Related papers: Precise Asymptotics for Spectral Methods in Mixed …

In this work, we propose a two-stage algorithm based on Bayesian modeling and computation aiming at quantifying analyte concentrations or quantities in complex mixtures with Raman spectroscopy. A hierarchical Bayesian model is built for…

The asymptotic mutual information (MI) analysis for multiple-input multiple-output (MIMO) systems over double-scattering channels has achieved engaging results, but the convergence rates of the mean, variance, and the distribution of the MI…

We extend a recently established asymptotic normality theorem for generalized linear mixed models to include the dispersion parameter. The new results show that the maximum likelihood estimators of all model parameters have asymptotically…

Missing values with mixed data types is a common problem in a large number of machine learning applications such as processing of surveys and in different medical applications. Recently, Gaussian copula models have been suggested as a means…

The matrix pencil method (MPM) is a well-known technique for estimating the parameters of exponentially damped sinusoids in noise by solving a generalized eigenvalue problem. However, in several cases, this is an ill-conditioned problem…

We present the completion of a data analysis pipeline that self-consistently separates global 21-cm signals from large systematics using a pattern recognition technique. In the first paper of this series, we obtain optimal basis vectors…

Linear mixture models are commonly used to represent hyperspectral datacube as a linear combinations of endmember spectra. However, determining of the number of endmembers for images embedded in noise is a crucial task. This paper proposes…

We consider jointly estimating the coefficient matrix and the error precision matrix in high-dimensional multivariate linear regression models. Bayesian methods in this context often face computational challenges, leading to previous…

State space models have long played an important role in signal processing. The Gaussian case can be treated algorithmically using the famous Kalman filter. Similarly since the 1970s there has been extensive application of Hidden Markov…

Transformers demonstrate significant advantages as the building block of modern LLMs. In this work, we study the capacities of Transformers in performing unsupervised learning. We show that multi-layered Transformers, given a sufficiently…

A common task is the determination of system parameters from spectroscopy, where one compares the experimental spectrum with calculated spectra, that depend on the desired parameters. Here we discuss an approach based on a machine learning…

Spectral embedding is a procedure which can be used to obtain vector representations of the nodes of a graph. This paper proposes a generalisation of the latent position network model known as the random dot product graph, to allow…

We consider the problem of signal estimation in a generalized linear model (GLM). GLMs include many canonical problems in statistical estimation, such as linear regression, phase retrieval, and 1-bit compressed sensing. Recent work has…

We give two prediction intervals (PI) for Generalized Linear Models that take model selection uncertainty into account. The first is a straightforward extension of asymptotic normality results and the second includes an extra optimization…

The replica method is a non-rigorous but well-known technique from statistical physics used in the asymptotic analysis of large, random, nonlinear problems. This paper applies the replica method, under the assumption of replica symmetry, to…

We study generalised linear regression and classification for a synthetically generated dataset encompassing different problems of interest, such as learning with random features, neural networks in the lazy training regime, and the hidden…

Linear thresholding models postulate that the conditional distribution of a response variable in terms of covariates differs on the two sides of a (typically unknown) hyperplane in the covariate space. A key goal in such models is to learn…

Mass spectrometry is the dominant technology in the field of proteomics, enabling high-throughput analysis of the protein content of complex biological samples. Due to the complexity of the instrumentation and resulting data, sophisticated…

In many real-world networks, data on the edges evolve in continuous time, naturally motivating representations based on point processes. Heterogeneity in edge types further gives rise to multiplex network point processes. In this work, we…

Large-margin classifiers are popular methods for classification. We derive the asymptotic expression for the generalization error of a family of large-margin classifiers in the limit of both sample size $n$ and dimension $p$ going to…