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The paper considers nonparametric kernel density/regression estimation from a stochastic optimization point of view. The estimation problem is represented through a family of stochastic optimization problems. Recursive constrained…
We consider the problem of fitting variational posterior approximations using stochastic optimization methods. The performance of these approximations depends on (1) how well the variational family matches the true posterior…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…
We study the problem of learning robust acoustic models in adverse environments, characterized by a significant mismatch between training and test conditions. This problem is of paramount importance for the deployment of speech recognition…
In this paper, we address a robust nonlinear state estimation problem under model uncertainty by formulating a dynamic minimax game: one player designs the robust estimator, while the other selects the least favorable model from an…
We address the problem of adaptive minimax estimation in white gaussian noise model under $L_p$--loss, $1\leq p\leq\infty,$ on the anisotropic Nikolskii classes. We present the estimation procedure based on a new data-driven selection…
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…
This work is devoted to convergence analysis of an exponential integrator scheme for semi-discretization in time of nonlinear stochastic wave equation. A unified framework is first set forth, which covers important cases of additive and…
This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…
A robust estimator for a wide family of mixtures of linear regression is presented. Robustness is based on the joint adoption of the Cluster Weighted Model and of an estimator based on trimming and restrictions. The selected model provides…
In the setting of additive regression model for continuous time process, we establish the optimal uniform convergence rates and optimal asymptotic quadratic error of additive regression. To build our estimate, we use the marginal…
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start…
We propose a method for learning linear models whose predictive performance is robust to causal interventions on unobserved variables, when noisy proxies of those variables are available. Our approach takes the form of a regularization term…
In the context of linear regression, we construct a data-driven convex loss function with respect to which empirical risk minimisation yields optimal asymptotic variance in the downstream estimation of the regression coefficients. At the…
We observe n possibly dependent random variables, the distribution of which is presumed to be stationary even though this might not be true, and we aim at estimating the stationary distribution. We establish a non-asymptotic deviation bound…
We consider a longitudinal data structure consisting of baseline covariates, time-varying treatment variables, intermediate time-dependent covariates, and a possibly time dependent outcome. Previous studies have shown that estimating the…
This paper considers the robust phase retrieval problem, which can be cast as a nonsmooth and nonconvex optimization problem. We propose a new inexact proximal linear algorithm with the subproblem being solved inexactly. Our contributions…
This paper discusses a general framework for designing robust state estimators for a class of discrete-time nonlinear systems. We consider systems that may be impacted by impulsive (sparse but otherwise arbitrary) measurement noise…
Cost-sensitive learning is a common type of machine learning problem where different errors of prediction incur different costs. In this paper, we design a generic nonparametric active learning algorithm for cost-sensitive classification.…