相关论文: Saddlepoint approximation for moment generating fu…

The paper is concerned with stochastic approximation procedures having three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function. We…

Mini-batch SGD with momentum is a fundamental algorithm for learning large predictive models. In this paper we develop a new analytic framework to analyze noise-averaged properties of mini-batch SGD for linear models at constant learning…

The graph Fourier transform (GFT) is in general dense and requires O(n^2) time to compute and O(n^2) memory space to store. In this paper, we pursue our previous work on the approximate fast graph Fourier transform (FGFT). The FGFT is…

We provide in this paper simulation algorithms for one-sided and two-sided truncated normal distributions. These algorithms are then used to simulate multivariate normal variables with restricted parameter space for any covariance…

The task of deducing three-dimensional molecular configurations from their two-dimensional graph representations holds paramount importance in the fields of computational chemistry and pharmaceutical development. The rapid advancement of…

Sampling from an unnormalized target distribution is an essential problem with many applications in probabilistic inference. Stein Variational Gradient Descent (SVGD) has been shown to be a powerful method that iteratively updates a set of…

Multidimensional fitting (MDF) method is a multivariate data analysis method recently developed and based on the fitting of distances. Two matrices are available: one contains the coordinates of the points and the second contains the…

The incomplete moment generating function (IMGF) has paramount relevance in communication theory, since it appears in a plethora of scenarios when analyzing the performance of communication systems. We here present a general method for…

In non-asymptotic learning, variance-type parameters of sub-Gaussian distributions are of paramount importance. However, directly estimating these parameters using the empirical moment generating function (MGF) is infeasible. To address…

In this note, we develop Fourier approximation methods for the solutions of first-order nonlocal mean-field games (MFG) systems. Using Fourier expansion techniques, we approximate a given MFG system by a simpler one that is equivalent to a…

We introduce Midpoint Generative Models (MGM), a principled framework for training one-step generative models. MGM is based on a simple symmetry of Flow Matching with linear interpolation: when the two endpoint distributions coincide, the…

In the present article we derive an explicit expression for the trun- cated mean and variance for the multivariate normal distribution with ar- bitrary rectangular double truncation. We use the moment generating ap- proach of Tallis (1961)…

This paper establishes the optimal sub-Gaussian variance proxy for truncated Gaussian and truncated exponential random variables. The proofs rely on first characterizing the optimal variance proxy as the unique solution to a set of two…

Low-rank tensor models are widely used in statistics. However, most existing methods rely heavily on the assumption that data follows a sub-Gaussian distribution. To address the challenges associated with heavy-tailed distributions…

Variational inference, such as the mean-field (MF) approximation, requires certain conjugacy structures for efficient computation. These can impose unnecessary restrictions on the viable prior distribution family and further constraints on…

Multi-fidelity modelling arises in many situations in computational science and engineering world. It enables accurate inference even when only a small set of accurate data is available. Those data often come from a high-fidelity model,…

This letter proposes the use of saddle point approximation (SPA) to evaluate the outage probability of wireless cellular networks. Unlike traditional numerical integration-based approaches, the SPA approach relies on cumulant generating…

Understanding stochastic gradient descent (SGD) and its variants is essential for machine learning. However, most of the preceding analyses are conducted under amenable conditions such as unbiased gradient estimator and bounded objective…

We present the new Guided Moments ($\texttt{GM}$) formalism for neutrino modeling in astrophysical scenarios like core-collapse supernovae and neutron star mergers. The truncated moments approximation ($\texttt{M1}$) and Monte-Carlo…

We derive a novel variational expectation maximization approach based on truncated posterior distributions. Truncated distributions are proportional to exact posteriors within subsets of a discrete state space and equal zero otherwise. The…