Inverse problems of various flavors span all of science, engineering, and design. Over the last five years, approaches based on neural networks have emerged as the tool of choice for solving such problems. However, a clear theoretical understanding of how well such approaches perform — together with quantitative sample-complexity and …
Several important families of computational and statistical results in machine learning and randomized algorithms rely on statistical independence of data. The scope of such results include the Johnson-Lindenstrauss Lemma (JLL), the Restricted Isometry Property (RIP), regression models, and stochastic optimization. In this talk, we will discuss a new result on …
In this talk, I will present the role of side information, simulators, and GANs for learning with scarce data. In the first part, I will talk about the role of similarity graphs in recommendation systems. In the second part, the role of simulators and GANs will be discussed.
When high-quality labeled training data are unavailable, an alternative is to learn from training sources that are biased in some way. This talk will cover my group’s recent work on three problems where a learner has access to multiple biased sources. First, we consider the problem of classification given multiple …
Fitting a model to a collection of observations is one of the quintessential questions in statistics. The standard assumption is that the data was generated by a model of a given type (e.g., a mixture model). This simplifying assumption is at best only approximately valid, as real datasets are typically …
This will be a two-part talk. In the first part, I will describe a method to sanitize datasets from containing information about sensitive attributes. This method uses adversarial networks to approximate a privacy-utility optimization problem. In the second part, I will describe a new objective in multi-armed stochastic bandits, that …
A restricted Boltzmann machine (RBM) is a type of undirected graphical model with one hidden and one visible layer of variables, where all variables in one layer are conditionally independent given variables in the other layer. In recent years, RBMs have risen to prominence due to their connection to deep …
We consider the global optimization of nonconvex quadratic programs and mixed-integer quadratic programs. We present a family of convex quadratic relaxations which are derived by convexifying nonconvex quadratic functions through perturbations of the quadratic matrix. We investigate the theoretical properties of these quadratic relaxations and show that they are equivalent …
In this talk, the change points of the time series of PM10 of the city of Bogotá are considered. The number of change points and their respective locations are determined using the genetic algorithm. This algorithm considers the interaction of two chromosomes (mother and father) and their mutations, to conceive new generations of descendants …
This talk will focus on how a Lagrangian perspective on dynamics is used to capture the time evolution of complex systems, e.g., granular flows, fluid-solid interaction problems, etc. In this context, the aspects that turn out to be more challenging are tied to the handling of friction, contact, geometry, large …