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We study the estimation of a high dimensional approximate factor model in the presence of both cross sectional dependence and heteroskedasticity. The classical method of principal components analysis (PCA) does not efficiently estimate the…
Estimates of the approximate factor model are increasingly used in empirical work. Their theoretical properties, studied some twenty years ago, also laid the ground work for analysis on large dimensional panel data models with cross-section…
The implicit theory that a simulation represents is precisely not in the individual choices but rather in the 'envelope' of possible trajectories - what is important is the shape of the whole envelope. Typically a huge amount of computation…
Factor Analysis has traditionally been utilized across diverse disciplines to extrapolate latent traits that influence the behavior of multivariate observed variables. Historically, the focus has been on analyzing data from a single study,…
The naive application of Reinforcement Learning algorithms to continuous control problems -- such as locomotion and manipulation -- often results in policies which rely on high-amplitude, high-frequency control signals, known colloquially…
Unidimensional factor models justify some of the most consequential summaries in science -- single scores, single ranks, and single leaderboards -- yet unidimensionality is usually assessed indirectly by fitting and evaluating models on…
Model-based reinforcement learning is a powerful tool, but collecting data to fit an accurate model of the system can be costly. Exploring an unknown environment in a sample-efficient manner is hence of great importance. However, the…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We consider a class of reinforcement-learning systems in which the agent follows a behavior policy to explore a discrete state-action space to find an optimal policy while adhering to some restriction on its behavior. Such restriction may…
In exploratory factor analysis, model parameters are usually estimated by maximum likelihood method. The maximum likelihood estimate is obtained by solving a complicated multivariate algebraic equation. Since the solution to the equation is…
A novel unsupervised learning method is proposed in this paper for biclustering large-dimensional matrix-valued time series based on an entirely new latent two-way factor structure. Each block cluster is characterized by its own row and…
Submodular functions and their optimization have found applications in diverse settings ranging from machine learning and data mining to game theory and economics. In this work, we consider the constrained maximization of a submodular…
Factor Analysis based on multivariate $t$ distribution ($t$fa) is a useful robust tool for extracting common factors on heavy-tailed or contaminated data. However, $t$fa is only applicable to vector data. When $t$fa is applied to matrix…
Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…
In optimal experimental design, the objective is to select a limited set of experiments that maximizes information about unknown model parameters based on factor levels. This work addresses the generalized D-optimal design problem, allowing…
Matrix factorization is a key tool in data analysis; its applications include recommender systems, correlation analysis, signal processing, among others. Binary matrices are a particular case which has received significant attention for…
Factor analysis is a classical data reduction technique that seeks a potentially lower number of unobserved variables that can account for the correlations among the observed variables. This paper presents an extension of the factor…
Pervasive cross-section dependence is increasingly recognized as a characteristic of economic data and the approximate factor model provides a useful framework for analysis. Assuming a strong factor structure where $\Lop\Lo/N^\alpha$ is…
The exploration-exploitation dilemma in reinforcement learning (RL) is a fundamental challenge to efficient RL algorithms. Existing algorithms for finite state and action discounted RL problems address this by assuming sufficient…
Many scientific questions in biomedical, environmental, and psychological research involve understanding the effects of multiple factors on outcomes. While factorial experiments are ideal for this purpose, randomized controlled treatment…