Related papers: The augmented van Trees inequality

We develop an adaptive monotone shrinkage estimator for regression models with the following characteristics: i) dense coefficients with small but important effects; ii) a priori ordering that indicates the probable predictive importance of…

Many machine learning and data science tasks require solving non-convex optimization problems. When the loss function is a sum of multiple terms, a popular method is the stochastic gradient descent. Viewed as a process for sampling the loss…

While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…

Bayesian Additive Regression Trees (BART) is a fully Bayesian approach to modeling with ensembles of trees. BART can uncover complex regression functions with high dimensional regressors in a fairly automatic way and provide Bayesian…

We consider stochastic gradient descent algorithms for minimizing a non-smooth, strongly-convex function. Several forms of this algorithm, including suffix averaging, are known to achieve the optimal $O(1/T)$ convergence rate in…

In statistical inference problems, we wish to obtain lower bounds on the minimax risk, that is to bound the performance of any possible estimator. A standard technique to obtain risk lower bounds involves the use of Fano's inequality. In an…

In the density estimation model, the question of adaptive inference using P\'olya tree-type prior distributions is considered. A class of prior densities having a tree structure, called spike-and-slab P\'olya trees, is introduced. For this…

Several recent works have explored stochastic gradient methods for variational inference that exploit the geometry of the variational-parameter space. However, the theoretical properties of these methods are not well-understood and these…

Many causal estimands, such as average treatment effects under unconfoundedness, can be written as continuous linear functionals of an unknown regression function. We study a weighting estimator that sets weights by a minimax procedure:…

We propose simultaneous mean-variance regression for the linear estimation and approximation of conditional mean functions. In the presence of heteroskedasticity of unknown form, our method accounts for varying dispersion in the regression…

Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis-specification of the likelihood. Here we consider generalised Bayesian…

We consider a linear model where the coefficients - intercept and slopes - are random with a law in a nonparametric class and independent from the regressors. Identification often requires the regressors to have a support which is the whole…

We develop new adaptive algorithms for variational inequalities with monotone operators, which capture many problems of interest, notably convex optimization and convex-concave saddle point problems. Our algorithms automatically adapt to…

We discuss the use of likelihood asymptotics for inference on risk measures in univariate extreme value problems, focusing on estimation of high quantiles and similar summaries of risk for uncertainty quantification. We study whether…

Recent studies show that transformer-based architectures emulate gradient descent during a forward pass, contributing to in-context learning capabilities - an ability where the model adapts to new tasks based on a sequence of prompt…

We develop likelihood-based bias reduction for nonlinear panel models with additive individual and time effects. In two-way panels, integrated-likelihood corrections are attractive but challenging because the required integration is high…

Bayesian shrinkage methods have generated a lot of recent interest as tools for high-dimensional regression and model selection. These methods naturally facilitate tractable uncertainty quantification and incorporation of prior information.…

A variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias…

This paper studies a Bayesian approach to non-asymptotic minimax adaptation in nonparametric estimation. Estimating an input function on the basis of output functions in a Gaussian white-noise model is discussed. The input function is…

This book chapter introduces regression approaches and regression adjustment for Approximate Bayesian Computation (ABC). Regression adjustment adjusts parameter values after rejection sampling in order to account for the imperfect match…