Improved domain shift methods

Most prediction methods assume that the sample that is used to train the model has the same distribution as the sample one wishes to predict. However, such an assumption is often unreasonable. We develop methods that are able to improve predictions in such settings.

Nonparametric inference in high dimensions

Because of the large volume of data available today, in several applications nonparametric methods have been gaining attention, since they allow one to make less assumptions about the data generating process. We are interested in developing nonparametric methods that can be used for settings where the number of covariates is also large. This poses several interesting computational and statistical problems that we address in our research.

Interpretability and efficiency in hypothesis tests

Hypothesis testing is a very common and widespread statistical tool. Unfortunately, such methodology still presents several challenges to statisticians and practitioners. For example, if A and B are two null hypothesis such that A implies B, there exist tests that, based on the same data, don’t reject A and reject B. Such outcomes are generally inconvenient to statisticians (who want to communicate the results to practitioners in a simple fashion) and non-statisticians (confused by conflicting pieces of information). Our work focuses on investigating how far one can have tests that are coherent in a logical sense, but that also have good statistical performance. We have also been developing agnostic hypothesis tests, in which one can accept, reject or remain agnostic with respect to a given hypothesis.

Bayesian methods

Bayesian methods are known to provide improved solutions for several prediction problems because they offer meningful regularization based on prior information. We have been applying Bayesian methods to solve many statistical and machine learning problems.

Interpretable Machine Learning

In practice, predictive power is not enough. In most problems, solutions that are only useful if they are easy to interpret.

Foundations of statistics

Understanding the foundations of statistics is key to developing meaningful applications.

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