相关论文: Conjugate Natural Selection

We consider the Bayesian optimal filtering problem: i.e. estimating some conditional statistics of a latent time-series signal from an observation sequence. Classical approaches often rely on the use of assumed or estimated transition and…

We propose a computer-assisted approach to the analysis of the worst-case convergence of nonlinear conjugate gradient methods (NCGMs). Those methods are known for their generally good empirical performances for large-scale optimization,…

Score-based diffusion models currently constitute the state of the art in continuous generative modeling. These methods are typically formulated via overdamped or underdamped Ornstein--Uhlenbeck-type stochastic differential equations, in…

The Kullback-Leibler (KL) divergence plays a central role in probabilistic machine learning, where it commonly serves as the canonical loss function. Optimization in such settings is often performed over the probability simplex, where the…

One of the focus areas of modern scientific research is to reveal mysteries related to genes and their interactions. The dynamic interactions between genes can be encoded into a gene regulatory network (GRN), which can be used to gain…

Analogies between evolutionary dynamics and statistical mechanics, such as Fisher's second-law-like "fundamental theorem of natural selection" and Wright's "fitness landscapes", have had a deep and fruitful influence on the development of…

Natural Gradient Descent (NGD) has emerged as a promising optimization algorithm for training neural network-based solvers for partial differential equations (PDEs), such as Physics-Informed Neural Networks (PINNs). However, its practical…

We study the Stochastic Gradient Descent (SGD) method in nonconvex optimization problems from the point of view of approximating diffusion processes. We prove rigorously that the diffusion process can approximate the SGD algorithm weakly…

With a computationally efficient approximation of the second-order information, natural gradient methods have been successful in solving large-scale structured optimization problems. We study the natural gradient methods for the large-scale…

Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value…

We consider optimal experimental design for parameter estimation in dynamical systems governed by controlled ordinary differential equations. In such problems, Fisher-based criteria are attractive because they lead to time-additive…

In this paper, we introduce proximal gradient temporal difference learning, which provides a principled way of designing and analyzing true stochastic gradient temporal difference learning algorithms. We show how gradient TD (GTD)…

Variational inference transforms posterior inference into parametric optimization thereby enabling the use of latent variable models where otherwise impractical. However, variational inference can be finicky when different variational…

This paper aims to enhance the use of the Frank-Wolfe (FW) algorithm for training deep neural networks. Similar to any gradient-based optimization algorithm, FW suffers from high computational and memory costs when computing gradients for…

We study online inference and asymptotic covariance estimation for the stochastic gradient descent (SGD) algorithm. While classical methods (such as plug-in and batch-means estimators) are available, they either require inaccessible…

We introduce a novel and efficient algorithm called the stochastic approximate gradient descent (SAGD), as an alternative to the stochastic gradient descent for cases where unbiased stochastic gradients cannot be trivially obtained.…

Studying the properties of stochastic noise to optimize complex non-convex functions has been an active area of research in the field of machine learning. Prior work has shown that the noise of stochastic gradient descent improves…

We propose a novel approach to sequential Bayesian inference based on variational Bayes (VB). The key insight is that, in the online setting, we do not need to add the KL term to regularize to the prior (which comes from the posterior at…

One way to avoid overfitting in machine learning is to use model parameters distributed according to a Bayesian posterior given the data, rather than the maximum likelihood estimator. Stochastic gradient Langevin dynamics (SGLD) is one…

This paper introduces a projected Sobolev natural gradient descent (NGD) method for computing ground states of the Gross-Pitaevskii equation. By projecting a continuous Riemannian Sobolev gradient flow onto the normalized neural network…