Change Point Detection based on Time-invariant Modeling of Time Series

Time series data, comprising sequential measurements of one or more variables over time, offer significant insights into the dynamics of generative systems when segmented based on statistical properties. Change Point Detection (CPD) refers to identifying abrupt changes in statistics within these sequences, which often indicate transitions between different underlying states. Given CPD's crucial role as a pre-processing step in various applications, numerous algorithms have been developed over the past several decades. However, many existing algorithms are tailored to specific datasets and typically require pre-knowledge related to the applications. Even when methods claim broad applicability, their simple assumptions-such as tracking changes solely through the similarity of coefficients of a pre-defined generative model-often limit their detection accuracy and practical adoption. This thesis aims to address these challenges by proposing generic unsupervised algorithms for CPD that can be effectively applied across diverse applications. Our approach begins with an autoencoder-based CPD model known as time-invariant representation (TIRE). While TIRE has demonstrated superior performance compared to many state-of-the-art CPD methods, several limitations need addressing: 1) the proposed time-invariant loss does not effectively prevent the leakage of information between time-invariant and time-variant features, resulting in reduced detection accuracy; 2) the presence of numerous tunable hyperparameters complicates its practical utilization; and 3) the original TIRE model was designed for low-dimensional time series data, making it unsuitable for multi-channel data. To overcome these issues, we propose a new loss function, termed ``diamond loss" to replace the combination of reconstruction loss and time-invariant loss. This new loss function imposes constraints on time-invariant and time-variant features, enhancing their separation and eliminating the need for a trade-off hyperparameter between the two loss terms. Additionally, we develop a multi-view TIRE structure that can automatically preserve CPD-related information from either the time domain, frequency domain, or both, within the time-invariant features without requiring domain-specific knowledge or compromising detection accuracy. Furthermore, we design a new multi-channel TIRE model that explicitly incorporates cross-channel information, making it more suitable for multi-channel time series datasets. In