TIMEX++] Framework For Improving Explainability In Deep Learning Of Time Series

Neural Network 09/12/2024

3 main points
✔️ Proposal for TIMEX++ with improved information bottleneck principle.
✔️ Improved explainability of time series data and avoidance of trivial solving and distribution shift problems.
✔️ Extend the applicability of TIMEX++ to other data modalities and complex tasks and advance automatic adjustment of hyperparameters to further improve performance and adaptability.

TimeX++: Learning Time-Series Explanations with Information Bottleneck
written by Zichuan Liu, Tianchun Wang, Jimeng Shi, Xu Zheng, Zhuomin Chen, Lei Song, Wenqian Dong, Jayantha Obeysekera, Farhad Shirani, Dongsheng Luo
(Submitted on 15 May 2024)
Comments: Accepted by International Conference on Machine Learning (ICML 2024)
Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

code：

The images used in this article are from the paper, the introductory slides, or were created based on them.

Summary

Optimization of signal transmission technologies is essential to drive the evolution of optical communications. This paper explores in detail the purpose of line coding technology and how it can be implemented. Line coding aims to improve bandwidth and power efficiency as well as enhance error detection and correction. It is also important to properly adjust the power spectral density of the signal to provide accurate timing information while maintaining DC balance.

This paper compares the characteristics of unipolar, polar, and bipolar signals and their spectral differences. This clearly shows the advantages and challenges of each encoding scheme. For example, bipolar signals have no DC component and are easy to detect errors, while unipolar signals have the highest power efficiency but have a DC component that must be used with caution.

In addition, effective pulse shaping techniques and practical pulse design from Nyquist pulses are discussed. These techniques play an important role in the design of realistic band-limited signals. Through this paper, advanced coding and pulse shaping techniques used at the forefront of optical communication technology are detailed, providing insight into the foundations upon which future communication infrastructures will be built.

Related Research

The world of optical communications is part of the infrastructure that supports our daily lives. However, there is a complex science behind optical communication technology, of which "line coding" and "pulse shaping" play a very important role. Here we introduce some of the related research presented in the paper.

Types of Signals and Their Differences

In optical communications, information is sent in the form of light, and there are several types of these optical signals. Specifically, there are unipolar, polar, and bipolar signals. Each signal has its own characteristics, advantages and disadvantages.

Unipolar signal: This signal is very power efficient, but it contains a DC component (zero-frequency component), which may distort the signal.

Polarized signals: These are more power efficient but less bandwidth efficient.

Bipolar signal: This signal has no DC component and is easy to detect errors. It also features the best bandwidth efficiency.

Differences in these signals have a significant impact on how data is sent and how efficiently it is sent.

Pulse Shaping and Bandwidth Efficiency

When sending a signal, it is important not only to turn it on and off, but also to devise the shape of the signal itself. This is called "pulse shaping. There are several pulse waveforms, such as rectangular pulses and cosine-square pulses, each of which has its own advantages. For example, a rectangular pulse is simple and straightforward, but is not well suited for actual use. The cosine-squared pulse offers a good balance between signal bandwidth and practicality.

Practical Application of Nyquist Pulse

Theoretically, the most efficient pulse is the Nyquist pulse, but in reality it is difficult to use it as is. Therefore, the Nyquist pulse is truncated to a practical form. This ensures that signals are sent efficiently and that bandwidth is not wasted.

Band-Limited Signal Realism

Under ideal conditions, the signal would have infinite bandwidth, but in practice such a thing is impossible. In a realistic system, the bandwidth of the signal must be limited. With band-limited signals, the Sinc function is used to adjust the power spectral density (PSD) of the signal. This allows for efficient and realistic signal transmission.

Proposed Method

TIMEX++ is a framework for improving the explainability of time series data.

Figure 2: Overall architecture of TIMEX++

The specific methods are described below.

Application of The Information Bottleneck (IB) Principle

Based on the information bottleneck (IB) principle, we aim to find a compact and informative sub-instance \(X'\) for the original time series instance \(X\) and its label \(Y\).

Original IB optimization problem:.

where \(X' = X \odot M\) and \(M[t,d] \sim \text{Bern}(\pi_{t,d})\). \(g(X) = \pi = [\pi_{t,d}]_{t \in [T], d \in [D]}}) is a function that outputs a probability distribution for a binary mask \(M\) that takes as input the original instance \(X\) and generates a subinstance \(X'\).

Trivial Solution and Avoidance of Distribution Shift

To solve the problem of the traditional IB principle, we modify the optimization problem as follows

where \(LC(Y; Y')\) is a measure of label consistency between the original label \(Y\) and the label \(Y'\) of the subinstance \(X'\). This modification avoids trivial solving and distribution shift problems.

TIMEX++ Framework

TIMEX++ consists of two main components: an explanation extractor and an explanation conditioner.

Description Extractor \(g_\phi}: g_phi

Purpose: Encode the input \(X\) into a probability mask \(\pi\).
Architecture: Encoder-decoder type transformer model is used to represent \(P(M | X)\).
Regularization: Minimizes continuity loss \(L_{con}\) and suppresses discontinuous shapes in the predictive distribution.
Binary Mask Generation: Generates a binary mask \(M\) using a straight-through estimator (STE).

Description Conditioner \(Ψ_θ\)

Objective: To generate a reference instance \(X_r\) using Gaussian padding technique, and then to generate an explanation embedding instance \(X\).
Architecture: Mapping the concatenation of \(M\) and \(X\) to \(X\) using the multilayer perceptron (MLP).
Loss Function:
KL Divergence Loss: ðLoss Þ

Reference Distance Loss: 1.0

Maintain Label Consistency

To maintain label consistency \(LC(Y; Y')\), we use Jensen-Shannon (JS) divergence to minimize the divergence between the original prediction \(f(X)\) and the prediction \(f(X̃)\) of the explanation embedded instance.

Total Loss Function

The overall learning objective of TIMEX++ is to minimize the total loss of

where \(\alpha\) and \(\beta\) are hyperparameters that adjust the loss weights. In this way, TIMEX++ generates an explanation embedding instance with label-preserving properties within the original data distribution.

In short, TIMEX++ is a framework that improves on the information bottleneck principle to improve the explainability of time series data. It uses a parametric network to create label-preserving explanatory embedded instances within the original data distribution. This solves the trivial solution and distribution shift problems.

Experiment

To evaluate the performance of TIMEX++, we experimented with several synthetic and real data sets.

Synthetic datasets: FreqShapes, SeqComb-UV, SeqComb-MV, LowVar

Real-world datasets: ECG, PAM, Epilepsy, Boiler

For each dataset, the performance of TIMEX++ was compared to other explanatory methods (e.g., Integrated Gradients, Dynamask, TIMEX, etc.).

Experimental Results

Composite Data Set

On the synthetic datasets, TIMEX++ performed consistently better than the other methods. In particular, TIMEX++ outperformed all other baseline methods in explanation accuracy (AUPRC, AUP, AUR) (see Table 1); TIMEX++ performed best or next best in all 9 cases (4 data sets x 3 evaluation metrics).

Table 1: Accuracy of Description (AUPRC, AUP, AUR)

Actual Data Set

On real data sets, TIMEX++ also showed superior performance compared to other methods. In particular, on the ECG data set, TIMEX++ accurately identified QRS interval associations, achieving the best AUPRC (0.6599), AUP (0.7260), and AUR (0.4595) (see Table 3).

Table 3: Accuracy of explanations in ECG data sets

Occlusion Experiments

In occlusion experiments on real data sets, TIMEX++ showed the most consistent results. In particular, TIMEX++ consistently maintained higher AUROC than the other methods on the Epilepsy, PAM, and Boiler data sets (see Figure 3).

Figure 3: Results of occlusion experiments on real data sets

Consideration

The superior performance of TIMEX++ is due to several important factors in its design. First, the improved information bottleneck principle effectively avoids trivial solution and distribution shift problems. In addition, the linkage between the explanation extractor and the explanation conditioner improved the consistency and accuracy of the explanations by generating label-preserving instances of explanation embedding within the original data distribution.

TIMEX++ has the potential to be a powerful tool for improving the interpretability of deep learning models, especially in sensitive domains such as medicine and environmental sciences. Experimental results demonstrate that TIMEX++ consistently outperforms other state-of-the-art explanatory methods, proving its utility and effectiveness.

Conclusion

This paper introduced TIMEX++, a new framework that significantly improves explainability in deep learning models of time series data. It improves on the information bottleneck principle and uses parametric networks to generate explanatory embedded instances with label-preserving properties within the original data distribution. Experimental results showed that TIMEX++ consistently outperforms traditional methods, confirming its utility.

Future prospects include further extending the applicability of TIMEX++ to other data modalities and complex tasks. It is also important to improve adaptability to different data sets by automating the adjustment of hyperparameters; TIMEX++ will help enable reliable model interpretation in highly sensitive areas such as medical and environmental sciences.

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