Section: Research Program

Robustness to outliers and heavy tails (with tractable algorithms)

The classical theory of robustness in statistics has recently received a lot of attention in the machine learning community. The reason is simple: large datasets are easily corrupted, due to – for instance – storage and transmission issues, and most learning algorithms are highly sensitive to dataset corruption. For example, the lasso can be completely misled by the presence of even a single outlier in a dataset. A major challenge in robust learning is to provide computationally tractable estimators with optimal subgaussian guarantees. A second important challenge in robust learning is to deal with datasets where every $(x_i,y_i)$ is slightly corrupted. In large-dimensional data, every single data point $x_i$ is likely to have several corrupted coordinates, and no estimator currently has strong theoretical guarantees for such data. A third important challenge is that of robust estimator selection or aggregation. Even if several robust estimators can be built, the final aggregation or selection step in a user's routine is usually based on empirical means. This is not robust, and may damage the global performance of the procedure. Instead, we can consider more sophisticated types of aggregation of the base robust estimators built so far. A convenient framework to do so is called adversarial learning (also known as: prediction of individual sequences). Here, data is not assumed to be stochastic, and it could even be chosen by an adversary.