Adaptive Upper Confidence Region Approach for Partially-Observable Sequential Change-Point Detection in Autocorrelated Multivariate Data Streams

Core Concepts

A novel adaptive upper confidence region approach (AUCRSS) is proposed to efficiently detect change points in partially-observable autocorrelated multivariate data streams by leveraging state space modeling, generalized likelihood ratio testing, and combinatorial multi-armed bandit optimization.

Abstract

The key highlights and insights of the content are: The authors formulate the problem of partially-observable sequential change-point detection for autocorrelated multivariate data streams using a state space model (SSM). This allows them to capture the complex cross-correlations and temporal autocorrelations in the data. A partially-observable Kalman filter algorithm is developed for online inference of the SSM parameters given the limited observations at each time point. A change-point detection scheme is proposed based on a generalized likelihood ratio test (GLRT), and the authors analyze how the detection power is related to the adaptive sampling strategy. By treating the detection power as a reward function, the problem is formulated as a combinatorial multi-armed bandit (CMAB) optimization problem. An adaptive upper confidence region algorithm is proposed to design the adaptive sampling policy. Theoretical analysis is provided to show the asymptotic properties of the proposed AUCRSS method, including its ability to balance exploration and exploitation, and its convergence to the optimal detection performance. Extensive numerical studies on synthetic data and a real-world case study demonstrate the effectiveness of AUCRSS compared to existing methods, especially in handling autocorrelated data and efficiently detecting change points with limited observations.

Stats

The authors use the following key metrics and figures to support their analysis: "Figure 1 shows sequentially collected data from six variables in a milling process, including AC spindle motor current (smcAC), DC spindle motor current (smcDC), table vibration (vibTable), spindle vibration (vibSpindle), acoustic emission at table (aeTable) and acoustic emission at spindle (aeSpindle)." "Figure 2a shows the Pearson correlation of these six variables, indicating strong positive and negative correlations between them." "Figure 2b shows the autocorrelation functions of the six variables, verifying the presence of strong autocorrelations in the data stream."

Quotes

"One characteristic of multivariate data stream is that different variables exhibit complex cross-correlations." "Another characteristic of streaming data is that observations at sequential time points are usually autocorrelated, especially when the sensing frequency is high."

Key Insights Distilled From

Partially-Observable Sequential Change-Point Detection for Autocorrelated Data via Upper Confidence Region

by Haijie Xu,Xi... at arxiv.org 04-02-2024

https://arxiv.org/pdf/2404.00220.pdf

Deeper Inquiries

How can the proposed AUCRSS method be extended to handle non-Gaussian or non-linear dynamics in the multivariate data streams

The AUCRSS method can be extended to handle non-Gaussian or non-linear dynamics in multivariate data streams by incorporating more flexible and robust modeling techniques. One approach is to utilize non-parametric methods that do not assume a specific distribution for the data. This can involve using kernel density estimation, Gaussian processes, or other non-parametric models to capture the underlying patterns in the data without relying on Gaussian assumptions. Additionally, incorporating machine learning algorithms such as neural networks or deep learning models can help capture non-linear relationships in the data. By integrating these advanced modeling techniques into the AUCRSS framework, the method can adapt to a wider range of data distributions and dynamics.

What are the potential limitations of the state space model formulation, and how can it be further generalized to capture more complex temporal and spatial dependencies in the data

The state space model formulation has some potential limitations that can be addressed to capture more complex temporal and spatial dependencies in the data. One limitation is the assumption of linearity in the relationships between the latent states and observed variables. To overcome this limitation, one can consider using non-linear state space models, such as nonlinear dynamical systems or deep state space models, which can capture more intricate relationships in the data. Additionally, incorporating spatial dependencies in the model can be achieved by extending the state space model to include spatial components, such as spatial autoregressive terms or spatial random effects. By enhancing the state space model with non-linear and spatial components, it can better capture the complex dependencies present in the data.

Given the connection between the change-point detection problem and the combinatorial multi-armed bandit framework, are there other optimization techniques beyond the upper confidence bound that could be leveraged to design even more efficient adaptive sampling strategies

Beyond the upper confidence bound, other optimization techniques can be leveraged to design more efficient adaptive sampling strategies for change-point detection in the combinatorial multi-armed bandit framework. One approach is to explore Thompson sampling, which involves sampling from the posterior distribution of the arms to balance exploration and exploitation. Another technique is to use reinforcement learning algorithms, such as Q-learning or deep Q-networks, to learn the optimal sampling policy over time. Additionally, evolutionary algorithms or genetic algorithms can be employed to search for the best sampling strategy in a more dynamic and adaptive manner. By integrating these optimization techniques, the adaptive sampling strategies can be further optimized for efficient change-point detection.