Related papers: Low-rank variance reduction for uncertain radiativ…

Continuous-time Markov chains describing interacting processes exhibit a state space that grows exponentially in the number of processes. This state-space explosion renders the computation or storage of the time-marginal distribution, which…

The low-rank tensor approximation is very promising for the compression of deep neural networks. We propose a new simple and efficient iterative approach, which alternates low-rank factorization with a smart rank selection and fine-tuning.…

In this paper, we present a predictor-corrector strategy for constructing rank-adaptive dynamical low-rank approximations (DLRAs) of matrix-valued ODE systems. The strategy is a compromise between (i) low-rank step-truncation approaches…

Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…

In this paper, we develop an asymptotic-preserving dynamical low-rank method for the multiscale linear kinetic transport equation. The proposed scheme is unconditionally stable in the diffusive regime while preserving the correct asymptotic…

Optimization in the Bures-Wasserstein space has been gaining popularity in the machine learning community since it draws connections between variational inference and Wasserstein gradient flows. The variational inference objective function…

We develop a Monte-Carlo based numerical method for solving discrete-time stochastic optimal control problems with inventory. These are optimal control problems in which the control affects only a deterministically evolving inventory…

High precision analytical approximation is proposed for variance-covariance based risk allocation in a portfolio of risky assets. A general case of a single-period multi-factor Merton-type model with stochastic recovery is considered. The…

Projected gradient descent and its Riemannian variant belong to a typical class of methods for low-rank matrix estimation. This paper proposes a new Nesterov's Accelerated Riemannian Gradient algorithm by efficient orthographic retraction…

In this study, we give an extension of Montanaro's arXiv/archive:1504.06987 quantum Monte Carlo method, tailored for computing expected values of random variables that exhibit infinite variance. This addresses a challenge in analyzing…

Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different…

Large Language Models (LLMs) are highly resource-intensive to fine-tune due to their enormous size. While low-rank adaptation is a prominent parameter-efficient fine-tuning approach, it suffers from sensitivity to hyperparameter choices,…

Stochastic optimization in learning and inference often relies on Markov chain Monte Carlo (MCMC) to approximate gradients when exact computation is intractable. However, finite-time MCMC estimators are biased, and reducing this bias…

We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…

Standard regularization methods that are used to compute solutions to ill-posed inverse problems require knowledge of the forward model. In many real-life applications, the forward model is not known, but training data is readily available.…

This article addresses online variational estimation in parametric state-space models. We propose a new procedure for efficiently computing the evidence lower bound and its gradient in a streaming-data setting, where observations arrive…

Low-rank training methods reduce the number of trainable parameters by re-parameterizing the weights with matrix decompositions (e.g., singular value decomposition). However, enforcing a fixed low-rank structure caps the rank of the weight…

This paper focuses on the identification of graphical autoregressive models with dynamical latent variables. The dynamical structure of latent variables is described by a matrix polynomial transfer function. Taking account of the sparse…

This paper is a broad and accessible survey of the methods we have at our disposal for Monte Carlo gradient estimation in machine learning and across the statistical sciences: the problem of computing the gradient of an expectation of a…

This work introduces meta estimators that combine multiple multifidelity techniques based on control variates, importance sampling, and information reuse to yield a quasi-multiplicative amount of variance reduction. The proposed meta…