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Finite mixture models are statistical models which appear in many problems in statistics and machine learning. In such models it is assumed that data are drawn from random probability measures, called mixture components, which are…

In the second paper of this series we extend our Bayesian reanalysis of the evidence for a cosmic variation of the fine structure constant to the semi-parametric modelling regime. By adopting a mixture of Dirichlet processes prior for the…

We construct a new class of infinite-dimensional diffusions taking values in a generalized Kingman simplex. Our model describes the temporal evolution of the relative frequencies of infinitely-many types which are "labeled" by an arbitrary…

Within a Bayesian framework, a comprehensive investigation of mixtures of finite mixtures (MFMs), i.e., finite mixtures with a prior on the number of components, is performed. This model class has applications in model-based clustering as…

In many real-world applications, data is not collected as one batch, but sequentially over time, and often it is not possible or desirable to wait until the data is completely gathered before analyzing it. Thus, we propose a framework to…

Scientific studies in many areas of biology routinely employ evolutionary analyses based on the probabilistic inference of phylogenetic trees from molecular sequence data. Evolutionary processes that act at the molecular level are highly…

Image segmentation is a fundamental step for the interpretation of Remote Sensing Images. Clustering or segmentation methods usually precede the classification task and are used as support tools for manual labeling. The most common…

Although discrete mixture modeling has formed the backbone of the literature on Bayesian density estimation, there are some well known disadvantages. We propose an alternative class of priors based on random nonlinear functions of a uniform…

We characterise the unbiasedness of the score function, viewed as an inference function for a class of finite mixture models. The models studied represent the situation where there is a stratification of the observations in a finite number…

We propose an approach to learn image representations that consist of disentangled factors of variation without exploiting any manual labeling or data domain knowledge. A factor of variation corresponds to an image attribute that can be…

We propose and develop a novel and effective perfect sampling methodology for simulating from posteriors corresponding to mixtures with either known (fixed) or unknown number of components. For the latter we consider the Dirichlet…

Score-based diffusion models have demonstrated outstanding empirical performance in machine learning and artificial intelligence, particularly in generating high-quality new samples from complex probability distributions. Improving the…

The goal of fair clustering is to find clusters such that the proportion of sensitive attributes (e.g., gender, race, etc.) in each cluster is similar to that of the entire dataset. Various fair clustering algorithms have been proposed that…

In social science research, understanding latent structures in populations through survey data with categorical responses is a common and important task. Traditional methods like Factor Analysis and Latent Class Analysis have limitations,…

We propose a method based on finite mixture models for classifying a set of observations into number of different categories. In order to demonstrate the method, we show how the component densities for the mixture model can be derived by…

Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the algorithm fails to account for any uncertainty in…

Precise estimation of uncertainty in predictions for AI systems is a critical factor in ensuring trust and safety. Deep neural networks trained with a conventional method are prone to over-confident predictions. In contrast to Bayesian…

Recognition of objects with subtle differences has been used in many practical applications, such as car model recognition and maritime vessel identification. For discrimination of the objects in fine-grained detail, we focus on deep…

We propose a general approach to handle data contaminations that might disrupt the performance of feature selection and estimation procedures for high-dimensional linear models. Specifically, we consider the co-occurrence of mean-shift and…

Class-Incremental Learning is a challenging problem in machine learning that aims to extend previously trained neural networks with new classes. This is especially useful if the system is able to classify new objects despite the original…