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This thesis responds to the challenges of using a large number, such as thousands, of features in regression and classification problems. There are two situations where such high dimensional features arise. One is when high dimensional…
We develop a Bayesian approach for selecting the model which is the most supported by the data within a class of marginal models for categorical variables formulated through equality and/or inequality constraints on generalised logits…
In cluster analysis interest lies in probabilistically capturing partitions of individuals, items or observations into groups, such that those belonging to the same group share similar attributes or relational profiles. Bayesian posterior…
We present a variation of a quantum algorithm for the machine learning task of classification with graph-structured data. The algorithm implements a feature extraction strategy that is based on Gaussian boson sampling (GBS) a near term…
We propose a general algorithmic framework for Bayesian model selection. A spike-and-slab Laplacian prior is introduced to model the underlying structural assumption. Using the notion of effective resistance, we derive an EM-type algorithm…
Clustering is a well-known and studied problem, one of its variants, called contiguity-constrained clustering, accepts as a second input a graph used to encode prior information about cluster structure by means of contiguity constraints…
A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…
Motivation: Modelling methods that find structure in data are necessary with the current large volumes of genomic data, and there have been various efforts to find subsets of genes exhibiting consistent patterns over subsets of treatments.…
Clustering is a difficult and widely-studied data mining task, with many varieties of clustering algorithms proposed in the literature. Nearly all algorithms use a similarity measure such as a distance metric (e.g. Euclidean distance) to…
Probabilistic graphical models (PGMs) are widely used to discover latent structure in data, but their success hinges on selecting an appropriate model design. In practice, model specification is difficult and often requires iterative…
Probabilistic Graphical Models (PGM) are very useful in the fields of machine learning and data mining. The crucial limitation of those models,however, is the scalability. The Bayesian Network, which is one of the most common PGMs used in…
Regression models are used for inference and prediction in a wide range of applications providing a powerful scientific tool for researchers and analysts from different fields. In many research fields the amount of available data as well as…
Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take…
Linear mixed models are widely used for analyzing hierarchically structured data involving missingness and unbalanced study designs. We consider a Bayesian clustering method that combines linear mixed models and predictive projections. For…
In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of $2$ sub-gaussian distributions. Our work is motivated by the application of clustering individuals according to their population…
Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…
Score-based Generative Models (SGMs) is one leading method in generative modeling, renowned for their ability to generate high-quality samples from complex, high-dimensional data distributions. The method enjoys empirical success and is…
This article introduces novel and practicable Bayesian factor analysis frameworks that are computationally feasible for moderate to large spatiotemporal data. Previous Bayesian analysis of spatiotemporal data has utilized a Bayesian factor…
When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…
High-dimensional feature selection is a central problem in a variety of application domains such as machine learning, image analysis, and genomics. In this paper, we propose graph-based tests as a useful basis for feature selection. We…