Related papers: Optimal Estimation in Orthogonally Invariant Gener…
How do statistical dependencies in measurement noise influence high-dimensional inference? To answer this, we study the paradigmatic spiked matrix model of principal components analysis (PCA), where a rank-one matrix is corrupted by…
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…
Orthogonal time frequency space (OTFS) modulation has emerged as a promising solution to support high-mobility wireless communications, for which, cost-effective data detectors are critical. Although graph neural network (GNN)-based data…
It is common practice to collect observations of feature and response pairs from different environments. A natural question is how to identify features that have consistent prediction power across environments. The invariant causal…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
Approximate message passing (AMP) refers to a class of efficient algorithms for statistical estimation in high-dimensional problems such as compressed sensing and low-rank matrix estimation. This paper analyzes the performance of AMP in the…
Efficiently finding the maximum a posteriori (MAP) configuration of a graphical model is an important problem which is often implemented using message passing algorithms. The optimality of such algorithms is only well established for…
We propose an estimator of prediction error using an approximate message passing (AMP) algorithm that can be applied to a broad range of sparse penalties. Following Stein's lemma, the estimator of the generalized degrees of freedom, which…
The generalized approximate message passing (GAMP) algorithm is an efficient method of MAP or approximate-MMSE estimation of $x$ observed from a noisy version of the transform coefficients $z = Ax$. In fact, for large zero-mean i.i.d…
This work explores multi-modal inference in a high-dimensional simplified model, analytically quantifying the performance gain of multi-modal inference over that of analyzing modalities in isolation. We present the Bayes-optimal performance…
We consider the problem of jointly optimum modulation and estimation of a real-valued random parameter, conveyed over an additive white Gaussian noise (AWGN) channel, where the performance metric is the large deviations behavior of the…
Computational models of complex physical systems often rely on simplifying assumptions which inevitably introduce model error, with consequent predictive errors. Given data on model observables, the estimation of parameterized model-error…
One method for obtaining generalizable solutions to machine learning tasks when presented with diverse training environments is to find \textit{invariant representations} of the data. These are representations of the covariates such that…
Generalized approximate message passing (GAMP) is a computationally efficient algorithm for estimating an unknown signal $w_0\in\mathbb{R}^N$ from a random linear measurement $y= Xw_0 + \epsilon\in\mathbb{R}^M$, where…
Generalized linear mixed models are useful in studying hierarchical data with possibly non-Gaussian responses. However, the intractability of likelihood functions poses challenges for estimation. We develop a new method suitable for this…
To fast approximate maximum likelihood estimators with massive data, this paper studies the Optimal Subsampling Method under the A-optimality Criterion (OSMAC) for generalized linear models. The consistency and asymptotic normality of the…
We extend the generalized approximate message passing (G-AMP) approach, originally proposed for high-dimensional generalized-linear regression in the context of compressive sensing, to the generalized-bilinear case, which enables its…
High-dimensional time series appear in many scientific setups, demanding a nuanced approach to model and analyze the underlying dependence structure. Theoretical advancements so far often rely on stringent assumptions regarding the sparsity…
Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…
We consider the problem of estimating the common mean of independently sampled data, where samples are drawn in a possibly non-identical manner from symmetric, unimodal distributions with a common mean. This generalizes the setting of…