Related papers: Maximum Entropy Least Squares Solutions of Overdet…
Quantifying the complexity and irregularity of time series data is a primary pursuit across various data-scientific disciplines. Sample entropy (SampEn) is a widely adopted metric for this purpose, but its reliability is sensitive to the…
Maximum entropy method is a constructive criterion for setting up a probability distribution maximally non-committal to missing information on the basis of partial knowledge, usually stated as constrains on expectation values of some…
Classical least squares estimators are well-known to be robust with respect to moment assumptions concerning the error distribution in a wide variety of finite-dimensional statistical problems; generally only a second moment assumption is…
This paper deals with the problem of finding the globally optimal subset of h elements from a larger set of n elements in d space dimensions so as to minimize a quadratic criterion, with an special emphasis on applications to computing the…
Precoding design for maximizing weighted sum-rate (WSR) is a fundamental problem for downlink of massive multi-user multiple-input multiple-output (MU-MIMO) systems. It is well-known that this problem is generally NP-hard due to the…
Recent contributions have framed linear system identification as a nonparametric regularized inverse problem. Relying on $\ell_2$-type regularization which accounts for the stability and smoothness of the impulse response to be estimated,…
In high-dimensional linear regression, the goal pursued here is to estimate an unknown regression function using linear combinations of a suitable set of covariates. One of the key assumptions for the success of any statistical procedure in…
We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of…
We focus on finding sparse and least-$\ell_1$-norm solutions for unconstrained nonlinear optimal control problems. Such optimization problems are non-convex and non-smooth, nevertheless recent versions of Newton method for under-determined…
In this paper we consider large-scale smooth optimization problems with multiple linear coupled constraints. Due to the non-separability of the constraints, arbitrary random sketching would not be guaranteed to work. Thus, we first…
For optimization on large-scale data, exactly calculating its solution may be computationally difficulty because of the large size of the data. In this paper we consider subsampled optimization for fast approximating the exact solution. In…
This work concerns the minimization of the pseudospectral abscissa of a matrix-valued function dependent on parameters analytically. The problem is motivated by robust stability and transient behavior considerations for a linear control…
An empirical best linear unbiased prediction (EBLUP) estimator is utilized for efficient inference in small-area estimation. To measure its uncertainty, we need to estimate its mean squared error (MSE) since the true MSE cannot generally be…
We develop a new approach for the estimation of a multivariate function based on the economic axioms of quasiconvexity (and monotonicity). On the computational side, we prove the existence of the quasiconvex constrained least squares…
Recent studies of under-determined linear systems of equations with sparse solutions showed a great practical and theoretical efficiency of a particular technique called $\ell_1$-optimization. Seminal works \cite{CRT,DOnoho06CS} rigorously…
Lately, a New Transmuted Logistic-exponential (NTLE) distribution was introduced and studied as an extension of the Logistic-Exponential Distribution (LED) with wider applicability in lifetime modelling. However, the maximum likelihood…
We study a quantity called discrete layered entropy, which approximates the Shannon entropy within a logarithmic gap. Compared to the Shannon entropy, the discrete layered entropy is piecewise linear, approximates the expected length of the…
An approximate mean square error (MSE) expression for the performance analysis of implicitly defined estimators of non-random parameters is proposed. An implicitly defined estimator (IDE) declares the minimizer/maximizer of a selected…
This paper studies adaptive first-order least-squares finite element methods for second-order elliptic partial differential equations in non-divergence form. Unlike the classical finite element method which uses weak formulations of PDEs…
We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from…