Related papers: Bayesian nonparametric multivariate convex regress…
Nonconvex optimization is central to modern machine learning, but the general framework of nonconvex optimization yields weak convergence guarantees that are too pessimistic compared to practice. On the other hand, while convexity enables…
We study the problem of estimating a multivariate convex function defined on a convex body in a regression setting with random design. We are interested in optimal rates of convergence under a squared global continuous $l_2$ loss in the…
We propose a computationally efficient Learning Model Predictive Control (LMPC) scheme for constrained optimal control of a class of nonlinear systems where the state and input can be reconstructed using lifted outputs. For the considered…
Tensor-valued data are being encountered increasingly more commonly, in the biological, natural as well as the social sciences. The learning of the unknown model parameter vector given such data, involves covariance modelling of such data,…
In the Bayesian approach to inverse problems, data are often informative, relative to the prior, only on a low-dimensional subspace of the parameter space. Significant computational savings can be achieved by using this subspace to…
Planning under process and measurement uncertainties is a challenging problem. In its most general form it can be modeled as a Partially Observed Markov Decision Process (POMDP) problem. However POMDPs are generally difficult to solve when…
Statistical inverse learning aims at recovering an unknown function $f$ from randomly scattered and possibly noisy point evaluations of another function $g$, connected to $f$ via an ill-posed mathematical model. In this paper we blend…
We study full Bayesian procedures for high-dimensional linear regression. We adopt data-dependent empirical priors introduced in [1]. In their paper, these priors have nice posterior contraction properties and are easy to compute. Our paper…
We introduce a novel uncertainty estimation for classification tasks for Bayesian convolutional neural networks with variational inference. By normalizing the output of a Softplus function in the final layer, we estimate aleatoric and…
We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…
We propose a Machine Learning approach for optimal macroeconomic density forecasting in a high-dimensional setting where the underlying model exhibits a known group structure. Our approach is general enough to encompass specific forecasting…
Change-plane regression identifies subpopulations through an interpretable linear threshold rule, but likelihood-based inference for the hard-threshold boundary is nonregular: objectives are non-smooth, the boundary is weakly identified…
Bayesian optimization has proven to be a highly effective methodology for the global optimization of unknown, expensive and multimodal functions. The ability to accurately model distributions over functions is critical to the effectiveness…
In this paper, we investigate the matrix estimation problem in the multi-response regression model with measurement errors. A nonconvex error-corrected estimator based on a combination of the amended loss function and the nuclear norm…
We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…
Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…
We consider the problem of estimating the unknown response function in the Gaussian white noise model. We first utilize the recently developed Bayesian maximum a posteriori "testimation" procedure of Abramovich et al. (2007) for recovering…
We investigate high-dimensional nonconvex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property…
In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general H\"{o}lder class and estimate it via a nonparametric local polynomial approach that consists of…
Hierarchical learning models, such as mixture models and Bayesian networks, are widely employed for unsupervised learning tasks, such as clustering analysis. They consist of observable and hidden variables, which represent the given data…