Related papers: Replica Analysis for Generalized Linear Regression…

In Generalized Linear Estimation (GLE) problems, we seek to estimate a signal that is observed through a linear transform followed by a component-wise, possibly nonlinear and noisy, channel. In the Bayesian optimal setting, Generalized…

We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…

This paper gives a replica analysis for the minimum mean square error (MSE) of a massive multiple-input multiple-output (MIMO) system by using Bayesian inference. The Bayes-optimal estimator is adopted to estimate the data symbols and the…

A general class of nonlinear Least Square Error (LSE) precoders in multi-user multiple-input multiple-output systems is analyzed using the replica method from statistical mechanics. A single cell downlink channel with $N$ transmit antennas…

We consider the problem of parameter estimation from a generalized linear model with a random design matrix that is orthogonally invariant in law. Such a model allows the design have an arbitrary distribution of singular values and only…

We propose a distributed method for simultaneous inference for datasets with sample size much larger than the number of covariates, i.e., N >> p, in the generalized linear models framework. When such datasets are too big to be analyzed…

Reconfigurable intelligent surface (RIS) is a promising technique to improve the performance of future wireless communication systems at low energy consumption. To reap the potential benefits of RIS-aided beamforming, it is vital to enhance…

In this paper, we extend the bilinear generalized approximate message passing (BiG-AMP) approach, originally proposed for high-dimensional generalized bilinear regression, to the multi-layer case for the handling of cascaded problem such as…

To reap the promised gain achieved by distributed reconfigurable intelligent surfaces (RISs)-enhanced communications in a wireless network, timing synchronization among these metasurfaces is an essential prerequisite in practice. This paper…

We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and…

We investigate the concept of algorithmic replicability introduced by Impagliazzo et al. 2022, Ghazi et al. 2021, Ahn et al. 2024 in an online setting. In our model, the input sequence received by the online learner is generated from…

Minimizing the Mean Squared Error (MSE) is a key objective in machine learning and is commonly used for imputing missing values. While this approach provides accurate point estimates, it introduces systematic biases in downstream analyses.…

The computational complexity of simultaneous inference methods in high-dimensional linear regression models quickly increases with the number variables. This paper proposes a computationally efficient method based on the Moore-Penrose…

We consider distributed statistical optimization in one-shot setting, where there are $m$ machines each observing $n$ i.i.d. samples. Based on its observed samples, each machine sends a $B$-bit-long message to a server. The server then…

Generalized linear models are a popular tool in applied statistics, with their maximum likelihood estimators enjoying asymptotic Gaussianity and efficiency. As all models are wrong, it is desirable to understand these estimators' behaviours…

We study a fundamental transfer learning process from source to target linear regression tasks, including overparameterized settings where there are more learned parameters than data samples. The target task learning is addressed by using…

In linear regression we wish to estimate the optimum linear least squares predictor for a distribution over $d$-dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the…

The idea that signals reside in a union of low dimensional subspaces subsumes many low dimensional models that have been used extensively in the recent decade in many fields and applications. Until recently, the vast majority of works have…

We propose a new approach to mixed-frequency regressions in a high-dimensional environment that resorts to Group Lasso penalization and Bayesian techniques for estimation and inference. In particular, to improve the prediction properties of…

This paper proposes a novel distributed reduced--rank scheme and an adaptive algorithm for distributed estimation in wireless sensor networks. The proposed distributed scheme is based on a transformation that performs dimensionality…