Related papers: Linear Models are Most Favorable among Generalized…

We study Bayesian group-regularized estimation in high-dimensional generalized linear models (GLMs) under a continuous spike-and-slab prior. Our framework covers both canonical and non-canonical link functions and subsumes logistic,…

The Bayes linear estimator is derived by minimizing the Bayes risk with respect to the squared loss function. Non-unbiased estimators such as ordinary ridge, typical shrinkage, fractional rank, and restricted least squares estimators, as…

The paper considers model selection in regression under the additional structural constraints on admissible models where the number of potential predictors might be even larger than the available sample size. We develop a Bayesian formalism…

We study the implicit regularization of optimization methods for linear models interpolating the training data in the under-parametrized and over-parametrized regimes. Since it is difficult to determine whether an optimizer converges to…

Linear Autoencoders (LAEs) have shown strong performance in state-of-the-art recommender systems. However, this success remains largely empirical, with limited theoretical understanding. In this paper, we investigate the generalizability --…

Canonical correlation analysis is a widely used multivariate statistical technique for exploring the relation between two sets of variables. This paper considers the problem of estimating the leading canonical correlation directions in…

General log-linear models specified by non-negative integer design matrices have a potentially wide range of applications, although using models without the genuine overall effect, that is, ones which cannot be reparameterized to include a…

We consider learning methods based on the regularization of a convex empirical risk by a squared Hilbertian norm, a setting that includes linear predictors and non-linear predictors through positive-definite kernels. In order to go beyond…

We study the sample complexity of the best-case Empirical Risk Minimizer in the setting of stochastic convex optimization. We show that there exists an instance in which the sample size is linear in the dimension, learning is possible, but…

We propose a class of transformation hazard models for right-censored failure time data. It includes the proportional hazards model (Cox) and the additive hazards model (Lin and Ying) as special cases. Due to the requirement of a…

For normal canonical models, and more generally a vast array of general spherically symmetric location-scale models with a residual vector, we consider estimating the (univariate) location parameter when it is lower bounded. We provide…

We exhibit a strong link between frequentist PAC-Bayesian risk bounds and the Bayesian marginal likelihood. That is, for the negative log-likelihood loss function, we show that the minimization of PAC-Bayesian generalization risk bounds…

In the last few decades both the volume of high-quality observing data on variable stars and common access to them have boomed; however the standard used methods of data processing and interpretation have lagged behind this progress. The…

Generalized linear models (GLMs) form one of the most popular classes of models in statistics. The gamma variant is used, for instance, in actuarial science for the modelling of claim amounts in insurance. A flaw of GLMs is that they are…

Modern machine learning usually involves predictors in the overparameterised setting (number of trained parameters greater than dataset size), and their training yields not only good performance on training data, but also good…

Gaussian processes retain the linear model either as a special case, or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However from the perspective of the Bayesian posterior, the…

We propose a unified framework for likelihood-based regression modeling when the response variable has finite support. Our work is motivated by the fact that, in practice, observed data are discrete and bounded. The proposed methods assume…

We generalize the notion of minimax convergence rate. In contrast to the standard definition, we do not assume that the sample size is fixed in advance. Allowing for varying sample size results in time-robust minimax rates and estimators.…

We extend the notion of minimax fairness in supervised learning problems to its natural conclusion: lexicographic minimax fairness (or lexifairness for short). Informally, given a collection of demographic groups of interest, minimax…

We consider a general class of non-linear Bellman equations. These open up a design space of algorithms that have interesting properties, which has two potential advantages. First, we can perhaps better model natural phenomena. For…