相关论文: Learning Surrogate Potential Mean Field Games via …

Gaussian process regression is widely applied in computational science and engineering for surrogate modeling owning to its kernel-based and probabilistic nature. In this work, we propose a Bayesian approach that integrates the variability…

Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and non-differentiable functions, these smoothness assumptions are often too…

Gaussian processes (GPs) provide a framework for Bayesian inference that can offer principled uncertainty estimates for a large range of problems. For example, if we consider regression problems with Gaussian likelihoods, a GP model enjoys…

We develop Bayesian machine learning methods for mixed data sampling (MIDAS) regressions. This involves handling frequency mismatches and specifying functional relationships between many predictors and the dependent variable. We use…

In a regular mean field game (MFG), the agents are assumed to be insignificant, they do not realize their effect on the population level and this may result in a phenomenon coined as the Tragedy of the Commons by the economists. However, in…

Many inferential tasks involve fitting models to observed data and predicting outcomes at new covariate values, requiring interpolation or extrapolation. Conventional methods select a single best-fitting model, discarding fits that were…

This paper introduces a novel two-stage machine learning-based surrogate modeling framework to address inverse problems in scientific and engineering fields. In the first stage of the proposed framework, a machine learning model termed the…

Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many…

In recent years, surrogate models have been successfully used in likelihood-free inference to decrease the number of simulator evaluations. The current state-of-the-art performance for this task has been achieved by Bayesian Optimization…

This paper introduces an active learning framework for manifold Gaussian Process (GP) regression, combining manifold learning with strategic data selection to improve accuracy in high-dimensional spaces. Our method jointly optimizes a…

We introduce a scalable Gaussian process (GP) framework with deep product kernels for data-driven learning of parametrized spatio-temporal fields over fixed or parameter-dependent domains. The proposed framework learns a continuous…

Multitask Gaussian processes (MTGP) are the Gaussian process (GP) framework's solution for multioutput regression problems in which the $T$ elements of the regressors cannot be considered conditionally independent given the observations.…

Gaussian processes (GPs) defined through intrinsic random fields provide a flexible framework for modeling spatial phenomena, and have been advocated in a variety of applications over the past several decades. Nevertheless, their adoption…

This paper presents a self-supervised learning framework, named MGF, for general-purpose speech representation learning. In the design of MGF, speech hierarchy is taken into consideration. Specifically, we propose to use generative learning…

Mean-field game theory relies on approximating games that are intractable to model due to a very large to infinite population of players. While these kinds of games can be solved analytically via the associated system of partial…

The recent mean field game (MFG) formalism facilitates otherwise intractable computation of approximate Nash equilibria in many-agent settings. In this paper, we consider discrete-time finite MFGs subject to finite-horizon objectives. We…

We analyze a system of partial differential equations that model a potential mean field game of controls, briefly MFGC. Such a game describes the interaction of infinitely many negligible players competing to optimize a personal value…

Multi-output Gaussian process (MGP) models have attracted significant attention for their flexibility and uncertainty-quantification capabilities, and have been widely adopted in multi-source transfer learning scenarios due to their ability…

This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…

This paper studies a large population dynamic game involving nonlinear stochastic dynamical systems with agents of the following mixed types: (i) a major agent, and (ii) a population of $N$ minor agents where $N$ is very large. The major…