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The modified Method of Successive Approximations (MSA) is an iterative scheme for approximating solutions to stochastic control problems in continuous time based on Pontryagin Optimality Principle which, starting with an initial open loop…
There is growing interest in improving our algorithmic understanding of fundamental statistical problems such as mean estimation, driven by the goal of understanding the limits of what we can extract from valuable data. The state of the art…
Recent research has revived and amplified interest in algorithms for undiscounted average reward reinforcement learning in infinite-horizon, non-episodic (continuing) tasks. Semi-Markov decision processes (SMDPs) are of particular interest.…
We address the problem of sequentially selecting and observing processes from a given set to find the anomalies among them. The decision-maker observes a subset of the processes at any given time instant and obtains a noisy binary indicator…
When the individual studies assembled for a meta-analysis report means ($\mu_C$, $\mu_T$) for their treatment (T) and control (C) arms, but those data are on different scales or come from different instruments, the customary measure of…
An empirical best linear unbiased prediction (EBLUP) estimator is utilized for efficient inference in small-area estimation. To measure its uncertainty, we need to estimate its mean squared error (MSE) since the true MSE cannot generally be…
Partially observable Markov decision processes (POMDPs) is a rich mathematical framework that embraces a large class of complex sequential decision-making problems under uncertainty with limited observations. However, the complexity of…
Stochastic optimization finds a wide range of applications in operations research and management science. However, existing stochastic optimization techniques usually require the information of random samples (e.g., demands in the…
We present a procedure that adds a number of desirable features to standard exponential analysis algorithms, among which output reliability, a divide-and-conquer approach, the automatic detection of the exponential model order, robustness…
In this paper we propose a new iterative algorithm to solve the fair PCA (FPCA) problem. We start with the max-min fair PCA formulation originally proposed in [1] and derive a simple and efficient iterative algorithm which is based on the…
Contemporary domain adaptation methods are very effective at aligning feature distributions of source and target domains without any target supervision. However, we show that these techniques perform poorly when even a few labeled examples…
The propensity score (PS) is often used to control for large numbers of covariates in high-dimensional healthcare database studies. The least absolute shrinkage and selection operator (LASSO) has become the most widely used tool for fitting…
The problem of estimating ARMA models is computationally interesting due to the nonconcavity of the log-likelihood function. Recent results were based on the convex minimization. Joint model selection using penalization by a convex norm,…
We consider learning problems over training sets in which both, the number of training examples and the dimension of the feature vectors, are large. To solve these problems we propose the random parallel stochastic algorithm (RAPSA). We…
Optimizer is an essential component for the success of deep learning, which guides the neural network to update the parameters according to the loss on the training set. SGD and Adam are two classical and effective optimizers on which…
The combination of reduced basis and collocation methods enables efficient and accurate evaluation of the solutions to parameterized PDEs. In this paper, we study the stochastic collocation methods that can be combined with reduced basis…
In high dimensions, most machine learning methods are brittle to even a small fraction of structured outliers. To address this, we introduce a new meta-algorithm that can take in a base learner such as least squares or stochastic gradient…
The Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) is one of the most advanced algorithms in numerical black-box optimization. For noisy objective functions, several approaches were proposed to mitigate the noise, e.g.,…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
This study presents an application of machine learning (ML) methods for detecting the presence of stenoses and aneurysms in the human arterial system. Four major forms of arterial disease -- carotid artery stenosis (CAS), subclavian artery…