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The reparameterization gradient has become a widely used method to obtain Monte Carlo gradients to optimize the variational objective. However, this technique does not easily apply to commonly used distributions such as beta or gamma…

Machine Learning · Statistics 2016-10-20 Francisco J. R. Ruiz , Michalis K. Titsias , David M. Blei

A non trivial problem that arises in several applications is the estimation of the mean of a truncated normal distribution. In this paper, an iterative deterministic scheme for approximating this mean is proposed. It has been inspired from…

Performance-based engineering for natural hazards facilitates the design and appraisal of structures with rigorous evaluation of their uncertain structural behavior under potentially extreme stochastic loads expressed in terms of failure…

Computational Engineering, Finance, and Science · Computer Science 2023-05-11 Srinivasan Arunachalam , Seymour M. J. Spence

This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…

Statistics Theory · Mathematics 2020-08-14 Valentin De Bortoli , Alain Durmus , Ana F. Vidal , Marcelo Pereyra

We introduce a generalization of the Adaptive Multilevel Splitting algorithm in the discrete time dynamic setting, namely when it is applied to sample rare events associated with paths of Markov chains. By interpreting the algorithm as a…

An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…

Artificial Intelligence · Computer Science 2013-04-10 Ross D. Shachter

Inferring the sequence of states from observations is one of the most fundamental problems in Hidden Markov Models. In statistical physics language, this problem is equivalent to computing the marginals of a one-dimensional model with a…

Disordered Systems and Neural Networks · Physics 2015-05-13 Antoine Sinton

It is known that standard stochastic Galerkin methods encounter challenges when solving partial differential equations with high-dimensional random inputs, which are typically caused by the large number of stochastic basis functions…

Numerical Analysis · Mathematics 2024-01-30 Guanjie Wang , Smita Sahu , Qifeng Liao

We develop a generalized gradient expansion of the inhomogeneous dynamical mean-field theory method for determining properties of ultracold atoms in a trap. This approach goes beyond the well-known local density approximation and at higher…

Quantum Gases · Physics 2016-08-17 J. K. Freericks , Shuyang Han , Karlis Mikelsons , H. R. Krishnamurthy

We provide a numerically robust and fast method capable of exploiting the local geometry when solving large-scale stochastic optimisation problems. Our key innovation is an auxiliary variable construction coupled with an inverse Hessian…

Machine Learning · Statistics 2018-02-14 Adrian Wills , Thomas Schön

In this article, we derive Stein's method for approximating a spatial random graph by a generalised random geometric graph, which has vertices given by a finite Gibbs point process and edges based on a general connection function. Our main…

Probability · Mathematics 2024-11-06 Dominic Schuhmacher , Leoni Carla Wirth

A rescaled Markov chain converges uniformly in probability to the solution of an ordinary differential equation, under carefully specified assumptions. The presentation is much simpler than those in the outside literature. The result may be…

Probability · Mathematics 2007-05-23 R. W. R. Darling

Stein's method for Gaussian process approximation can be used to bound the differences between the expectations of smooth functionals $h$ of a c\`adl\`ag random process $X$ of interest and the expectations of the same functionals of a well…

Probability · Mathematics 2024-02-15 A. D. Barbour , Nathan Ross , Guangqu Zheng

Gaussian Markov random fields (GMRFs) are useful in a broad range of applications. In this paper we tackle the problem of learning a sparse GMRF in a high-dimensional space. Our approach uses the l1-norm as a regularization on the inverse…

Machine Learning · Computer Science 2012-06-18 John Duchi , Stephen Gould , Daphne Koller

State space models have long played an important role in signal processing. The Gaussian case can be treated algorithmically using the famous Kalman filter. Similarly since the 1970s there has been extensive application of Hidden Markov…

Statistics Theory · Mathematics 2007-06-13 Peter Bickel , Yaacov Ritov , Tobias Rydén

A common challenge in estimating parameters of probability density functions is the intractability of the normalizing constant. While in such cases maximum likelihood estimation may be implemented using numerical integration, the approach…

Methodology · Statistics 2018-02-20 Shiqing Yu , Mathias Drton , Ali Shojaie

A stochastic incremental subgradient algorithm for the minimization of a sum of convex functions is introduced. The method sequentially uses partial subgradient information and the sequence of partial subgradients is determined by a general…

Optimization and Control · Mathematics 2021-08-24 Rafael Massambone , Eduardo F. Costa , Elias S. Helou

With a scalar potential and a bivector potential, the vector field associated with the drift of a diffusion is decomposed into a generalized gradient field, a field perpendicular to the gradient, and a divergence-free field. We give such…

Statistical Mechanics · Physics 2021-05-26 Ying-Jen Yang , Yu-Chen Cheng

The randomized projection (RP) method is a simple iterative scheme for solving linear feasibility problems and has recently gained popularity due to its speed and low memory requirement. This paper develops an accelerated variant of the…

Optimization and Control · Mathematics 2022-11-21 Lin Zhu , Yuan Lei , Jiaxin Xie

We develop and analyze the Generalized Multiplicative Gradient (GMG) method for solving a class of convex optimization problems over symmetric cones, where the objective function does not have Lipschitz gradient over the feasible region.…

Optimization and Control · Mathematics 2026-03-06 Renbo Zhao