per}$|0.908|1.090|1.117\n\n1. Above experimental results suggest that **$\\gamma^{NS}$ and $\\gamma^{Per}$ effectively adapt to datasets with varying statistical properties**. Specifically, for datasets with stronger non-stationarity (higher ADF test values), $\\gamma^{NS}$ tends to be larger than $\\gamma^{Per}$, and vice versa. This behavior aligns with expectations, further supporting the robustness of the proposed method.\n\n2. The $\\gamma$ parameter scales the original NSG and PG sequences by directly adjusting their values. However, **this scaling effect is further regulated by the $\\lambda$ parameter** (Equation 11). As demonstrated in Figure 7 (Section 4.3), $\\lambda$ dynamically adapts to different data characteristics. Moreover, additional experiments show that $\\gamma$ exhibits minimal variation across different datasets, indicating that $\\lambda$ remains the primary adjustment mechanism.\n\n3. Overfitting is a common challenge in deep learning, particularly in meta-learning approaches. While limited method is entirely immune to this issue, our approach has been extensively evaluated on nine real-world datasets with diverse characteristics (Table 2, Section 4.2). These experiments demonstrate that MG exhibits strong generalization capabilities, effectively handling imputation tasks across various datasets.\n\n\n### **Q3: Explaining when NSG and PG help**\n\nOur current results already hint at a clear pattern: datasets with pronounced level shifts (HD) gain most from the NSG, whereas those with strong seasonal peaks (Weather, Traffic) benefit chiefly from PG. As demonstrated in the ablation study in Section 4.3, the Augmented Dickey-Fuller (ADF) scores align closely with the guidance module that yields the most significant performance gain.\n\n||HD|Electricity|Weather|TCPC\n-|-|-|-|-|\nADF test value|1.958|-8.444|-26.681|-22.199\nvanilla|0.112|0.276|0.088|0.177\nonly NSG|0.047|0.182|0.053|0.076\nonly PG|0.051|0.186|0.051|0.072\nMG|0.046|0.180|0.049|0.069\n\n\n### **Q4: Time-varying missing patterns**\nTo test MG in a setting where the gap rate itself changes over time, we injected a sinusoidally varying drop-probability:\n\n$p(i) = 0.25 + 0.15 \\cdot \\sin\\left(\\frac{2\\pi i}{T}\\right)$ .\n\nwhich swings the missing rate smoothly between 0.10 and 0.40. Even with this dynamically shifting pattern, MG delivers large error reductions:\n\n||HD|ETTh1|Weather|TCPC\n-|-|-|-|-\nTransformer|0.035|0.184|0.061|0.094\nTransformer+MG|0.009|0.109|0.037|0.024\nTimesNet|0.010|0.121|0.040|0.028\nTimesNet+MG|0.008|0.095|0.038|0.013\n\nThe results show that MG continues to significantly improve model performance. This confirms that the Meta Guidance mechanism adapts effectively even when missingness itself follows a non-stationary, time-dependent process.\n\n### **Q5: Related work positioning**\nWe agree the current survey is too generic. Since MG is a modular component that can be integrated into most deep learning methods, our approach is most appropriately positioned in Section 2.2, line 79, under \"Deep Learning-Based Imputation.\" In the next version, we will refine the paper's structure, including the Related Work section, to better align with the core contributions and enhance overall clarity and readability.\n\n\n### **Q7: Down-stream predictive value of MG-imputed data**\n\nTo test whether MG's gains translate into better forecasting accuracy, we trained two standard forecasters—TimesNet and iTransformer—on the Weather dataset under two input conditions:\n\nForecasting task|TimesNet|iTransformer\n-|-|-\nRaw series with 25 % missing|0.327|0.287 \nSame series after MG imputation|0.220|0.237 \n\nThe substantial MAE drops confirm that MG not only reduces reconstruction error but also enhances the predictive signal needed for downstream tasks."}, {"review_id": "rHBG6ZfM63", "reviewer": "Reviewer_bot2", "summary": "The paper presents a novel plugin module called Meta Guidance for multivariate time series with missing values. Meta Guidance dynamically fuses NSG and PG via a learnable meta-weighting mechanism, allowing models to adaptively focus on temporal dynamics based on data characteristics. MG can be seamlessly integrated into popular deep imputation models (Transformers, CSDI, SAITS, TimesNet, etc.), yielding an average 27.39% improvement over state-of-the-art methods on nine real-world datasets.", "questions": "1. Why NSG and PG are designed in Channel-independent style? In my opinion, different channels may exhibits different non-stationary levels and different periodicities. \n2. In Eq. 7, for each previous period, the PG only consider the exact one time point. So for periodic data with high noise levels or even anomalies, could this affect the model's robustness to noise? Would additionally considering the neighboring points of each periodic point be a more robust approach?", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Pros:\n1. The paper is well-structured and easy to follow.\n2. The proposed method is plug-and-play with strong adaptability, and brings effective performance improvements across a variety of models.\n3. The paper provides thorough experiments, including comparison with several backbones on 9 datasets and under different missing mechanisms.\n\nCons:\n1. Periodicity detection relies on FFT, assuming stable periodic patterns. This may not generalize well to irregular periodicities. \n2. Some baselines are absent. PatchTST[1] has been proven to be an effective and efficient on time series tasks, the paper should further investigate its effectiveness when applied to methods employing patch trick (This trick is widely used for time series models). Also, the non-stationary transformer[2] also consider the non-stationary factor. It should be included as a baseline.\n[1] A Time Series is Worth 64 Words: Long-term Forecasting with Transformers. ICLR 2023.\n[2] Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting, NeurIPS 2022.", "was_revised": true, "final_justification": "I appreciate the authors' rebuttal for addressing my concerns. However, considering the current state of the paper and the responses provided to other reviewers, I am unable to raise my score to 'Accept'. Therefore, I will maintain my original rating of ​​Borderline Accept​​.", "rebuttal": "# Response to Reviewer bot2\nThank you for your encouraging evaluation and for the constructive suggestions. Below we address each concern in turn. Unless explicitly noted, all new results will be included in the camera-ready version and the public code release.\n\n### **W1: Robustness of FFT-based Periodic Guidance**\nOur Periodic Guidance (PG) does not depend on a single, fixed cycle: we extract the top-k dominant frequencies per channel via an FFT power spectrum and fuse their contributions proportionally to their amplitudes . This multi-frequency design already captures moderate drift or co-existing cycles. Moreover, the meta-weight $\\lambda$ learned by Meta Guidance automatically down-weights PG whenever periodic cues weaken, as confirmed by the markedly lower $\\lambda$ on weak-seasonality datasets (e.g., Weather vs. HD) in Fig. 6 . Ablation on k further shows that adding or dropping secondary peaks has only a modest impact, indicating graceful behaviour even when periodicities are less regular . Together, the use of multiple FFT peaks plus adaptive blending ensures PG generalises beyond perfectly stable cycles; when periodic information becomes unreliable, NSG naturally takes the lead, preventing degradation.\n\n\n### **W2: PatchTST & Non-stationary Transformer baselines**\n\nWe conducted additional experiments by incorporating MG into PatchTST and the Non-stationary Transformer, and evaluated their performance across multiple datasets. The results are summarized below.\n\n||Electricity|ETTh1|TCPC\n-|-|-|-|\nPatchTST|0.161|0.232|0.074 \nPatchTST+MG|0.147|0.216|0.057 \nNS Transformer|0.194|0.195|0.086 \nNS Transformer+MG|0.175|0.176|0.067 \n\nAcross these strong baselines, MG consistently yields additional RMSE reductions of 7-23 %, confirming that our guidance layer complements both the patch trick and built-in non-stationary modelling.\n\n\n\n\n### **Q1: Rationale for channel-independent NSG and PG**\n\nEach variable in a multivariate series often follows its own drift and cycle (e.g., temperature vs. wind speed). We therefore generate one guidance vector per channel so that (i) non-stationary level shifts and dominant periods are captured in the scale that is truly relevant to that variable, and (ii) heterogeneous units and magnitudes are not blended prematurely. Cross-channel relationships are still learned—but by the backbone's self-attention or diffusion layers, which are expressly designed for that purpose and can exploit richer, high-dimensional context than a lightweight guidance head.\n\nTo test whether this separation harms correlated variables, we conducted an additional experiment in which the MG from all channels are averaged and then applied to all channels:\n\n||HD|Weather|TCPC|ETTh1\n-|-|-|-|-\nTransformer|0.112|0.088|0.177|0.236 \n+MG (channel-independent)|0.046|0.049|0.069|0.169 \n+MG (channel-aware)|0.067|0.055|0.082|0.175 \n\nOur new experiments confirm that the channel-independent MG does not impair—and in fact enhances—multivariate imputation. Keeping each variable's guidance separate lets the backbone attend to genuine inter-channel relations without conflating the distinct temporal dynamics of individual series, thereby delivering the strongest and most efficient performance.\n\n\n### **Q2: Why single-point PG remains robust to noise**\nAlthough Eq.7 samples the central value at each previous period, PG actually weighted averages several periods before passing the signal to the backbone. This multi-period ensemble already dilutes an occasional outlier. Moreover, the meta-weight $\\lambda$ is learned jointly with the backbone: if a periodic reference conflicts with nearby non-stationary neighbours, $\\lambda$ shifts emphasis toward NSG, automatically down-weighting the noisy PG cue."}]

Author rebuttal:

Meta-review: This work introduces a plug-and-play module named Meta Guidance (MG), which improves multivariate time series imputation by combining Non-Stationary Guidance (NSG) and Periodic Guidance (PG) mechanisms. The method uses a learnable parameter λ to dynamically weight guidance from nearby temporal measurements versus corresponding periodic timesteps. MG integrates seamlessly with existing architectures and achieves consistent 27% performance improvements across nine datasets.

The plug-and-play design enables broad compatibility with existing imputation methods (from Reviewer NQxZ, Reviewer sQEU, Reviewer bot2). Extensive experiments demonstrate consistent improvements across multiple datasets, missing mechanisms, and baseline comparisons (from Reviewer NQxZ, Reviewer i1nN, Reviewer sQEU, Reviewer bot2).

There are some initial comments from reviewers: (1) Missing comparisons with other non-stationarity/periodicity approaches and key baselines like PatchTST and Non-stationary Transformers (from Reviewer i1nN, Reviewer bot2). (2) The channel-independent design may mislead imputation for datasets requiring inter-channel dependencies (from Reviewer i1nN). (3) Limited analysis of the critical λ parameter's impact across different datasets (from Reviewer NQxZ, Reviewer i1nN). The method focuses on individual missing points rather than consecutive missing patterns common in real scenarios (Reviewer NQxZ). 

Authors have addressed most of them, and reviewers acknowledge that the author responses are informative.
Decision: Accept (poster)