The best encoding is the one that is interpretable in nature. In this work, we introduce a novel model that incorporates an interpretable bottleneck-termed the Filter Bank (FB)-at the outset of a Variational Autoencoder (VAE). This arrangement compels the VAE to attend on the most informative segments of the input signal, fostering the learning of a novel encoding ${f_0}$ which boasts enhanced interpretability and clusterability over traditional latent spaces. By deliberately constraining the VAE with this FB, we intentionally constrict its capacity to access broad input domain information, promoting the development of an encoding that is discernible, separable, and of reduced dimensionality. The evolutionary learning trajectory of ${f_0}$ further manifests as a dynamic hierarchical tree, offering profound insights into cluster similarities. Additionally, for handling intricate data configurations, we propose a tailored decoder structure that is symmetrically aligned with FB's architecture. Empirical evaluations highlight the superior efficacy of ISVAE, which compares favorably to state-of-the-art results in clustering metrics across real-world datasets.

Change-point detection (CPD) aims to locate abrupt transitions in the generative model of a sequence of observations. When Bayesian methods are considered, the standard practice is to infer the posterior distribution of the change-point locations. However, for complex models (high-dimensional or heterogeneous), it is not possible to perform reliable detection. To circumvent this problem, we propose to use a hierarchical model, which yields observations that belong to a lower-dimensional manifold. Concretely, we consider a latent-class model with an unbounded number of categories, which is based on the chinese-restaurant process (CRP). For this model we derive a continual learning mechanism that is based on the sequential construction of the CRP and the expectation-maximization (EM) algorithm with a stochastic maximization step. Our results show that the proposed method is able to recursively infer the number of underlying latent classes and perform CPD in a reliable manner.

This paper addresses the problem of change-point detection on sequences of high-dimensional and heterogeneous observations, which also possess a periodic temporal structure. Due to the dimensionality problem, when the time between change-points is on the order of the dimension of the model parameters, drifts in the underlying distribution can be misidentified as changes. To overcome this limitation we assume that the observations lie in a lower dimensional manifold that admits a latent variable representation. In particular, we propose a hierarchical model that is computationally feasible, widely applicable to heterogeneous data and robust to missing instances. Additionally, to deal with the observations' periodic dependencies, we employ a circadian model where the data periodicity is captured by non-stationary covariance functions. We validate the proposed technique on synthetic examples and we demonstrate its utility in the detection of changes for human behavior characterization.

Statistical shape models enhance machine learning algorithms providing prior information about deformation. A Point Distribution Model (PDM) is a popular landmark-based statistical shape model for segmentation. It requires choosing a model order, which determines how much of the variation seen in the training data is accounted for by the PDM. A good choice of the model order depends on the number of training samples and the noise level in the training data set. Yet the most common approach for choosing the model order simply keeps a predetermined percentage of the total shape variation. In this paper, we present a technique for choosing the model order based on information-theoretic criteria, and we show empirical evidence that the model order chosen by this technique provides a good trade-off between over- and underfitting.