Give us a call or drop by anytime, we endeavor to answer all inquiries within 24 hours.
PO Box 16122 Collins Street West Victoria, Australia
info@domain.com / example@domain.com
Phone: + (066) 0760 0260 / + (057) 0760 0560
Title: Some Results on Label Shift and Label Noise Abstract: In this talk I will discuss distribution shift, both as an obstacle to be overcome to achieve generalization, and as a device for obtaining generalization guarantees. In the first part, I will discuss the problem of label shift, where the proportion among the labels can […]
What are the optimal algorithms for learning from data? Have we found them already, or are better ones out there to be discovered? Making these questions precise, and answering them, requires taking on the mathematically deep interplay between statistical and computational constraints. It also requires reconciling our theoretical toolbox with surprising new phenomena arising from practice, which seem to violate conventional rules of thumb regarding algorithm and model design. I will discuss progress along these lines: in terms of designing new algorithms for basic learning problems, controlling generalization in large statistical models, and understanding key statistical questions for generative modeling.
In this lecture we shall present some recent results on the interplay between control and Machine Learning, and more precisely, Supervised Learning and Universal Approximation. We adopt the perspective of the simultaneous or ensemble control of systems of Residual Neural Networks (ResNets). Roughly, each item to be classified corresponds to a different initial datum for the Cauchy problem of the ResNets, leading to an ensemble of solutions to be driven to the corresponding targets, associated to the labels, by means of the same control. We present a genuinely nonlinear and constructive method, allowing to show that such an ambitious goal can be achieved, estimating the complexity of the control strategies. This property is rarely fulfilled by the classical dynamical systems in Mechanics and the very nonlinear nature of the activation function governing the ResNet dynamics plays a determinant role. It allows deforming half of the phase space while the other half remains invariant, a property that classical models in mechanics do not fulfill. The turnpike property is also analyzed in this context, showing that a suitable choice of the cost functional used to train the ResNet leads to more stable and robust dynamics. This lecture is inspired in joint work, among others, with Borjan Geshkovski (MIT), Carlos Esteve (Cambridge), Domènec Ruiz-Balet (IC, London) and Dario Pighin (Sherpa.ai).
A key challenge in cryptography is to ensure that a protocol resists all computationally feasible attacks, even when an adversary decides to follow a completely arbitrary and unpredictable strategy. This often turns out to be notoriously difficult -- for example, proofs of security must typically extract an adversary's implicit input, but this is at odds […]
Reinforcement learning (RL) is a pillar for modern artificial intelligence. Compared to classical statistical learning, several new statistical and computational phenomena arise from RL problems, leading to different trade-offs in the choice of the estimators, tuning of their parameters, and the design of efficient algorithms. In many settings, asymptotic and/or worst-case theory fails to provide the relevant guidance.
In this talk, I present recent advances that involve a more refined approach to RL, one that leads to non-asymptotic and instance-optimal guarantees. The bulk of this talk focuses on function approximation methods for policy evaluation. I establish a novel class of optimal and instance-dependent oracle inequalities for projected Bellman equations, as well as efficient computational algorithms achieving them. Among other results, I will highlight how the instance-optimal guarantees guide the selection of tuning parameters in temporal different methods, and tackle the instability issue with general function classes. Drawing on this perspective, I will also discuss a novel class of stochastic approximation methods that yield optimal statistical guarantees for policy optimization problems.
In many scientific settings we use a statistical model to describe a high-dimensional distribution over many variables. Such models are often represented as a weighted graph encoding the dependencies between different variables and are known as graphical models. Graphical models arise in a wide variety of scientific fields throughout science and engineering.
Human language is extraordinarily complex. Nevertheless, we readily acquire language as children, when we are most cognitively limited, and we comprehend language as adults with striking efficiency. My research seeks to understand the mental algorithms that allow us to accomplish this feat, with particular focus on how memory and prediction mechanisms are recruited to overcome the bottlenecks of real-time language processing. In this talk, I will review results from three of my lines of inquiry into this question. First, using diverse naturalistic reading datasets, I will show evidence that prediction is a central concern of the human language processing system. Second, using fMRI measures of naturalistic story listening, I will show evidence that memory and prediction processes are dissociable in the brain's response to language, that syntactic structure building plays a major role in ordinary language comprehension, and that the neural resources that are responsible for structure building are largely specialized for language. Third, I will show evidence from computational modeling that memory and prediction pressures independently encourage discovery of phonological regularities from natural speech. Together, these results support an intricate coordination of memory and prediction abilities for language learning and comprehension. I will conclude by outlining planned directions for my future lab, integrating neuroimaging, behavioral methods, natural language processing, and computational modeling to study language learning and processing.
The size and complexity of today's graphs present challenges that necessitate the discovery of new algorithms. One central area of research in this endeavor is computing and estimating distances in graphs. In this talk I will discuss two fundamental families of distance problems in the context of modern graphs: Diameter/Radius/Eccentricities and Hopsets/Shortcut Sets. The best-known algorithm for computing the diameter (largest distance) of a graph is the naive algorithm of computing all-pairs shortest paths and returning the largest distance. Unfortunately, this can be prohibitively slow for massive graphs. Thus, it is important to understand how fast and how accurately the diameter of a graph can be approximated. I will present tight bounds for this problem via conditional lower bounds from fine-grained complexity. Secondly, for a number of settings relevant to modern graphs (e.g. parallel algorithms, streaming algorithms, dynamic algorithms), distance computation is more efficient when the input graph has low hop-diameter. Thus, a useful preprocessing step is to add a set of edges (a hopset) to the graph that reduces the hop-diameter of the graph, while preserving important distance information. I will present progress on upper and lower bounds for hopsets.