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Recently, there has been a surge in methodological development for the difference-in-differences (DiD) approach to evaluate causal effects. Standard methods in the literature rely on the parallel trends assumption to identify the average…
The instrumental variable (IV) design is a common approach to address hidden confounding bias. For validity, an IV must impact the outcome only through its association with the treatment. In addition, IV identification has required a…
We study the relationship between model complexity and out-of-sample performance in the context of mean-variance portfolio optimization. Representing model complexity by the number of assets, we find that the performance of low-dimensional…
The Doubly Robust (DR) estimation of ATE can be carried out in 2 steps, where in the first step, the treatment and outcome are modeled, and in the second step the predictions are inserted into the DR estimator. The model misspecification in…
I analyze a linear instrumental variables model with a single endogenous regressor and many instruments. I use invariance arguments to construct a new minimum distance objective function. With respect to a particular weight matrix, the…
In this paper, we investigate the matrix estimation problem in the multi-response regression model with measurement errors. A nonconvex error-corrected estimator based on a combination of the amended loss function and the nuclear norm…
This paper presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error…
Multireference alignment (MRA) refers to the problem of recovering a signal from noisy samples subject to random circular shifts. Expectation--maximization (EM) and variational approaches use statistical modeling to achieve high accuracy at…
The study on the implicit regularization induced by gradient-based optimization is a longstanding pursuit. In the present paper, we characterize the implicit regularization of momentum gradient descent (MGD) with early stopping by comparing…
We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on…
We present a uniform analysis of biased stochastic gradient methods for minimizing convex, strongly convex, and non-convex composite objectives, and identify settings where bias is useful in stochastic gradient estimation. The framework we…
We propose a multi-threshold change plane regression model which naturally partitions the observed subjects into subgroups with different covariate effects. The underlying grouping variable is a linear function of covariates and thus…
To improve the efficiency of Monte Carlo estimation, practitioners are turning to biased Markov chain Monte Carlo procedures that trade off asymptotic exactness for computational speed. The reasoning is sound: a reduction in variance due to…
This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a…
Randomized experiments are the gold standard for evaluating the effects of changes to real-world systems. Data in these tests may be difficult to collect and outcomes may have high variance, resulting in potentially large measurement error.…
Randomized mechanisms, which map a set of bids to a probability distribution over outcomes rather than a single outcome, are an important but ill-understood area of computational mechanism design. We investigate the role of randomized…
In this paper, we discuss causal inference on the efficacy of a treatment or medication on a time-to-event outcome with competing risks. Although the treatment group can be randomized, there can be confoundings between the compliance and…
Nonparametric Instrumental Variables (NPIV) analysis is based on a conditional moment restriction. We show that if this moment condition is even slightly misspecified, say because instruments are not quite valid, then NPIV estimates can be…
Randomized matrix algorithms have become workhorse tools in scientific computing and machine learning. To use these algorithms safely in applications, they should be coupled with posterior error estimates to assess the quality of the…
Model selection aims to identify a sufficiently well performing model that is possibly simpler than the most complex model among a pool of candidates. However, the decision-making process itself can inadvertently introduce non-negligible…