Related papers: Generalised Bayes Linear Inference
Bayesian statistical inference for Generalized Linear Models (GLMs) with parameters lying on a constrained space is of general interest (e.g., in monotonic or convex regression), but often constructing valid prior distributions supported on…
We investigate the data distribution valuation problem, which aims to quantify the values of data distributions from their samples. This is a recently proposed problem that is related to but different from classical data valuation and can…
Bayesian statistics is an integral part of contemporary applied science. bayesics provides a single framework, unified in syntax and output, for performing the most commonly used statistical procedures, ranging from one- and two-sample…
Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…
Datasets are growing not just in size but in complexity, creating a demand for rich models and quantification of uncertainty. Bayesian methods are an excellent fit for this demand, but scaling Bayesian inference is a challenge. In response…
We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the…
The key distinguishing property of a Bayesian approach is marginalization instead of optimization, not the prior, or Bayes rule. Bayesian inference is especially compelling for deep neural networks. (1) Neural networks are typically…
Generalised Bayesian learning algorithms are increasingly popular in machine learning, due to their PAC generalisation properties and flexibility. The present paper aims at providing a self-contained survey on the resulting PAC-Bayes…
Geographic Information Systems (GIS) and related technologies have generated substantial interest among statisticians with regard to scalable methodologies for analyzing large spatial datasets. A variety of scalable spatial process models…
Due to the ease of modern data collection, applied statisticians often have access to a large set of covariates that they wish to relate to some observed outcome. Generalized linear models (GLMs) offer a particularly interpretable framework…
Convolutional neural networks (CNNs) provide flexible function approximations for a wide variety of applications when the input variables are in the form of images or spatial data. Although CNNs often outperform traditional statistical…
Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalisation constants requires summation over large or possibly infinite sets, which can be impractical. This paper…
The application of Bayesian methods in cosmology and astrophysics has flourished over the past decade, spurred by data sets of increasing size and complexity. In many respects, Bayesian methods have proven to be vastly superior to more…
Bayesian inference provides an attractive online-learning framework to analyze sequential data, and offers generalization guarantees which hold even with model mismatch and adversaries. Unfortunately, exact Bayesian inference is rarely…
A stream of algorithmic advances has steadily increased the popularity of the Bayesian approach as an inference paradigm, both from the theoretical and applied perspective. Even with apparent successes in numerous application fields, a…
The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…
Raking is widely used in categorical data modeling and survey practice but faced with methodological and computational challenges. We develop a Bayesian paradigm for raking by incorporating the marginal constraints as a prior distribution…
The key distinguishing property of a Bayesian approach is marginalization, rather than using a single setting of weights. Bayesian marginalization can particularly improve the accuracy and calibration of modern deep neural networks, which…
Explosive growth in data and availability of cheap computing resources have sparked increasing interest in Big learning, an emerging subfield that studies scalable machine learning algorithms, systems, and applications with Big Data.…
A fundamental question in theoretical machine learning is generalization. Over the past decades, the PAC-Bayesian approach has been established as a flexible framework to address the generalization capabilities of machine learning…