Related papers: ML(n)BiCGStab: Reformulation, Analysis and Impleme…

Krylov subspace recycling is a process for accelerating the convergence of sequences of linear systems. Based on this technique, the recycling BiCG algorithm has been developed recently. Here, we now generalize and extend this recycling…

Computing the marginal likelihood (ML) of a model requires marginalizing out all of the parameters and latent variables, a difficult high-dimensional summation or integration problem. To make matters worse, it is often hard to measure the…

Combinatorial optimisation problems framed as mixed integer linear programmes (MILPs) are ubiquitous across a range of real-world applications. The canonical branch-and-bound algorithm seeks to exactly solve MILPs by constructing a search…

A well known identifiability issue in factor analytic models is the invariance with respect to orthogonal transformations. This problem burdens the inference under a Bayesian setup, where Markov chain Monte Carlo (MCMC) methods are used to…

We tackle the problem of multiscale regression for predictors that are spatially or temporally indexed, or with a pre-specified multiscale structure, with a Bayesian modular approach. The regression function at the finest scale is expressed…

We present a reformulation of the regression and classification, which aims to validate the result of a machine learning algorithm. Our reformulation simplifies the original problem and validates the result of the machine learning algorithm…

Mesh-free numerical methods offer flexibility in discretising complex geometries, showing potential where mesh-based methods struggle. While high-order approximations can be obtained via consistency correction using linear systems, they…

Bayesian inference of Gibbs random fields (GRFs) is often referred to as a doubly intractable problem, since the likelihood function is intractable. The exploration of the posterior distribution of such models is typically carried out with…

Bayesian model comparison (BMC) offers a principled approach for assessing the relative merits of competing computational models and propagating uncertainty into model selection decisions. However, BMC is often intractable for the popular…

LIBS2ML is a library based on scalable second order learning algorithms for solving large-scale problems, i.e., big data problems in machine learning. LIBS2ML has been developed using MEX files, i.e., C++ with MATLAB/Octave interface to…

A common assumption in machine learning is that samples are independently and identically distributed (i.i.d). However, the contributions of different samples are not identical in training. Some samples are difficult to learn and some…

In this work we introduce a comprehensive algorithmic pipeline for multiple parametric model estimation. The proposed approach analyzes the information produced by a random sampling algorithm (e.g., RANSAC) from a machine…

This article considers Bayesian model inference on binary model spaces. Binary model spaces are used by a large class of models, including graphical models, variable selection, mixture distributions, and decision trees. Traditional…

Motivation: In recent years, the availability of multi-omics data has increased substantially. Multi-omics data integration methods mainly aim to leverage different molecular layers to gain a complete molecular description of biological…

It involves the completely novel ways of integrating ML algorithms with traditional statistical modelling that has changed the way we analyze data, do predictive analytics or make decisions in the fields of the data. In this paper, we study…

We propose two approaches for selecting variables in latent class analysis (i.e.,mixture model assuming within component independence), which is the common model-based clustering method for mixed data. The first approach consists in…

Estimating nonlinear functionals of probability distributions from samples is a fundamental statistical problem. The "plug-in" estimator obtained by applying the target functional to the empirical distribution of samples is biased.…

Multilevel models (MLMs) are a central building block of the Bayesian workflow. They enable joint, interpretable modeling of data across hierarchical levels and provide a fully probabilistic quantification of uncertainty. Despite their…

Most modern supervised statistical/machine learning (ML) methods are explicitly designed to solve prediction problems very well. Achieving this goal does not imply that these methods automatically deliver good estimators of causal…

Restricted Boltzmann Machines (RBM) are bi-layer neural networks used for the unsupervised learning of model distributions from data. The bipartite architecture of RBM naturally defines an elegant sampling procedure, called Alternating…