Related papers: Minimax estimation in linear models with unknown d…
Missing values arise in most real-world data sets due to the aggregation of multiple sources and intrinsically missing information (sensor failure, unanswered questions in surveys...). In fact, the very nature of missing values usually…
We consider the linear regression model with observation error in the design. In this setting, we allow the number of covariates to be much larger than the sample size. Several new estimation methods have been recently introduced for this…
Motivated by the FPTAS for connectivity interdiction of Huang et al. (IPCO'24), we isolate the part of the argument that does not use cuts. The setting is a minimization problem over a feasible-set family $\mathcal F$ with a linear…
Optimal estimation and inference for both the minimizer and minimum of a convex regression function under the white noise and nonparametric regression models are studied in a nonasymptotic local minimax framework, where the performance of a…
Structural matrix-variate observations routinely arise in diverse fields such as multi-layer network analysis and brain image clustering. While data of this type have been extensively investigated with fruitful outcomes being delivered, the…
The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…
We propose a new pivotal method for estimating high-dimensional matrices. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix $A\_0$ corrupted by noise. We propose a new method for estimating…
This paper considers the partially functional linear model (PFLM) where all predictive features consist of a functional covariate and a high dimensional scalar vector. Over an infinite dimensional reproducing kernel Hilbert space, the…
Suppose a linear model y = Hx + n, where inputs x, n are independent Gaussian mixtures. The problem is to design the transfer matrix H so as to minimize the mean square error (MSE) when estimating x from y. This problem has important…
We construct minimax optimal non-asymptotic confidence sets for low rank matrix recovery algorithms such as the Matrix Lasso or Dantzig selector. These are employed to devise adaptive sequential sampling procedures that guarantee recovery…
This work deals with the ill-posed inverse problem of reconstructing a function $f$ given implicitly as the solution of $g = Af$, where $A$ is a compact linear operator with unknown singular values and known eigenfunctions. We observe the…
We consider the estimation of quadratic functionals in a Gaussian sequence model where the eigenvalues are supposed to be unknown and accessible through noisy observations only. Imposing smoothness assumptions both on the signal and the…
High-dimensional models often have a large memory footprint and must be quantized after training before being deployed on resource-constrained edge devices for inference tasks. In this work, we develop an information-theoretic framework for…
The effect of measurement errors in discriminant analysis is investigated. Given observations $Z=X+\epsilon$, where $\epsilon$ denotes a random noise, the goal is to predict the density of $X$ among two possible candidates $f$ and $g$. We…
The problem of optimal linear estimation of linear functionals depending on the unknown values of a periodically correlated stochastic process from observations of the process with additive noise is considered. Formulas for calculating the…
We propose a general methodology for the construction and analysis of minimax estimators for a wide class of functionals of finite dimensional parameters, and elaborate on the case of discrete distributions, where the alphabet size $S$ is…
We propose a framework for sensitivity analysis of linear programs (LPs) in minimization form, allowing for simultaneous perturbations in the objective coefficients and right-hand sides, where the perturbations are modeled in a compact,…
We consider the problem of recovering a lowrank matrix M from a small number of random linear measurements. A popular and useful example of this problem is matrix completion, in which the measurements reveal the values of a subset of the…
We describe a new framework for distilling information from word lattices to improve the accuracy of speech recognition and obtain a more perspicuous representation of a set of alternative hypotheses. In the standard MAP decoding approach…
Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…