Related papers: Data Analysis: Generalizations of the Local Approx…
Sample average approximation (SAA) is a technique for obtaining approximate solutions to stochastic programs that uses the average from a random sample to approximate the expected value that is being optimized. Since the outcome from…
The Metropolis process (MP) and Simulated Annealing (SA) are stochastic local search heuristics that are often used in solving combinatorial optimization problems. Despite significant interest, there are very few theoretical results…
The method of extrapolating asymptotic series, based on the Self-Similar Approximation Theory, is developed. Several important questions are answered, which makes the foundation of the method unambiguous and its application straightforward.…
Sample average approximation (SAA), a popular method for tractably solving stochastic optimization problems, enjoys strong asymptotic performance guarantees in settings with independent training samples. However, these guarantees are not…
Extensions of singular spectrum analysis (SSA) for processing of non-rectangular images and time series with gaps are considered. A circular version is suggested, which allows application of the method to the data given on a circle or on a…
This paper presents a local energy distribution based hyperparameter determination for stochastic simulated annealing (SSA). SSA is capable of solving combinatorial optimization problems faster than typical simulated annealing (SA), but…
We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
We consider stochastic optimization problems which use observed data to estimate essential characteristics of the random quantities involved. Sample average approximation (SAA) or empirical (plug-in) estimation are very popular ways to use…
We consider a new class of Parareal algorithms, which use ideas from localized reduced basis methods to construct the coarse solver from spectral approximations of the transfer operators mapping initial values for a given time interval to…
Two-timescale Stochastic Approximation (SA) algorithms are widely used in Reinforcement Learning (RL). Their iterates have two parts that are updated using distinct stepsizes. In this work, we develop a novel recipe for their finite sample…
Spatial autoregressive (SAR) models are important tools for studying network effects. However, with an increasing emphasis on data privacy, data providers often implement privacy protection measures that make classical SAR models…
Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…
We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function…
We consider a setting in which $N$ agents aim to speedup a common Stochastic Approximation (SA) problem by acting in parallel and communicating with a central server. We assume that the up-link transmissions to the server are subject to…
Due to the complicated procedure and costly hardware, Simultaneous Localization and Mapping (SLAM) has been heavily dependent on public datasets for drill and evaluation, leading to many impressive demos and good benchmark scores. However,…
Data augmentation is widely used for machine learning; however, an effective method to apply data augmentation has not been established even though it includes several factors that should be tuned carefully. One such factor is sample…
In the transformative landscape of smart cities, the integration of the cutting-edge web technologies into time series forecasting presents a pivotal opportunity to enhance urban planning, sustainability, and economic growth. The…
This paper presents a new method for spatially adaptive local (constant) likelihood estimation which applies to a broad class of nonparametric models, including the Gaussian, Poisson and binary response models. The main idea of the method…
Stochastic Approximation (SA) is a popular approach for solving fixed-point equations where the information is corrupted by noise. In this paper, we consider an SA involving a contraction mapping with respect to an arbitrary norm, and show…