Related papers: Robust extrapolation problem for stochastic sequen…
This paper addresses the problem of estimating the Hurst exponent of the fractional Brownian motion from continuous time noisy sample. Consistent estimation in the setup under consideration is possible only if either the length of the…
We consider the problem of estimating functionals of discrete distributions, and focus on tight nonasymptotic analysis of the worst case squared error risk of widely used estimators. We apply concentration inequalities to analyze the random…
While extensive work has been done to correct for biases due to measurement error in scalar-valued covariates prone to errors in generalized linear regression models, limited work has been done to address biases associated with functional…
We introduce computational methods that allow for effective estimation of a flexible, parametric non-stationary spatial model when the field size is too large to compute the multivariate normal likelihood directly. In this method, the field…
Linear fixed point equations in Hilbert spaces arise in a variety of settings, including reinforcement learning, and computational methods for solving differential and integral equations. We study methods that use a collection of random…
We propose a time-implicit, finite-element based space-time discretization of the necessary and sufficient optimality conditions for the stochastic linear-quadratic optimal control problem with the stochastic heat equation driven by linear…
We consider the problem of estimating the slope parameter in functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of second order stationary random functions X1,...,Xn. An orthogonal series estimator of…
We explore the connection between outlier-robust high-dimensional statistics and non-convex optimization in the presence of sparsity constraints, with a focus on the fundamental tasks of robust sparse mean estimation and robust sparse PCA.…
We present a stochastic setting for optimization problems with nonsmooth convex separable objective functions over linear equality constraints. To solve such problems, we propose a stochastic Alternating Direction Method of Multipliers…
Stationary reciprocal processes defined on a finite interval of the integer line can be seen as a special class of Markov random fields restricted to one dimension. Non stationary reciprocal processes have been extensively studied in the…
This article improves on existing methods to estimate the spectral density of stationary and nonstationary time series assuming a Gaussian process prior. By optimising an appropriate eigendecomposition using a smoothing spline covariance…
Based on the tools of limiting variational analysis, we derive a sequential necessary optimality condition for nonsmooth mathematical programs which holds without any additional assumptions. In order to ensure that stationary points in this…
An important estimation problem that is closely related to large-scale multiple testing is that of estimating the null density and the proportion of nonnull effects. A few estimators have been introduced in the literature; however, several…
The problem of non-monotone $k$-submodular maximization under a knapsack constraint ($\kSMK$) over the ground set size $n$ has been raised in many applications in machine learning, such as data summarization, information propagation, etc.…
We consider the estimation of the slope function in functional linear regression, where scalar responses are modeled in dependence of random functions. Cardot and Johannes [J. Multivariate Anal. 101 (2010) 395-408] have shown that a…
The most common way of estimating the anomalous diffusion exponent from single-particle trajectories consists in a linear fitting of the dependence of the time averaged mean square displacement on the lag time at the log-log scale. However,…
Functional constrained optimization is becoming more and more important in machine learning and operations research. Such problems have potential applications in risk-averse machine learning, semisupervised learning, and robust optimization…
We consider the model $Z_i=X_i+\varepsilon_i$, for i.i.d. $X_i$'s and $\varepsilon_i$'s and independent sequences $(X_i)_{i\in{\mathbb{N}}}$ and $(\varepsilon_i)_{i\in{\mathbb{N}}}$. The density $f_{\varepsilon}$ of $\varepsilon_1$ is…
We investigate the asymptotic properties of a finite-time horizon linear-quadratic optimal control problem driven by a multiscale stochastic process with multiplicative Brownian noise. We approach the problem by considering the associated…
Semi-functional linear regression models postulate a linear relationship between a scalar response and a functional covariate, and also include a non-parametric component involving a univariate explanatory variable. It is of practical…