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We develop a fully discrete, semi-implicit mixed finite element method for approximating solutions to a class of fourth-order stochastic partial differential equations (SPDEs) with non-globally Lipschitz and non-monotone nonlinearities,…

This paper provides a new approach to derive various arbitrary high order finite difference formulae for the numerical differentiation of analytic functions. In this approach, various first and second order formulae for the numerical…

A new algorithm for estimating the time-varying frequency of a noiseless sinusoidal signal is considered. It is assumed that the amplitude and frequency of the sinusoidal signal are unknown functions of time, but are solutions of linear…

Estimators of doubly robust functionals typically rely on estimating two complex nuisance functions, such as the propensity score and conditional outcome mean for the average treatment effect functional. We consider the problem of how to…

Quantization has become a predominant approach for model compression, enabling deployment of large models trained on GPUs onto smaller form-factor devices for inference. Quantization-aware training (QAT) optimizes model parameters with…

Stochastic optimization is fundamental to modern machine learning. Recent research has extended the study of stochastic first-order methods (SFOMs) from light-tailed to heavy-tailed noise, which frequently arises in practice, with clipping…

We propose STARS, a randomized derivative-free algorithm for unconstrained optimization when the function evaluations are contaminated with random noise. STARS takes dynamic, noise-adjusted smoothing step-sizes that minimize the…

Approximate group analysis technique, that is, the technique combining the methodology of group analysis and theory of small perturbations, is applied to finite-difference equations approximating ordinary differential equations.…

In this paper we analyze the finite element approximation of the Stokes equations with non-smooth Dirichlet boundary data. To define the discrete solution, we first approximate the boundary datum by a smooth one and then apply a standard…

Our proposal is on a new stochastic optimizer for non-convex and possibly non-smooth objective functions typically defined over large dimensional design spaces. Towards this, we have tried to bridge noise-assisted global search and faster…

Variational inference has become a widely used method to approximate posteriors in complex latent variables models. However, deriving a variational inference algorithm generally requires significant model-specific analysis, and these…

The problem of interest is the minimization of a nonlinear function subject to nonlinear equality constraints using a sequential quadratic programming (SQP) method. The minimization must be performed while observing only noisy evaluations…

Decentralized optimization is typically studied under the assumption of noise-free transmission. However, real-world scenarios often involve the presence of noise due to factors such as additive white Gaussian noise channels or…

The minimization of convex functions which are only available through partial and noisy information is a key methodological problem in many disciplines. In this paper we consider convex optimization with noisy zero-th order information,…

Numerical approximation of a stochastic partial integro-differential equation driven by a space- time white noise is studied by truncating a series representation of the noise, with finite element method for spatial discretization and…

In this paper, the problem of safe global maximization (it should not be confused with robust optimization) of expensive noisy black-box functions satisfying the Lipschitz condition is considered. The notion "safe" means that the objective…

Disturbance noises are always bounded in a practical system, while fusion estimation is to best utilize multiple sensor data containing noises for the purpose of estimating a quantity--a parameter or process. However, few results are…

When measurements from dynamical systems are noisy, it is useful to have estimation algorithms that have low sensitivity to measurement noises and outliers. In the first set of results described in this paper we obtain optimal estimators…

In this paper, we present a unified and general framework for analyzing the batch updating approach to nonlinear, high-dimensional optimization. The framework encompasses all the currently used batch updating approaches, and is applicable…

In this paper, we consider non-smooth stochastic convex optimization with two function evaluations per round under infinite noise variance. In the classical setting when noise has finite variance, an optimal algorithm, built upon the…