A grand challenge in machine learning is the development of computational algorithms that match or outperform humans in perceptual inference tasks that are complicated by nuisance variation. For instance, visual object recognition involves the unknown object position, orientation, and scale, while speech recognition involves the unknown voice pronunciation, pitch, and speed. Recently, a new breed of deep learning algorithms have emerged for high-nuisance inference tasks that routinely yield pattern recognition systems with super-human capabilities. Similar results in language translation, robotics, and games like Chess and Go plus billions of dollars in venture capital have fueled a deep learning bubble and public perception that actual progress is being made towards general artificial intelligence. But fundamental questions remain, such as: Why do deep learning methods work? When do they work? And how can they be fixed when they don't work? Intuitions abound, but a coherent framework for understanding, analyzing, and synthesizing deep learning architectures remains elusive. This talk will discuss the important implications of this lack of understanding for consumers, practitioners, and researchers of machine learning. We will also briefly overview recent progress on answering the above questions based on probabilistic graphs and splines.

In two phase materials, each phase having a non-local response in time, we were surprised to discover that for appropriate driving fields the response somehow untangles at specific times, allowing one to directly infer useful information about the geometry of the material, such as the volume fractions of the phases. The underlying mathematics, showing how the appropriate driving fields may be designed, rests on the existence of approximate, measure independent, linear relations between the values that Markov functions take at a given set of possibly complex points, not belonging to the interval [-1,1] where the measure is supported. The problem is reduced to simply one of polynomial approximation of a given function on the interval [-1,1]. This allows one to obtain explicit estimates of the error of the approximation, in terms of the number of points and the minimum distance of the points to the interval [-1,1]. In the context of the motivating problem, the analysis also yields bounds on the response at any particular time for any driving field, and allows one to estimate the response at a given frequency using an appropriately designed driving field that effectively is turned on only for a fixed interval of time. The approximation extends directly to Markov-type functions with a positive semi-definite operator valued measure, and this has applications to determining the shape of an inclusion in a body from boundary flux measurements at a specific time, when the time-dependent boundary potentials are suitably tailored. This is joint work with Ornella Mattei and Mihai Putinar.

Almost all decisions made in the upstream oil and gas industry, from exploration to development and production, must account for subsurface uncertainty. Despite advances in computational and data sciences, effective decision support under subsurface uncertainty remains extremely challenging. In this talk, a holistic view of the key components, both technical and cognitive, involved in the decision support process are presented. Both decision making and inference are approached from a Bayesian point of view. We review the computational challenges and some recent progresses. The need to manage computational complexity through goal-oriented inference (GOI) is highlighted. In addition, we examine the challenges associated with specification of priors and validation of the efficacy of the decision process, which are of fundamental importance in practice but have received relatively little attention in research.

Forward performance processes are defined via time-consistent optimality and incorporate "real-time" incoming information. On the other hand, popular performance criteria - for example, mean-variance optimization, hyperbolic discounting, probability distortions - are by nature time-inconsistent. How to define forward performance criteria in time-inconsistent settings then becomes a challenging problem, both conceptually and technically. In this talk, I will discuss the case of probability distortions and introduce the concept of forward rank-dependent performance processes. Among others, I will show how forward probability distortions are affected by “real-time” changes in the stochastic environment and, also, present a striking equivalence between forward rank-dependent criteria and time-monotone forward processes under appropriate measure-changes. A byproduct of the work is a novel result on the so-called dynamic utilities and on time-inconsistent problems in the classical (backward) setting.