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This paper considers the robust and efficient implementation of Gaussian process regression with a Student-t observation model. The challenge with the Student-t model is the analytically intractable inference which is why several…

Machine Learning · Statistics 2012-06-28 Pasi Jylänki , Jarno Vanhatalo , Aki Vehtari

Robust Bayesian analysis has been mainly devoted to detecting and measuring robustness w.r.t. the prior distribution. Many contributions in the literature aim to define suitable classes of priors which allow the computation of variations of…

Statistics Theory · Mathematics 2025-09-04 Antonio Di Noia , Fabrizio Ruggeri , Antonietta Mira

A robust estimator is proposed for the parameters that characterize the linear regression problem. It is based on the notion of shrinkages, often used in Finance and previously studied for outlier detection in multivariate data. A thorough…

Methodology · Statistics 2020-02-07 Elisa Cabana , Rosa E. Lillo , Henry Laniado

Despite their importance in supporting experimental conclusions, standard statistical tests are often inadequate for research areas, like the life sciences, where the typical sample size is small and the test assumptions difficult to…

Methodology · Statistics 2011-04-15 Pietro Berkes , Jozsef Fiser

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…

Artificial Intelligence · Computer Science 2020-09-01 Zhenyu A. Liao , Charupriya Sharma , James Cussens , Peter van Beek

Recent reports have described that learning Bayesian networks are highly sensitive to the chosen equivalent sample size (ESS) in the Bayesian Dirichlet equivalence uniform (BDeu). This sensitivity often engenders some unstable or…

Machine Learning · Computer Science 2012-02-20 Maomi Ueno

Consider a multinomial regression model where the response, which indicates a unit's membership in one of several possible unordered classes, is associated with a set of predictor variables. Such models typically involve a matrix of…

Applications · Statistics 2009-01-28 Paul Gustafson , Geneviève Lefebvre

We introduce flexible robust functional regression models, using various heavy-tailed processes, including a Student $t$-process. We propose efficient algorithms in estimating parameters for the marginal mean inferences and in predicting…

Methodology · Statistics 2017-05-17 Chunzheng Cao , Jian Qing Shi , Youngjo Lee

We show that there may exist an inherent tension between the goal of adversarial robustness and that of standard generalization. Specifically, training robust models may not only be more resource-consuming, but also lead to a reduction of…

Machine Learning · Statistics 2019-09-10 Dimitris Tsipras , Shibani Santurkar , Logan Engstrom , Alexander Turner , Aleksander Madry

We study objective Bayesian inference for linear regression models with residual errors distributed according to the class of two-piece scale mixtures of normal distributions. These models allow for capturing departures from the usual…

Applications · Statistics 2016-05-09 F. J. Rubio , K. Yu

Frequentist and Bayesian methods differ in many aspects, but share some basic optimal properties. In real-life classification and regression problems, situations exist in which a model based on one of the methods is preferable based on some…

Methodology · Statistics 2023-08-29 Tanujit Chakraborty , Gauri Kamat , Ashis Kumar Chakraborty

Student-$t$ processes have recently been proposed as an appealing alternative non-parameteric function prior. They feature enhanced flexibility and predictive variance. In this work the use of Student-$t$ processes are explored for…

Machine Learning · Statistics 2016-12-02 Joachim van der Herten , Ivo Couckuyt , Tom Dhaene

We study counterfactual regression, which aims to map input features to outcomes under hypothetical scenarios that differ from those observed in the data. This is particularly useful for decision-making when adapting to sudden shifts in…

Methodology · Statistics 2025-04-08 Kwangho Kim

We consider the on-line predictive version of the standard problem of linear regression; the goal is to predict each consecutive response given the corresponding explanatory variables and all the previous observations. The standard…

Statistics Theory · Mathematics 2009-06-18 Vladimir Vovk , Ilia Nouretdinov , Alex Gammerman

Bayesian Dark Knowledge is a method for compressing the posterior predictive distribution of a neural network model into a more compact form. Specifically, the method attempts to compress a Monte Carlo approximation to the parameter…

Machine Learning · Computer Science 2019-06-11 Meet P. Vadera , Benjamin M. Marlin

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…

Machine Learning · Statistics 2024-06-18 Tomoya Wakayama

We consider an agent who represents uncertainty about the environment via a possibly misspecified model. Each period, the agent takes an action, observes a consequence, and uses Bayes' rule to update her belief about the environment. This…

Theoretical Economics · Economics 2019-10-24 Ignacio Esponda , Demian Pouzo , Yuichi Yamamoto

Bayesian networks are basic graphical models, used widely both in statistics and artificial intelligence. These statistical models of conditional independence structure are described by acyclic directed graphs whose nodes correspond to…

Optimization and Control · Mathematics 2010-12-01 Raymond Hemmecke , Silvia Lindner , Milan Studený

A semi-parametric, non-linear regression model in the presence of latent variables is applied towards learning network graph structure. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex system of…

Machine Learning · Statistics 2018-07-03 Jonathan Mei , José M. F. Moura

Heckman selection model is the most popular econometric model in analysis of data with sample selection. However, selection models with Normal errors cannot accommodate heavy tails in the error distribution. Recently, Marchenko and Genton…

Computation · Statistics 2014-01-08 Peng Ding