相关论文: Mean Field Optimization Problem Regularized by Fis…

Mean field game theory studies the behavior of a large number of interacting individuals in a game theoretic setting and has received a lot of attention in the past decade (Lasry and Lions, Japanese journal of mathematics, 2007). In this…

For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…

Lorentzian distributions have been largely employed in statistical mechanics to obtain exact results for heterogeneous systems. Analytic continuation of these results is impossible even for slightly deformed Lorentzian distributions, due to…

We propose a novel approach to the problem of mutual information (MI) estimation via introducing a family of estimators based on normalizing flows. The estimator maps original data to the target distribution, for which MI is easier to…

We propose a novel supervised learning method to optimize the kernel in the maximum mean discrepancy generative adversarial networks (MMD GANs), and the kernel support vector machines (SVMs). Specifically, we characterize a distributionally…

Distributionally robust optimization (DRO) problems are increasingly seen as a viable method to train machine learning models for improved model generalization. These min-max formulations, however, are more difficult to solve. We therefore…

We study two-layer neural networks in the mean field limit, where the number of neurons tends to infinity. In this regime, the optimization over the neuron parameters becomes the optimization over the probability measures, and by adding an…

We present a multi-agent algorithm for multi-objective optimization problems, which extends the class of consensus-based optimization methods and relies on a scalarization strategy. The optimization is achieved by a set of interacting…

We develop and analyze a projected particle Langevin optimization method to learn the distribution in the Sch\"{o}nberg integral representation of the radial basis functions from training samples. More specifically, we characterize a…

We propose a novel learning framework based on neural mean-field dynamics for inference and estimation problems of diffusion on networks. Our new framework is derived from the Mori-Zwanzig formalism to obtain an exact evolution of the node…

The classical dynamic programming-based optimal stochastic control methods fail to cope with nonseparable dynamic optimization problems as the principle of optimality no longer applies in such situations. Among these notorious nonseparable…

Normalizing flows model a complex target distribution in terms of a bijective transform operating on a simple base distribution. As such, they enable tractable computation of a number of important statistical quantities, particularly…

In this paper, we analyze the impact of compressed sensing with complex random matrices on Fisher information and the Cram\'{e}r-Rao Bound (CRB) for estimating unknown parameters in the mean value function of a complex multivariate normal…

We develop a novel procedure for estimating the optimizer of general convex stochastic optimization problems of the form $\min_{x\in\mathcal{X}} \mathbb{E}[F(x,\xi)]$, when the given data is a finite independent sample selected according to…

We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete)…

We study the complexity of sampling from the stationary distribution of a mean-field SDE, or equivalently, the complexity of minimizing a functional over the space of probability measures which includes an interaction term. Our main insight…

We consider machine learning, particularly regression, using locally-differentially private datasets. The Wasserstein distance is used to define an ambiguity set centered at the empirical distribution of the dataset corrupted by local…

The von Mises-Fisher distribution as an exponential family can be expressed in terms of either its natural or its mean parameters. Unfortunately, however, the normalization function for the distribution in terms of its mean parameters is…

A statistical framework is introduced for a broad class of problems involving synchronization or registration of data across a sensor network in the presence of noise. This framework enables an estimation-theoretic approach to the design…

Despite superior performance in many situations, deep neural networks are often vulnerable to adversarial examples and distribution shifts, limiting model generalization ability in real-world applications. To alleviate these problems,…