Related papers: High-dimensional macroeconomic forecasting using m…
In this paper, we propose an information geometry (IG) framework to solve the standard linear regression problem. The proposed framework is an extension of the one for computing the mean of complex multivariate Gaussian distribution. By…
Deep generative priors are a powerful tool for reconstruction problems with complex data such as images and text. Inverse problems using such models require solving an inference problem of estimating the input and hidden units of the…
Modeling nonstationary processes is of paramount importance to many scientific disciplines including environmental science, ecology, and finance, among others. Consequently, flexible methodology that provides accurate estimation across a…
Approximate message passing (AMP) has emerged both as a popular class of iterative algorithms and as a powerful analytic tool in a wide range of statistical estimation problems and statistical physics models. A well established line of AMP…
This paper presents a pre-processing and a distance which improve the performance of machine learning algorithms working on independent and identically distributed stochastic processes. We introduce a novel non-parametric approach to…
Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not…
Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a…
Approximate Message Passing (AMP) algorithms enable precise characterization of certain classes of random objects in the high-dimensional limit, and have found widespread applications in fields such as signal processing, statistics, and…
Generalized linear models (GLMs) -- such as logistic regression, Poisson regression, and robust regression -- provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
In many contexts, there is interest in selecting the most important variables from a very large collection, commonly referred to as support recovery or variable, feature or subset selection. There is an enormous literature proposing a rich…
When studying interacting systems, computing their statistical properties is a fundamental problem in various fields such as physics, applied mathematics, and machine learning. However, this task can be quite challenging due to the…
Designing efficient sparse recovery algorithms that could handle noisy quantized measurements is important in a variety of applications -- from radar to source localization, spectrum sensing and wireless networking. We take advantage of the…
Data assimilation is a core component of numerical weather prediction systems. The large quantity of data processed during assimilation requires the computation to be distributed across increasingly many compute nodes, yet existing…
Time series forecasts of different temporal granularity are widely used in real-world applications, e.g., sales prediction in days and weeks for making different inventory plans. However, these tasks are usually solved separately without…
We develop a non-parametric multivariate time series model that remains agnostic on the precise relationship between a (possibly) large set of macroeconomic time series and their lagged values. The main building block of our model is a…
The standard linear regression (SLR) problem is to recover a vector $\mathbf{x}^0$ from noisy linear observations $\mathbf{y}=\mathbf{Ax}^0+\mathbf{w}$. The approximate message passing (AMP) algorithm recently proposed by Donoho, Maleki,…
We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix…
Approximate Message Passing (AMP), originally designed to solve high-dimensional linear inverse problems, has found broad applications in signal processing and statistical inference. Among its key variants, Vector Approximate Message…