Machine Learning for Set-Identified Linear Models

This paper provides estimation and inference methods for an identified set where the selection among a very large number of covariates is based on modern machine learning tools. I characterize the boundary of the identified set (i.e., support function) using a semiparametric moment condition. Combining Neyman-orthogonality and sample splitting ideas, I construct a root-N consistent, uniformly asymptotically Gaussian estimator of the support function and propose a weighted bootstrap procedure to conduct inference about the identified set. I provide a general method to construct a Neyman-orthogonal moment condition for the support function. Applying my method to Lee (2008)'s endogenous selection model, I provide the asymptotic theory for the sharp (i.e., the tightest possible) bounds on the Average Treatment Effect in the presence of high-dimensional covariates. Furthermore, I relax the conventional monotonicity assumption and allow the sign of the treatment effect on the selection (e.g., employment) to be determined by covariates. Using JobCorps data set with very rich baseline characteristics, I substantially tighten the bounds on the JobCorps effect on wages under weakened monotonicity assumption

Certifying and removing disparate impact

What does it mean for an algorithm to be biased? In U.S. law, unintentional bias is encoded via disparate impact, which occurs when a selection process has widely different outcomes for different groups, even as it appears to be neutral. This legal determination hinges on a definition of a protected class (ethnicity, gender, religious practice) and an explicit description of the process. When the process is implemented using computers, determining disparate impact (and hence bias) is harder. It might not be possible to disclose the process. In addition, even if the process is open, it might be hard to elucidate in a legal setting how the algorithm makes its decisions. Instead of requiring access to the algorithm, we propose making inferences based on the data the algorithm uses. We make four contributions to this problem. First, we link the legal notion of disparate impact to a measure of classification accuracy that while known, has received relatively little attention. Second, we propose a test for disparate impact based on analyzing the information leakage of the protected class from the other data attributes. Third, we describe methods by which data might be made unbiased. Finally, we present empirical evidence supporting the effectiveness of our test for disparate impact and our approach for both masking bias and preserving relevant information in the data. Interestingly, our approach resembles some actual selection practices that have recently received legal scrutiny.Comment: Extended version of paper accepted at 2015 ACM SIGKDD Conference on Knowledge Discovery and Data Minin

Interpretable statistics for complex modelling: quantile and topological learning

As the complexity of our data increased exponentially in the last decades, so has our need for interpretable features. This thesis revolves around two paradigms to approach this quest for insights. In the first part we focus on parametric models, where the problem of interpretability can be seen as a “parametrization selection”. We introduce a quantile-centric parametrization and we show the advantages of our proposal in the context of regression, where it allows to bridge the gap between classical generalized linear (mixed) models and increasingly popular quantile methods. The second part of the thesis, concerned with topological learning, tackles the problem from a non-parametric perspective. As topology can be thought of as a way of characterizing data in terms of their connectivity structure, it allows to represent complex and possibly high dimensional through few features, such as the number of connected components, loops and voids. We illustrate how the emerging branch of statistics devoted to recovering topological structures in the data, Topological Data Analysis, can be exploited both for exploratory and inferential purposes with a special emphasis on kernels that preserve the topological information in the data. Finally, we show with an application how these two approaches can borrow strength from one another in the identification and description of brain activity through fMRI data from the ABIDE project

Non Parametric Models with Instrumental Variables

This paper gives a survey of econometric models characterized by a relation between observable and unobservable random elements where these unobservable terms are assumed to be independent of another set of observable variables called instrumental variables. This kind of specification is usefull to address the question of endogeneity or of selection bias for example. These models are treated non parametrically and in all the example we consider the functional parameter of interest is defined as the solution of a linear or non linear integral equation. The estimation procedure then requires to solve a (generally ill-posed) inverse problem. We illustrate the main questions (construction of the equation, identification, numerical solution, asymptotic properties, selection of the regularization parameter) by the different models we present.