FIC-TSC: Learning Time Series Classification with Fisher Information Constraint

TL;DR

FIC-TSC introduces a Fisher Information Constraint to train time series classifiers that are robust to train/test distribution shifts. By using a diagonal Fisher Information Matrix and gradient renormalization, the method constrains the optimization to flatter regions of the loss landscape, promoting better generalization without extra backpropagation. The authors provide theoretical connections between the FIM constraint, sharpness, and convergence, and validate the approach across 30 UEA and 85 UCR datasets, outperforming 14 state-of-the-art baselines while maintaining efficient training. Empirical results show substantial sharpness reduction and consistent accuracy gains, including strong performance under explicit domain shifts in healthcare data. Overall, FIC-TSC offers a principled, scalable framework for robust time series classification in diverse, real-world domains.

Abstract

Analyzing time series data is crucial to a wide spectrum of applications, including economics, online marketplaces, and human healthcare. In particular, time series classification plays an indispensable role in segmenting different phases in stock markets, predicting customer behavior, and classifying worker actions and engagement levels. These aspects contribute significantly to the advancement of automated decision-making and system optimization in real-world applications. However, there is a large consensus that time series data often suffers from domain shifts between training and test sets, which dramatically degrades the classification performance. Despite the success of (reversible) instance normalization in handling the domain shifts for time series regression tasks, its performance in classification is unsatisfactory. In this paper, we propose \textit{FIC-TSC}, a training framework for time series classification that leverages Fisher information as the constraint. We theoretically and empirically show this is an efficient and effective solution to guide the model converge toward flatter minima, which enhances its generalizability to distribution shifts. We rigorously evaluate our method on 30 UEA multivariate and 85 UCR univariate datasets. Our empirical results demonstrate the superiority of the proposed method over 14 recent state-of-the-art methods.

Figures (11)

• Figure 1: A conceptual visualization of Flat and Sharp Minima. The Y-axis indicates loss, and the X-axis represents the variables (neural network parameters). Under train (blue) and test (purple) data domains, due to potential distribution shift, the landscapes differ, i.e., with the same network parameter, the loss is often different. A flat minimum can potentially lead to a low test error, while a sharp minimum potentially leads to a high test error.
• Figure 2: Histograms representing sequences from the two selected classes of exemplary datasets with train/test distribution shift. The dissimilarity matrix illustrates the min-max normalized Wasserstein-1 distance between class distribution from different sets. A lower value implies two distributions are more similar. It is observed that distribution shifts exist between the entire training and testing sets and within the same classes across these sets.
• Figure 3: An illustration of the negative effect of Instance Normalization (IN). Left: The original input, and Right: Input after applying IN. It is observed that IN can reduce the difference of two class distributions. This may be disadvantageous for classification.
• Figure 4: Comparison of classification accuracy between baseline and the model applying IN. Avg. indicates Average accuracy across all datasets. It is observed that IN does not have any positive effect on the model for most datasets. A statistical test is conducted in Appendix \ref{['appendix:stats1']}.
• Figure 5: The accuracy improvement of our method over the baseline (i.e. standard training without using any constraint). We present the average accuracy improvement at the end.

Theorems & Definitions (18)

• definition 1
• definition 2
• Remark 1
• Remark 2
• lemma 1
• Remark 3
• definition 3
• corollary 1
• proof
• theorem 4