Related papers: Exact Gaussian Moment Matching for Residual Networ…

A hierarchical Bayesian approach that permits simultaneous inference for the regression coefficient matrix and the error precision (inverse covariance) matrix in the multivariate linear model is proposed. Assuming a natural ordering of the…

This paper studies the approximation and generalization abilities of score-based neural network generative models (SGMs) in estimating an unknown distribution $P_0$ from $n$ i.i.d. observations in $d$ dimensions. Assuming merely that $P_0$…

Bayesian methods in machine learning, such as Gaussian processes, have great advantages com-pared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to…

We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms…

In deep learning, a central issue is to understand how neural networks efficiently learn high-dimensional features. To this end, we explore the gradient descent learning of a general Gaussian Multi-index model…

Understanding when neural networks can be learned efficiently is a fundamental question in learning theory. Existing hardness results suggest that assumptions on both the input distribution and the network's weights are necessary for…

To have a superior generalization, a deep learning neural network often involves a large size of training sample. With increase of hidden layers in order to increase learning ability, neural network has potential degradation in accuracy.…

Generalized linear models (GLMs) arise in high-dimensional machine learning, statistics, communications and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing,…

We propose an algorithm for simultaneously detecting and locating changepoints in a time series, and a framework for predicting the distribution of the next point in the series. The kernel of the algorithm is a system of equations that…

We provide a unifying view of a large family of previous imitation learning algorithms through the lens of moment matching. At its core, our classification scheme is based on whether the learner attempts to match (1) reward or (2)…

We consider fully connected and feedforward deep neural networks with dependent and possibly heavy-tailed weights, as introduced in [26], to address limitations of the standard Gaussian prior. It has been proved in [26] that, as the number…

Efficiently learning mixture of Gaussians is a fundamental problem in statistics and learning theory. Given samples coming from a random one out of k Gaussian distributions in Rn, the learning problem asks to estimate the means and the…

Though Gaussian graphical models have been widely used in many scientific fields, relatively limited progress has been made to link graph structures to external covariates. We propose a Gaussian graphical regression model, which regresses…

We propose a novel regularization loss that enforces standard Gaussianity, encouraging samples to align with a standard Gaussian distribution. This facilitates a range of downstream tasks involving optimization in the latent space of…

Low Earth orbit (LEO) satellites are leveraged to support new position, navigation, and timing (PNT) service alternatives to GNSS. These alternatives require accurate propagation of satellite position and velocity with a realistic…

Bayesian estimation of Gaussian graphical models has proven to be challenging because the conjugate prior distribution on the Gaussian precision matrix, the G-Wishart distribution, has a doubly intractable partition function. Recent…

In this paper we study algorithms to find a Gaussian approximation to a target measure defined on a Hilbert space of functions; the target measure itself is defined via its density with respect to a reference Gaussian measure. We employ the…

State-of-the-art image-set matching techniques typically implicitly model each image-set with a Gaussian distribution. Here, we propose to go beyond these representations and model image-sets as probability distribution functions (PDFs)…

Many real-world multivariate time series are collected from a network of physical objects embedded with software, electronics, and sensors. The quasi-periodic signals generated by these objects often follow a similar repetitive and periodic…

Neural networks with wide layers have attracted significant attention due to their equivalence to Gaussian processes, enabling perfect fitting of training data while maintaining generalization performance, known as benign overfitting.…