Related papers: Bayesian variable selection for high dimensional g…
Cross-validation (CV) methods are popular for selecting the tuning parameter in the high-dimensional variable selection problem. We show the mis-alignment of the CV is one possible reason of its over-selection behavior. To fix this issue,…
We demonstrate a measure for the effective number of parameters constrained by a posterior distribution in the context of cosmology. In the same way that the mean of the Shannon information (i.e. the Kullback-Leibler divergence) provides a…
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…
We take a Bayesian perspective to illustrate a connection between training speed and the marginal likelihood in linear models. This provides two major insights: first, that a measure of a model's training speed can be used to estimate its…
Due to its linear complexity, naive Bayes classification remains an attractive supervised learning method, especially in very large-scale settings. We propose a sparse version of naive Bayes, which can be used for feature selection. This…
Shape restriction, like monotonicity or convexity, imposed on a function of interest, such as a regression or density function, allows for its estimation without smoothness assumptions. The concept of $k$-monotonicity encompasses a family…
The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…
We consider sparse Bayesian estimation in the classical multivariate linear regression model with $p$ regressors and $q$ response variables. In univariate Bayesian linear regression with a single response $y$, shrinkage priors which can be…
We discuss Bayesian model uncertainty analysis and forecasting in sequential dynamic modeling of multivariate time series. The perspective is that of a decision-maker with a specific forecasting objective that guides thinking about relevant…
Determining how to appropriately select the tuning parameter is essential in penalized likelihood methods for high-dimensional data analysis. We examine this problem in the setting of penalized likelihood methods for generalized linear…
Bayesian model selection methods provide a self-consistent probabilistic framework to test the validity of competing scenarios given a set of data. We present a case study application to strong gravitational lens parametric models. Our goal…
Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it is…
Motivation: Gene selection has become a common task in most gene expression studies. The objective of such research is often to identify the smallest possible set of genes that can still achieve good predictive performance. The problem of…
This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection…
We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…
Motivated by big data and the vast parameter spaces in modern machine learning models, optimisation approaches to Bayesian inference have seen a surge in popularity in recent years. In this paper, we address the connection between the…
Current causal discovery approaches require restrictive model assumptions in the absence of interventional data to ensure structure identifiability. These assumptions often do not hold in real-world applications leading to a loss of…
We develop a model-based empirical Bayes approach to variable selection problems in which the number of predictors is very large, possibly much larger than the number of responses (the so-called 'large p, small n' problem). We consider the…
Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…
Estimating some mathematical expectations from partially observed data and in particular missing outcomes is a central problem encountered in numerous fields such as transfer learning, counterfactual analysis or causal inference. Matching…