Theoretical properties of Bayesian Student-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e420" altimg="si2.svg"><mml:mi>t</mml:mi></mml:math> linear regression

Bayesian linear regression with Student-t assumptions

As an automatic method of determining model complexity using the training data alone, Bayesian linear regression provides us a principled way to select hyperparameters. But one often needs approximation inference if distribution assumption is beyond Gaussian distribution. In this paper, we propose a Bayesian linear regression model with Student-t assumptions (BLRS), which can be inferred exactl...

Bayesian Model Averaging for Linear Regression Models

We consider the problem of accounting for model uncertainty in linear regression models. Conditioning on a single selected model ignores model uncertainty, and thus leads to the underestimation of uncertainty when making inferences about quantities of interest. A Bayesian solution to this problem involves averaging over all possible models (i.e., combinations of predictors) when making inferenc...

Robust linear regression through PAC-Bayesian truncation

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Bayesian regression with multivariate linear splines

Linear regression through PAC-Bayesian truncation

ABSTRACT : We consider the problem of predicting as well as the best linear combination of d given functions in least squares regression under L∞ constraints on the linear combination. When the input distribution is known, there already exists an algorithm having an expected excess risk of order d/n, where n is the size of the training data. Without this strong assumption, standard results ofte...