48 research outputs found
Breaking the curse of dimensionality in regression
Models with many signals, high-dimensional models, often impose structures on
the signal strengths. The common assumption is that only a few signals are
strong and most of the signals are zero or close (collectively) to zero.
However, such a requirement might not be valid in many real-life applications.
In this article, we are interested in conducting large-scale inference in
models that might have signals of mixed strengths. The key challenge is that
the signals that are not under testing might be collectively non-negligible
(although individually small) and cannot be accurately learned. This article
develops a new class of tests that arise from a moment matching formulation. A
virtue of these moment-matching statistics is their ability to borrow strength
across features, adapt to the sparsity size and exert adjustment for testing
growing number of hypothesis. GRoup-level Inference of Parameter, GRIP, test
harvests effective sparsity structures with hypothesis formulation for an
efficient multiple testing procedure. Simulated data showcase that GRIPs error
control is far better than the alternative methods. We develop a minimax
theory, demonstrating optimality of GRIP for a broad range of models, including
those where the model is a mixture of a sparse and high-dimensional dense
signals.Comment: 51 page
An Exact and Robust Conformal Inference Method for Counterfactual and Synthetic Controls
We introduce new inference procedures for counterfactual and synthetic
control methods for policy evaluation. We recast the causal inference problem
as a counterfactual prediction and a structural breaks testing problem. This
allows us to exploit insights from conformal prediction and structural breaks
testing to develop permutation inference procedures that accommodate modern
high-dimensional estimators, are valid under weak and easy-to-verify
conditions, and are provably robust against misspecification. Our methods work
in conjunction with many different approaches for predicting counterfactual
mean outcomes in the absence of the policy intervention. Examples include
synthetic controls, difference-in-differences, factor and matrix completion
models, and (fused) time series panel data models. Our approach demonstrates an
excellent small-sample performance in simulations and is taken to a data
application where we re-evaluate the consequences of decriminalizing indoor
prostitution
A sufficient and necessary condition for identification of binary choice models with fixed effects
We study the identification of binary choice models with fixed effects. We
provide a condition called sign saturation and show that this condition is
sufficient for the identification of the model. In particular, we can guarantee
identification even with bounded regressors. We also show that without this
condition, the model is never identified unless the error distribution belongs
to a small class. A test is provided to check the sign saturation condition and
can be implemented using existing algorithms for the maximum score estimator.
We also discuss the practical implication of our results
Sparsity Double Robust Inference of Average Treatment Effects
Many popular methods for building confidence intervals on causal effects
under high-dimensional confounding require strong "ultra-sparsity" assumptions
that may be difficult to validate in practice. To alleviate this difficulty, we
here study a new method for average treatment effect estimation that yields
asymptotically exact confidence intervals assuming that either the conditional
response surface or the conditional probability of treatment allows for an
ultra-sparse representation (but not necessarily both). This guarantee allows
us to provide valid inference for average treatment effect in high dimensions
under considerably more generality than available baselines. In addition, we
showcase that our results are semi-parametrically efficient
Semidiscrete optimal transport with unknown costs
Semidiscrete optimal transport is a challenging generalization of the
classical transportation problem in linear programming. The goal is to design a
joint distribution for two random variables (one continuous, one discrete) with
fixed marginals, in a way that minimizes expected cost. We formulate a novel
variant of this problem in which the cost functions are unknown, but can be
learned through noisy observations; however, only one function can be sampled
at a time. We develop a semi-myopic algorithm that couples online learning with
stochastic approximation, and prove that it achieves optimal convergence rates,
despite the non-smoothness of the stochastic gradient and the lack of strong
concavity in the objective function