Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This talk develops new provably correct algorithms for solving large SDP problems by economizing on both the storage and the arithmetic costs. We present two methods: one based on sketching, and the other on complementarity. Numerical evidence shows that these methods are effective for a range of applications, including relaxations of MaxCut, abstract phase retrieval, and quadratic assignment, and can handle SDP instances where the matrix variable has over 10^13 entries.

We review targeted minimum loss estimation (TMLE), which provides a general template for the construction of asymptotically efficient plug-in estimators of a target estimand for infinite dimensional models.

We consider a class of distributed non-convex optimization problems, in which a number of agents are connected by a communication network, and they collectively optimize a sum of (possibly non-convex and non-smooth) local objective functions. This type of problem has gained some recent popularities, especially in the application of distributed training of deep neural networks.

Machine learning algorithms are ubiquitous in most scientific, industrial and personal domains, with many successful applications. As a scientific field, machine learning has always been characterized by the constant exchanges between theory and practice, with a stream of algorithms that exhibit both good empirical performance on real-world problems and some form of theoretical guarantees.

Stochastic iterative methods lie at the core of large-scale optimization and its modern applications to data science. Though such algorithms are routinely and successfully used in practice on highly irregular problems (e.g. deep neural networks), few performance guarantees are available outside of smooth or convex settings. In this talk, I will describe a framework for designing and analyzing stochastic methods on a large class of nonsmooth and nonconvex problems, with provable efficiency guarantees.

In many real-world problems learners cannot directly observe their own rewards but can still infer whether some particular action is successful. How should a learner take actions to balance its need of information while maximizing their reward in this setting? Partial monitoring is a framework introduced a few decades ago to model learning…

Tensor decomposition discovers latent structure in higher-order data sets and is the higher-order analogue of the matrix decomposition.

Discrete structure recovery is an important topic in modern high-dimensional inference. Examples of discrete structure include clustering labels, ranks of players, and signs of variables in a regression model.

Recent events have made evident the fact that algorithms can be discriminatory, reinforce human prejudices, accelerate the spread of misinformation, and are generally not as objective as they are widely thought to be.

We consider the properties and performance of word embeddings techniques in the context of political science research. In particular, we explore key parameter choices—including context window length, embedding vector dimensions and the use of pre-trained vs locally fit variants—with respect to efficiency and quality of inferences possible with these models. Reassuringly we show that results are generally robust to such choices for political corpora of various sizes and in various languages.