相关论文: Simple Solution for Designing the Piecewise Linear…

We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…

Motivated by a growing list of nontraditional statistical estimation problems of the piecewise kind, this paper provides a survey of known results supplemented with new results for the class of piecewise linear-quadratic programs. These are…

Two recent landmark experiments have performed Gaussian boson sampling (GBS) with a non-programmable linear interferometer and threshold detectors on up to 144 output modes (see Refs.~\onlinecite{zhong_quantum_2020,zhong2021phase}). Here we…

A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…

Gaussian mixtures are a common density representation in nonlinear, non-Gaussian Bayesian state estimation. Selecting an appropriate number of Gaussian components, however, is difficult as one has to trade of computational complexity…

Devising optimal operating strategies for a compressor station relies on the knowledge of compressor characteristics. As the compressor characteristics change with time and use, it is necessary to provide accurate models of the…

Many modern distributed real-time signal sensing/monitoring systems require quantization for efficient signal representation. These distributed sensors often have inherent computational and energy limitations. Motivated by this concern, we…

The design of the precoder the maximizes the mutual information in linear vector Gaussian channels with an arbitrary input distribution is studied. Precisely, the precoder optimal left singular vectors and singular values are derived. The…

We analyze the convergence of compressive sensing based sampling techniques for the efficient evaluation of functionals of solutions for a class of high-dimensional, affine-parametric, linear operator equations which depend on possibly…

We compute the closest convex piecewise linear-quadratic (PLQ) function with minimal number of pieces to a given univariate piecewise linear-quadratic function. The Euclidean norm is used to measure the distance between functions. First, we…

This paper proposes a new methodology to perform Bayesian inference for a class of multidimensional Cox processes in which the intensity function is piecewise constant. Poisson processes with piecewise constant intensity functions are…

We develop a simulation-based method for the online updating of Gaussian process regression and classification models. Our method exploits sequential Monte Carlo to produce a fast sequential design algorithm for these models relative to the…

We consider the problem of finding optimal piecewise constant approximations of one-dimensional signals. These approximations should consist of a specified number of segments (samples) and minimise the mean squared error to the original…

Compressive sensing is a methodology for the reconstruction of sparse or compressible signals using far fewer samples than required by the Nyquist criterion. However, many of the results in compressive sensing concern random sampling…

In this paper, we propose projected gradient descent (PGD) algorithms for signal estimation from noisy nonlinear measurements. We assume that the unknown $p$-dimensional signal lies near the range of an $L$-Lipschitz continuous generative…

Uncertainty quantification based on generalized polynomial chaos has been used in many applications. It has also achieved great success in variation-aware design automation. However, almost all existing techniques assume that the parameters…

We study the problem of deriving compressibility measures for Piecewise Linear Approximations (PLAs), i.e., error-bounded approximations of a set of two-dimensional increasing data points using a sequence of segments. Such approximations…

We study distributed coding of compressed sensing (CS) measurements using vector quantizer (VQ). We develop a distributed framework for realizing optimized quantizer that enables encoding CS measurements of correlated sparse sources…

In this paper, we examine the optimal quantization of signals for system identification. We deal with memoryless quantization for the output signals and derive the optimal quantization schemes. The objective functions are the errors of…

The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky…