Related papers: Decoding Mean Field Games from Population and Envi…
We consider the problem of representing collective behavior of large populations and predicting the evolution of a population distribution over a discrete state space. A discrete time mean field game (MFG) is motivated as an interpretable…
Mean field games (MFGs) model interactions in large-population multi-agent systems through population distributions. Traditional learning methods for MFGs are based on fixed-point iteration (FPI), where policy updates and induced population…
In this paper, we study a large population game with heterogeneous dynamics and cost functions solving a consensus problem. Moreover, the agents have communication constraints which appear as: (1) an Additive-White Gaussian Noise (AWGN)…
Gaussian Processes (GPs) are powerful non-parametric Bayesian models for regression of scalar fields, formulated under the assumption that measurement locations are perfectly known and the corresponding field measurements have Gaussian…
Gaussian processes (GPs) are popular nonparametric statistical models for learning unknown functions and quantifying the spatiotemporal uncertainty in data. Recent works have extended GPs to model scalar and vector quantities distributed…
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…
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.…
Constructing a classical potential suited to simulate a given atomic system is a remarkably difficult task. This chapter presents a framework under which this problem can be tackled, based on the Bayesian construction of nonparametric force…
We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to…
Conditional density estimation is complicated by multimodality, heteroscedasticity, and strong non-Gaussianity. Gaussian processes (GPs) provide a principled nonparametric framework with calibrated uncertainty, but standard GP regression is…
We demonstrate the versatility of mean-field games (MFGs) as a mathematical framework for explaining, enhancing, and designing generative models. In generative flows, a Lagrangian formulation is used where each particle (generated sample)…
We present a method enabling a large number of agents to learn how to flock, which is a natural behavior observed in large populations of animals. This problem has drawn a lot of interest but requires many structural assumptions and is…
Gaussian process (GP) regression is a non-parametric, Bayesian framework to approximate complex models. Standard GP regression can lead to an unbounded model in which some points can take infeasible values. We introduce a new GP method that…
Gaussian Process (GP) regression is a flexible modeling technique used to predict outputs and to capture uncertainty in the predictions. However, the GP regression process becomes computationally intensive when the training spatial dataset…
Earth observation from satellite sensory data poses challenging problems, where machine learning is currently a key player. In recent years, Gaussian Process (GP) regression has excelled in biophysical parameter estimation tasks from…
In this paper, we use mean field games (MFGs) to investigate approximations of $N$-player games with uniformly symmetrically continuous heterogeneous closed-loop actions. To incorporate agents' risk aversion (beyond the classical expected…
Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…
In this paper, we address linear-quadratic-Gaussian (LQG) risk-sensitive mean field games (MFGs) with common noise. In this framework agents are exposed to a common noise and aim to minimize an exponential cost functional that reflects…
Earth observation (EO) by airborne and satellite remote sensing and in-situ observations play a fundamental role in monitoring our planet. In the last decade, machine learning and Gaussian processes (GPs) in particular has attained…
Multi-task learning models using Gaussian processes (GP) have been developed and successfully applied in various applications. The main difficulty with this approach is the computational cost of inference using the union of examples from…