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Regularization methods allow one to handle a variety of inferential problems where there are more covariates than cases. This allows one to consider a potentially enormous number of covariates for a problem. We exploit the power of these…
The minimization of a nonconvex composite function can model a variety of imaging tasks. A popular class of algorithms for solving such problems are majorization-minimization techniques which iteratively approximate the composite nonconvex…
The economic and financial variables of economic agents determine macroeconomic variables. Current models consider agents' variables that are determined by the sums of values and volumes of agents' trades during some time interval {\Delta}.…
In most social choice settings, the participating agents express their preferences over the different alternatives in the form of linear orderings. While this clearly simplifies preference elicitation, it inevitably leads to poor…
We study the power of menus of contracts in principal-agent problems with adverse selection (agents can be one of several types) and moral hazard (we cannot observe agent actions directly). For principal-agent problems with $T$ types and…
Mean Field Games (MFGs) can potentially scale multi-agent systems to extremely large populations of agents. Yet, most of the literature assumes a single initial distribution for the agents, which limits the practical applications of MFGs.…
Becker (1973) presents a bilateral matching model in which scalar types describe agents. For this framework, he establishes the conditions under which positive sorting between agents' attributes is the unique market outcome. Becker's…
We propose a multiple imputation method based on principal component analysis (PCA) to deal with incomplete continuous data. To reflect the uncertainty of the parameters from one imputation to the next, we use a Bayesian treatment of the…
While generalizing well over natural inputs, neural networks are vulnerable to adversarial inputs. Existing defenses against adversarial inputs have largely been detached from the real world. These defenses also come at a cost to accuracy.…
We study principal components analyses in multivariate random and mixed effects linear models, assuming a spherical-plus-spikes structure for the covariance matrix of each random effect. We characterize the behavior of outlier sample…
In univariate data, there exist standard procedures for identifying dominating features that produce the largest observations. However, in the multivariate setting, the situation is quite different. This paper aims to provide tools and…
We study a bilevel \emph{max-max} optimization framework for principal-agent contract design, in which a principal chooses incentives to maximize utility while anticipating the agent's best response. This problem, central to moral hazard…
Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…
Multivalued treatment models have typically been studied under restrictive assumptions: ordered choice, and more recently unordered monotonicity. We show how treatment effects can be identified in a more general class of models that allows…
Modeling the purposeful behavior of imperfect agents from a small number of observations is a challenging task. When restricted to the single-agent decision-theoretic setting, inverse optimal control techniques assume that observed behavior…
Through the lense of multilevel model (MLM) specification and regularization, this is a connect-the-dots introductory summary of Small Area Estimation, e.g. small group prediction informed by a complex sampling design. While a comprehensive…
We investigate the power of randomness in the context of a fundamental Bayesian optimal mechanism design problem--a single seller aims to maximize expected revenue by allocating multiple kinds of resources to "unit-demand" agents with…
We consider the problem of rationalizing choice data by a preference satisfying an arbitrary collection of invariance axioms. Examples of such axioms include quasilinearity, homotheticity, independence-type axioms for mixture spaces,…
Polarization and unexpected correlations between opinions on diverse topics (including in politics, culture and consumer choices) are an object of sustained attention. However, numerous theoretical models do not seem to convincingly explain…
We consider a sequence of successively more restrictive definitions of abstraction for causal models, starting with a notion introduced by Rubenstein et al. (2017) called exact transformation that applies to probabilistic causal models,…