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An important step in the design of autonomous systems is to evaluate the probability that a failure will occur. In safety-critical domains, the failure probability is extremely small so that the evaluation of a policy through Monte Carlo…

Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to…

Federated learning provides a communication-efficient and privacy-preserving training process by enabling learning statistical models with massive participants while keeping their data in local clients. However, standard federated learning…

The paper studies a fundamental federated learning (FL) problem involving multiple clients with heterogeneous constrained resources. Compared with the numerous training parameters, the computing and communication resources of clients are…

In this paper, we investigate the problem of strong approximation of the solutions of stochastic differential equations (SDEs) when the drift coefficient is given in integral form. We investigate its upper error bounds, in terms of the…

Adam-type optimizers, as a class of adaptive moment estimation methods with the exponential moving average scheme, have been successfully used in many applications of deep learning. Such methods are appealing due to the capability on…

Understanding atomic structures is crucial, yet amorphous materials remain challenging due to their irregular and non-periodic nature. The Wavelet Transform Radial Distribution Function (WT-RDF) offers a physics-based framework for…

The phenomenon of data distribution evolving over time has been observed in a range of applications, calling the needs of adaptive learning algorithms. We thus study the problem of supervised gradual domain adaptation, where labeled data…

In this paper we provide a thorough, rigorous theoretical framework to assess optimality guarantees of sampling-based algorithms for drift control systems: systems that, loosely speaking, can not stop instantaneously due to momentum. We…

For certain types of statistical models, the characteristic function (Fourier transform) is available in closed form, whereas the probability density function has an intractable form, typically as an infinite sum of probability weighted…

We develop a statistical method to learn a molecular Hamiltonian matrix from a time-series of electron density matrices. We extend our previous method to larger molecular systems by incorporating physical properties to reduce…

We present a stochastic method for efficiently computing the solution of time-fractional partial differential equations (fPDEs) that model anomalous diffusion problems of the subdiffusive type. After discretizing the fPDE in space, the…

In this paper, we introduce a new algorithm for rare event estimation based on adaptive importance sampling. We consider a smoothed version of the optimal importance sampling density, which is approximated by an ensemble of interacting…

Adaptive optimization has achieved notable success for distributed learning while extending adaptive optimizer to federated Learning (FL) suffers from severe inefficiency, including (i) rugged convergence due to inaccurate gradient…

Diffusion probability models have shown significant promise in offline reinforcement learning by directly modeling trajectory sequences. However, existing approaches primarily focus on time-domain features while overlooking frequency-domain…

Motion prediction has been studied in different contexts with models trained on narrow distributions and applied to downstream tasks in human motion prediction and robotics. Simultaneously, recent efforts in scaling video prediction have…

One of the significant problems of streaming data classification is the occurrence of concept drift, consisting of the change of probabilistic characteristics of the classification task. This phenomenon destabilizes the performance of the…

We present an adaptive approach for robust learning from corrupted training sets. We identify corrupted and non-corrupted samples with latent Bernoulli variables and thus formulate the learning problem as maximization of the likelihood…

We propose the Fourier Adaptive Lite Diffusion Architecture (FALDA), a novel probabilistic framework for time series forecasting. First, we introduce the Diffusion Model for Residual Regression (DMRR) framework, which unifies…

We provide an overview of high dimensional dynamical systems driven by random matrices, focusing on applications to simple models of learning and generalization in machine learning theory. Using both cavity method arguments and path…