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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…

We discuss Bayesian inference for parameters selected using the data. First, we provide a critical analysis of the existing positions in the literature regarding the correct Bayesian approach under selection. Second, we propose two types of…

The behavior of many Bayesian models used in machine learning critically depends on the choice of prior distributions, controlled by some hyperparameters that are typically selected by Bayesian optimization or cross-validation. This…

We use the language of uninformative Bayesian prior choice to study the selection of appropriately simple effective models. We advocate for the prior which maximizes the mutual information between parameters and predictions, learning as…

Empirical Bayes (EB) improves the accuracy of simultaneous inference "by learning from the experience of others" (Efron, 2012). Classical EB theory focuses on latent variables that are iid draws from a fitted prior (Efron, 2019). Modern…

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

Predictive uncertainty quantification is crucial for reliable decision-making in various applied domains. Bayesian neural networks offer a powerful framework for this task. However, defining meaningful priors and ensuring computational…

The application of Bayesian inference for the purpose of model selection is very popular nowadays. In this framework, models are compared through their marginal likelihoods, or their quotients, called Bayes factors. However, marginal…

For a natural exponential family (NEF), one can associate in a natural way two standard families of conjugate priors, one on the natural parameter and the other on the mean parameter. These families of conjugate priors have been used to…

In this article, we present the elitist particle filter based on evolutionary strategies (EPFES) as an efficient approach for nonlinear system identification. The EPFES is derived from the frequently-employed state-space model, where the…

A wide range of machine learning algorithms iteratively add data to the training sample. Examples include semi-supervised learning, active learning, multi-armed bandits, and Bayesian optimization. We embed this kind of data addition into…

We present a new method for counterfactual explanations (CFEs) based on Bayesian optimisation that applies to both classification and regression models. Our method is a globally convergent search algorithm with support for arbitrary…

In this work we apply the methodology of integral priors to handle Bayesian model selection in binomial regression models with a general link function. These models are very often used to investigate associations and risks in…

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…

Purpose: Machine learning is broadly used for clinical data analysis. Before training a model, a machine learning algorithm must be selected. Also, the values of one or more model parameters termed hyper-parameters must be set. Selecting…

We have developed a frequentist approach for model selection which determines the consistency between any cosmological model and the data using the distribution of likelihoods from the iterative smoothing method. Using this approach, we…

We provide a flexible framework for selecting among a class of additive partial linear models that allows both linear and nonlinear additive components. In practice, it is challenging to determine which additive components should be…

Motivated by examples from genetic association studies, this paper considers the model selection problem in a general complex linear model system and in a Bayesian framework. We discuss formulating model selection problems and incorporating…

Model selection aims to identify a sufficiently well performing model that is possibly simpler than the most complex model among a pool of candidates. However, the decision-making process itself can inadvertently introduce non-negligible…

We propose a new method for conducting Bayesian prediction that delivers accurate predictions without correctly specifying the unknown true data generating process. A prior is defined over a class of plausible predictive models. After…