Related papers: Bayesian data selection
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…
Subset selection is a valuable tool for interpretable learning, scientific discovery, and data compression. However, classical subset selection is often avoided due to selection instability, lack of regularization, and difficulties with…
This work develops rigorous theoretical basis for the fact that deep Bayesian neural network (BNN) is an effective tool for high-dimensional variable selection with rigorous uncertainty quantification. We develop new Bayesian non-parametric…
Misleading or unnecessary data can have out-sized impacts on the health or accuracy of Machine Learning (ML) models. We present a Bayesian sequential selection method, akin to Bayesian experimental design, that identifies critically…
Bayesian model selection provides a formal method of determining the level of support for new parameters in a model. However, if there is not a specific enough underlying physical motivation for the new parameters it can be hard to assign…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…
Bayesian variable selection has gained much empirical success recently in a variety of applications when the number $K$ of explanatory variables $(x_1,...,x_K)$ is possibly much larger than the sample size $n$. For generalized linear…
Model selection is crucial to high-dimensional learning and inference for contemporary big data applications in pinpointing the best set of covariates among a sequence of candidate interpretable models. Most existing work assumes implicitly…
Feature selection is a critical step in the analysis of high-dimensional data, where the number of features often vastly exceeds the number of samples. Effective feature selection not only improves model performance and interpretability but…
For linear models with a diverging number of parameters, it has recently been shown that modified versions of Bayesian information criterion (BIC) can identify the true model consistently. However, in many cases there is little…
We propose a scalable algorithmic framework for exact Bayesian variable selection and model averaging in linear models under the assumption that the Gram matrix is block-diagonal, and as a heuristic for exploring the model space for general…
A data-driven block thresholding procedure for wavelet regression is proposed and its theoretical and numerical properties are investigated. The procedure empirically chooses the block size and threshold level at each resolution level by…
Bayesian optimal experimental design has immense potential to inform the collection of data so as to subsequently enhance our understanding of a variety of processes. However, a major impediment is the difficulty in evaluating optimal…
Optimum parameter estimation methods require knowledge of a parametric probability density that statistically describes the available observations. In this work we examine Bayesian and non-Bayesian parameter estimation problems under a…
We discuss a Bayesian model selection approach to high dimensional data in the deep under sampling regime. The data is based on a representation of the possible discrete states $s$, as defined by the observer, and it consists of $M$…
Boosting methods are widely used in statistical learning to deal with high-dimensional data due to their variable selection feature. However, those methods lack straightforward ways to construct estimators for the precision of the…
Data subset selection aims to find a smaller yet informative subset of a large dataset that can approximate the full-dataset training, addressing challenges associated with training neural networks on large-scale datasets. However, existing…
The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general…
We present a Bayesian model selection approach to estimate the intrinsic dimensionality of a high-dimensional dataset. To this end, we introduce a novel formulation of the probabilisitic principal component analysis model based on a…
A density estimation method in a Bayesian nonparametric framework is presented when recorded data are not coming directly from the distribution of interest, but from a length biased version. From a Bayesian perspective, efforts to…