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We propose an algebraic combinatorial method for solving large sparse linear systems of equations locally - that is, a method which can compute single evaluations of the signal without computing the whole signal. The method scales only in…
We consider a linear minimum mean squared error (LMMSE) estimation framework with model mismatch where the assumed model order is smaller than that of the underlying linear system which generates the data used in the estimation process. By…
Linear receivers are considered as an attractive low-complexity alternative to optimal processing for multi-antenna MIMO communications. In this paper we characterize the performance of MMSE MIMO receivers in the limit of large antenna…
This two-part work considers the minimum means square error (MMSE) estimation problem for a high dimensional multi-layer generalized linear model (ML-GLM), which resembles a feed-forward fully connected deep learning network in that each of…
We study the following basic machine learning task: Given a fixed set of $d$-dimensional input points for a linear regression problem, we wish to predict a hidden response value for each of the points. We can only afford to attain the…
The problem of estimating the regression function in a fixed design models with correlated observations is considered. Such observations are obtained from several experimental units, each of them forms a time series. Based on the…
As one of the central tasks in machine learning, regression finds lots of applications in different fields. An existing common practice for solving regression problems is the mean square error (MSE) minimization approach or its regularized…
In this article, we introduce iterative deterministic equivalents as a novel technique for the performance analysis of communication systems whose channels are modeled by complex combinations of independent random matrices. This technique…
This paper proposes a novel Bayesian reciprocity calibration method that consistently ensures uplink and downlink channel reciprocity in repeater-assisted multiple-input multiple-output (MIMO) systems. The proposed algorithm is formulated…
We take an information theoretic perspective on a classical sparse-sampling noisy linear model and present an analytical expression for the mutual information, which plays central role in a variety of communications/processing problems.…
We consider the estimation of an n-dimensional vector s from the noisy element-wise measurements of $\mathbf{s}\mathbf{s}^T$, a generic problem that arises in statistics and machine learning. We study a mismatched Bayesian inference…
We study the excess mean square error (EMSE) above the minimum mean square error (MMSE) in large linear systems where the posterior mean estimator (PME) is evaluated with a postulated prior that differs from the true prior of the input…
As datasets grow larger, they are often distributed across multiple machines that compute in parallel and communicate with a central machine through short messages. In this paper, we focus on sparse regression and propose a new procedure…
We propose a method for estimating the posterior distribution of a standard geostatistical model. After choosing the model formulation and specifying a prior, we use normal mixture densities to approximate the posterior distribution. The…
This paper presents an iterative geometric mean decomposition (IGMD) algorithm for multiple-input-multiple-output (MIMO) wireless communications. In contrast to the existing GMD algorithms, the proposed IGMD does not require the explicit…
An exact, closed form, and easy to compute expression for the mean integrated squared error (MISE) of a kernel estimator of a normal mixture cumulative distribution function is derived for the class of arbitrary order Gaussian-based…
Sparse linear regression is one of the classic problems in the field of statistics, which has deep connections and high intersections with optimization, computation, and machine learning. To address the effective handling of…
This paper studies a high-dimensional inference problem involving the matrix tensor product of random matrices. This problem generalizes a number of contemporary data science problems including the spiked matrix models used in sparse…
Reconfigurable intelligent surfaces (RISs) are eminently suitable for improving the reliability of wireless communications by jointly designing the active beamforming at the base station (BS) and the passive beamforming at the RIS.…
A difficulty in MSE estimation occurs because we do not specify a full distribution for the survey weights. This obfuscates the use of fully parametric bootstrap procedures. To overcome this challenge, we develop a novel MSE estimator. We…