相关论文: A Stochastic Analysis Approach to Tensor Field The…

We develop a new approach for detecting changes in the behavior of stochastic processes and random fields based on tensor product representations such as the Karhunen-Lo\`{e}ve expansion. From the associated eigenspaces of the covariance…

Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…

The sampling of probability distributions specified up to a normalization constant is an important problem in both machine learning and statistical mechanics. While classical stochastic sampling methods such as Markov Chain Monte Carlo…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

This article introduces a novel approach to the mathematical development of Ordinary Least Squares and Neural Network regression models, diverging from traditional methods in current Machine Learning literature. By leveraging Tensor…

We introduce a novel approach based on stochastic optimization to find the optimal sampling distribution for the data-driven stability analysis of switched linear systems. Our goal is to address limitations of existing approaches, in…

We theoretically and experimentally investigate tensor-based regression and classification. Our focus is regularization with various tensor norms, including the overlapped trace norm, the latent trace norm, and the scaled latent trace norm.…

In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations…

A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting approximation is a four tuple Markov…

System identification in scenarios where the observed number of variables is less than the degrees of freedom in the dynamics is an important challenge. In this work we tackle this problem by using a recognition network to increase the…

Reliability analysis is a sub-field of uncertainty quantification that assesses the probability of a system performing as intended under various uncertainties. Traditionally, this analysis relies on deterministic models, where experiments…

Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as…

In this paper, we study the estimation of the threshold predictive regression model with hybrid stochastic local unit root predictors. We demonstrate the estimation procedure and derive the asymptotic distribution of the least square…

A new unbiased Monte Carlo technique called Tensor Network Monte Carlo (TNMC) is introduced based on sampling all possible renormalizations (or course-grainings) of tensor networks, in this case matrix-product states. Tensor networks are a…

How can we learn the laws underlying the dynamics of stochastic systems when their trajectories are sampled sparsely in time? Existing methods either require temporally resolved high-frequency observations, or rely on geometric arguments…

Based on the tensor tree network with the Born machine framework, we propose a general method for constructing a generative model by expressing the target distribution function as the amplitude of the quantum wave function represented by a…

Bottom-Up Hidden Tree Markov Model is a highly expressive model for tree-structured data. Unfortunately, it cannot be used in practice due to the intractable size of its state-transition matrix. We propose a new approximation which lies on…

After collecting data from observations or experiments, the next step is to build an appropriate mathematical or stochastic model to describe the data so that further studies can be done with the help of the models. In this article, the…

We consider supervised learning (regression/classification) problems with tensor-valued input. We derive multi-linear sufficient reductions for the regression or classification problem by modeling the conditional distribution of the…

In this survey we review some recent rigorous results on large N problems in quantum field theory, stochastic quantization and singular stochastic PDEs, and their mean field limit problems. In particular we discuss the O(N) linear sigma…