We are in the middle of a remarkable rise in the use and capability of artificial intelligence. Much of this growth has been fueled by the success of deep learning architectures: models that map from observables to outputs via multiple layers of latent representations. These deep learning algorithms are effective tools for unstructured prediction, and they can be combined in AI systems to solve...

We consider regression when the predictor is measured with error and an instrumental variable is available. The regression function can be modeled linearly, nonlinearly, or nonparametrically. Our major new result shows that the regression function and all parameters in the measurement error model are identified under relatively weak conditions, much weaker than previously known to imply identif...

Instrumental-variable (IV) methods were invented over 70 years ago, but remain uncommon in epidemiology. Over the past decade or so, non-parametric versions of IV methods have appeared that connect IV methods to causal and measurement-error models important in epidemiological applications. This paper provides an introduction to those developments, illustrated by an application of IV methods to ...

In this note, we propose to use sparse methods (e.g. LASSO, Post-LASSO, √ LASSO, and Post√ LASSO) to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p, in the canonical Gaussian case. The methods apply even when p is much larger than the sample size, n. We derive asymptotic distributions for the resulting IV estim...

The framework of this paper is supervised learning using classification trees. Two types of variables play a role in the definition of the classification rule, namely a response variable and a set of predictors. The tree classifier is built up by a recursive partitioning of the prediction space such to provide internally homogeneous groups of objects with respect to the response classes. In the...

In this paper a new class of Instrumental Variables estimators for linear processes and in particular ARMA models is developed. Previously, IV estimators based on lagged observations as instruments have been used to account for unmodelled MA(q) errors in the estimation of the AR parameters. Here it is shown that these IV methods can be used to improve efficiency of linear time series estimators...

As is well understood among clinical researchers, medical diagnoses often suffer from substantial measurement error. This is particularly true for mental health diagnoses.1 Reliance on inaccurate diagnosis indicators can substantially compromise researchers’ and clinicians’ ability to reliably evaluate treatment approaches, measure clinical progress, or estimate relationships between patient at...

In nonparametric instrumental variables estimation, the function being estimated is the solution to an integral equation. A solution may not exist if, for example, the instrument is not valid. This paper discusses the problem of testing the null hypothesis that a solution exists against the alternative that there is no solution. We give necessary and sufficient conditions for existence of a sol...

My 1997 JHR paper neither endorsed nor condemned the use of instrumental variables (IV) to estimate the parameters of economic models. Its main goal was to remind readers of some basic points developed in a series of papers with Richard Robb (1985, 1986), We establish that when responses to "treatment" or a policy intervention vary across persons even after conditioning on observable variables ...