Related papers: Near Minimax Line Spectral Estimation
We study the fixed design segmented regression problem: Given noisy samples from a piecewise linear function $f$, we want to recover $f$ up to a desired accuracy in mean-squared error. Previous rigorous approaches for this problem rely on…
A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…
We develop a finite-sample optimal estimator for regression discontinuity design when the outcomes are bounded, including binary outcomes as the leading case. Our estimator achieves minimax mean squared error among linear shrinkage…
In this paper, we study the estimation of partially linear models for spatial data distributed over complex domains. We use bivariate splines over triangulations to represent the nonparametric component on an irregular two-dimensional…
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…
Reconstruction of undersampled periodic signals of unknown period is an important signal processing operation. It is especially difficult operation when the sequences of samples are short and no information on the inter-sequence time…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
We establish the optimal nonergodic sublinear convergence rate of the proximal point algorithm for maximal monotone inclusion problems. First, the optimal bound is formulated by the performance estimation framework, resulting in an infinite…
Recently we find several candidates of quantum algorithms that may be implementable in near-term devices for estimating the amplitude of a given quantum state, which is a core sub- routine in various computing tasks such as the Monte Carlo…
A considerable amount of research in harmonic analysis has been devoted to non-linear estimators of signals contaminated by additive Gaussian noise. They are implemented by thresholding coefficients in a frame, which provide a sparse signal…
We propose and analyze a sequential quadratic programming algorithm for minimizing a noisy nonlinear smooth function subject to noisy nonlinear smooth equality constraints. The algorithm uses a step decomposition strategy and, as a result,…
Spectral partitioning is a simple, nearly-linear time, algorithm to find sparse cuts, and the Cheeger inequalities provide a worst-case guarantee for the quality of the approximation found by the algorithm. Local graph partitioning…
This paper studies sensor calibration in spectral estimation where the true frequencies are located on a continuous domain. We consider a uniform array of sensors that collects measurements whose spectrum is composed of a finite number of…
We consider the problem of optimizing signal transmission through multi-channel noisy devices. We investigate an array of bithreshold noisy devices which are connected in parallel and convergent on a summing center. Utilizing the concept of…
The estimation of the amplitude of a sine wave from the sequence of its quantized samples is a typical problem in instrumentation and measurement. A standard approach for its solution makes use of a least squares estimator (LSE) that,…
The problem of monotone submodular maximization has been studied extensively due to its wide range of applications. However, there are cases where one can only access the objective function in a distorted or noisy form because of the…
We propose new estimates for the frontier of a set of points. They are defined as kernel estimates covering all the points and whose associated support is of smallest surface. The estimates are written as linear combinatio- ns of kernel…
It was recently shown [7, 9] that "properly built" linear and polyhedral estimates nearly attain minimax accuracy bounds in the problem of recovery of unknown signal from noisy observations of linear images of the signal when the signal set…
In this paper, we address the problem of simultaneous classification and estimation of hidden parameters in a sensor network with communications constraints. In particular, we consider a network of noisy sensors which measure a common…
We study the problem of scheduling sensors in a resource-constrained linear dynamical system, where the objective is to select a small subset of sensors from a large network to perform the state estimation task. We formulate this problem as…