相关论文: Direction Selection in Stochastic Directional Dist…

The Short-Time Fourier Transform (STFT) has been a staple of signal processing, often being the first step for many audio tasks. A very familiar process when using the STFT is the search for the best STFT parameters, as they often have…

We study efficiency of non-parametric estimation of diffusions (stochastic differential equations driven by Brownian motion) from long stationary trajectories. First, we introduce estimators based on conditional expectation which is…

We present a method for providing statistical guarantees on runtime safety and goal reachability for integrated planning and control of a class of systems with unknown nonlinear stochastic underactuated dynamics. Specifically, given a…

Sufficient dimension reduction is a powerful tool to extract core information hidden in the high-dimensional data and has potentially many important applications in machine learning tasks. However, the existing nonlinear sufficient…

We formulate and study a general family of (continuous-time) stochastic dynamics for accelerated first-order minimization of smooth convex functions. Building on an averaging formulation of accelerated mirror descent, we propose a…

Stochastic convex optimization problems with nonlinear functional constraints are ubiquitous in signal processing applications including constrained least-squares, set-membership adaptive filtering, and trajectory optimization under…

Distortion Risk Measures (DRMs) capture risk preferences in decision-making and serve as general criteria for managing uncertainty. This paper proposes gradient descent algorithms for DRM optimization based on two dual representations: the…

We consider the estimation of the slope function in functional linear regression, where scalar responses are modeled in dependence of random functions. Cardot and Johannes [J. Multivariate Anal. 101 (2010) 395-408] have shown that a…

Reliability estimation of Machine Learning (ML) models is becoming a crucial subject. This is particularly the case when such \mbox{models} are deployed in safety-critical applications, as the decisions based on model predictions can result…

We consider a problem of statistical estimation of an unknown drift parameter for a stochastic differential equation driven by fractional Brownian motion. Two estimators based on discrete observations of solution to the stochastic…

Safe operation of systems such as robots requires them to plan and execute trajectories subject to safety constraints. When those systems are subject to uncertainties in their dynamics, it is challenging to ensure that the constraints are…

We develop a formalism for calculating forces on the nuclei within the linear-scaling stochastic density functional theory (sDFT) in a nonorthogonal atom-centered basis-set representation (Fabian et al. WIREs Comput Mol Sci. 2019;e1412.…

The availability of massive vehicle trajectory data enables the modeling of road-network constrained movement as travel-cost distributions rather than just single-valued costs, thereby capturing the inherent uncertainty of movement and…

Nonparametric estimators for the mean and the covariance functions of functional data are proposed. The setup covers a wide range of practical situations. The random trajectories are, not necessarily differentiable, have unknown regularity,…

Understanding stochastic gradient descent (SGD) and its variants is essential for machine learning. However, most of the preceding analyses are conducted under amenable conditions such as unbiased gradient estimator and bounded objective…

This paper addresses the question of whether it can be beneficial for an optimization algorithm to follow directions of negative curvature. Although prior work has established convergence results for algorithms that integrate both descent…

The use of proximal point operators for optimization can be computationally expensive when the dimensionality of a function (i.e., the number of variables) is high. In this study, we sought to reduce the cost of calculating proximal point…

Understanding the implicit bias of training algorithms is of crucial importance in order to explain the success of overparametrised neural networks. In this paper, we study the dynamics of stochastic gradient descent over diagonal linear…

We present a stochastic descent algorithm for unconstrained optimization that is particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and…

This work proposes a framework, embedded within the Performance Estimation framework (PEP), for obtaining worst-case performance guarantees on stochastic first-order methods. Given a first-order method, a function class, and a noise model…