Related papers: Piecewise Convex Function Estimation and Model Sel…
We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced…
In this paper an iterated function system on the space of distribution functions is built. The inverse problem is introduced and studied by convex optimization problems. Some applications of this method to approximation of distribution…
We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior…
Random and structured noise both affect seismic data, hiding the reflections of interest (primaries) that carry meaningful geophysical interpretation. When the structured noise is composed of multiple reflections, its adaptive cancellation…
Auxiliary information is increasingly available from administrative and other data sources, but it is often incomplete and of non-probability origin. We propose a two-step small area estimation approach in which the first step relies on…
We study the problem of selecting limited features to observe such that models trained on them can perform well simultaneously across multiple subpopulations. This problem has applications in settings where collecting each feature is…
We give a statement on extension with estimates of convex functions defined on a linear subspace, inspired by similar extension results concerning metrics on positive line bundles
We study the problem of estimating the value of a known smooth function $f$ at an unknown point $\boldsymbol{\mu} \in \mathbb{R}^n$, where each component $\mu_i$ can be sampled via a noisy oracle. Sampling more frequently components of…
Suppose that we wish to estimate a finite-dimensional summary of one or more function-valued features of an underlying data-generating mechanism under a nonparametric model. One approach to estimation is by plugging in flexible estimates of…
This paper studies the numerical solution of strictly convex unconstrained optimization problems by linesearch Newton-CG methods. We focus on methods employing inexact evaluations of the objective function and inexact and possibly random…
Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…
Demixing is the problem of identifying multiple structured signals from a superimposed, undersampled, and noisy observation. This work analyzes a general framework, based on convex optimization, for solving demixing problems. When the…
This work studies the computational aspects of multivariate convex regression in dimensions $d \ge 5$. Our results include the \emph{first} estimators that are minimax optimal (up to logarithmic factors) with polynomial runtime in the…
A popular class of problem in statistics deals with estimating the support of a density from $n$ observations drawn at random from a $d$-dimensional distribution. The one-dimensional case reduces to estimating the end points of a univariate…
Reasoning about uncertainty is vital in many real-life autonomous systems. However, current state-of-the-art planning algorithms cannot either reason about uncertainty explicitly, or do so with a high computational burden. Here, we focus on…
We consider the problem of estimating fold-changes in the expected value of a multivariate outcome observed with unknown sample-specific and category-specific perturbations. This challenge arises in high-throughput sequencing studies of the…
This paper proposes a new estimation procedure for the ambiguity function of a non-stationary time series. The stochastic properties of the empirical ambiguity function calculated from a single sample in time are derived. Different…
Given a random sample of points from some unknown distribution, we propose a new data-driven method for estimating its probability support $S$. Under the mild assumption that $S$ is $r$-convex, the smallest $r$-convex set which contains the…
Consider the estimation of an unknown parameter vector in a linear measurement model. Centralized sensor selection consists in selecting a set of k_s sensor measurements, from a total number of m potential measurements. The performance of…
In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault…