Are uGLAD? Time will tell!

TL;DR

This work proposes a domain agnostic multivariate segmentation framework which draws a parallel between the CI graph nodes and the variables of the time series, and designs a first-order and second-order based trajectory tracking algorithms to study the evolution of these graphs across distinct intervals.

Abstract

We frequently encounter multiple series that are temporally correlated in our surroundings, such as EEG data to examine alterations in brain activity or sensors to monitor body movements. Segmentation of multivariate time series data is a technique for identifying meaningful patterns or changes in the time series that can signal a shift in the system's behavior. However, most segmentation algorithms have been designed primarily for univariate time series, and their performance on multivariate data remains largely unsatisfactory, making this a challenging problem. In this work, we introduce a novel approach for multivariate time series segmentation using conditional independence (CI) graphs. CI graphs are probabilistic graphical models that represents the partial correlations between the nodes. We propose a domain agnostic multivariate segmentation framework $\texttt{tGLAD}$ which draws a parallel between the CI graph nodes and the variables of the time series. Consider applying a graph recovery model $\texttt{uGLAD}$ to a short interval of the time series, it will result in a CI graph that shows partial correlations among the variables. We extend this idea to the entire time series by utilizing a sliding window to create a batch of time intervals and then run a single $\texttt{uGLAD}$ model in multitask learning mode to recover all the CI graphs simultaneously. As a result, we obtain a corresponding temporal CI graphs representation. We then designed a first-order and second-order based trajectory tracking algorithms to study the evolution of these graphs across distinct intervals. Finally, an `Allocation' algorithm is used to determine a suitable segmentation of the temporal graph sequence. $\texttt{tGLAD}$ provides a competitive time complexity of $O(N)$ for settings where number of variables $D<<N$. We demonstrate successful empirical results on a Physical Activity Monitoring data.

Figures (4)

• Figure 1: Overview of Sparse Graph Recovery methods. We focus on methods that recover undirected graphs which capture direct dependence among their nodes or features. tGLAD framework utilizes a recently developed deep model, uGLAD, that outputs a conditional independence graph between in the features. Our framework can potentially use other methods and will be interesting topic for future explorations. (partly borrowed from shrivastava2023neural)
• Figure 2: tGLAD framework. (A) The time series is divided into multiple intervals by using a sliding window to create a batch of intervals. (B) Run a single uGLAD model in multitask learning (or batch) mode setting to recover a CI graph for every input batch. This gives a corresponding set of temporal CI graphs. The entire input is processed in a single step as opposed to obtaining a CI graph for each interval individually. (C$_1$) Get the first order distance, $dG$ sequence, of the temporal CI graphs which captures the distance between the consecutive graphs. This is supposed to give higher values at the segmentation points. (C$_2$) Again take a first order distance of the sequence in the previous step and then its absolute value to get $d2G$ sequence, which further accentuates the values at the segmentation points. (D) Apply a threshold to zero out the smaller values of $d2G$ and identify the segmentation blocks using an 'Allocation' algorithm.
• Figure 3: Design choices for tGLAD. Examining the segmentation accuracy on the PAMAP2 dataset which records body sensor data. We vary the window size on the x-axis and for each window size, we evaluate the performance for varying batch sizes (M). The stride length was fixed at 100 for all the experiments.
• Figure : Allocating segments