Detecting Hierarchical Changes in Latent Variable Models
This work provides a method for interpreting the causes of changes in latent variable models, which is important for researchers and practitioners working with dynamic data streams.
This paper proposes an information-theoretic framework to detect hierarchical changes in latent variable models from data streams, specifically addressing changes in data distribution, latent variable distribution, and the number of latent variables. The framework utilizes MDL change statistics and DNML code-length calculation to identify the level of change, demonstrating effectiveness in change interpretability and detection on stochastic block models.
This paper addresses the issue of detecting hierarchical changes in latent variable models (HCDL) from data streams. There are three different levels of changes for latent variable models: 1) the first level is the change in data distribution for fixed latent variables, 2) the second one is that in the distribution over latent variables, and 3) the third one is that in the number of latent variables. It is important to detect these changes because we can analyze the causes of changes by identifying which level a change comes from (change interpretability). This paper proposes an information-theoretic framework for detecting changes of the three levels in a hierarchical way. The key idea to realize it is to employ the MDL (minimum description length) change statistics for measuring the degree of change, in combination with DNML (decomposed normalized maximum likelihood) code-length calculation. We give a theoretical basis for making reliable alarms for changes. Focusing on stochastic block models, we employ synthetic and benchmark datasets to empirically demonstrate the effectiveness of our framework in terms of change interpretability as well as change detection.