COPA 2020

Doctor Rauf Izmailov

Perspecta Labs

Professor Vladimir Vapnik

Facebook AI Research

Complete Statistical Theory of Learning: Learning Using Statistical Invariants

Statistical theory of learning devoted to methods for which the obtained approximations converge to the desired function with increasing number of observations. The theory uses instruments that provide convergence in L2 norm of space of functions, i.e., the so-called strong mode of convergence. However, in Hilbert space, along with convergence in the space of functions there also exists the so-called weak mode of convergence, i.e., convergence in the space of functionals. The weak mode of convergence (under some conditions) also leads to the convergence of approximations to the desired function in L2 metrics, although it uses different mechanisms to achieve that convergence.

This talk discusses new learning methods which use both mechanisms (weak and strong) of convergence simultaneously. Such methods allow one
(1) to find the admissible set of functions (i.e., the collection of an appropriate approximating functions) and
(2) to find the desired approximation in this set. Since only two modes of convergence exist in Hilbert space, we call the theory that uses both of them the complete statistical theory of learning.

Along with general reasoning, the talk presents algorithms which constitute a new learning paradigm called Learning Using Statistical Invariants (LUSI). LUSI algorithms were developed for sets of functions belonging to Reproducing Kernel Hilbert Space (RKHS), which include modified SVM method (LUSI-SVM method). Also, talk presents LUSI modification of Neural Networks methods (LUSI-NN). LUSI methods require for learning less training examples.

In conclusion, the talk discusses the general (philosophical) framework of new learning paradigm including concept of intelligence.

Professor Marco Campi

Department of Information Engineering, University of Brescia, Italy

Risk and Complexity in Prediction Problems

(joint work with Simone Garatti)

We show that the risk (probability with which a shortfall occurs) and complexity (number of relevant data-points to determine a solution) are strictly connected concepts in a general data-driven decision-making framework.

When these concepts are applied to prediction, they lead to extremely tight evaluations of the distribution of the probability of prediction error.

These results are relevant to all approaches in prediction theory that contain a compression scheme, including SVM (Support Vector Machine), SVR (Support Vector regression), SVDD (Support Vector Data Description) and others.

Tutorials

Chair: TBD

"Conformal Prediction"

Henrik Linusson
(Home Page)

Predictive distributions (PD) can be informally seen a form of regression where, instead of a single value, the prediction is a probability distribution on the label space. While PDs tend to be associated primarily with Bayesian methods, the tutorial will introduce Conformal Predictive Distributions (CPD), which are instead formulated in a frequentist framework and as such do not require priors. CPD are closely related to Conformal Predictors, with which they share some properties. Some examples from real-world applications will illustrate the use of CPDs. A discussion of suitable metrics and diagnostic tools to evaluate probabilistic predictions will conclude the talk.

"Venn Predictors"

Ulf Johansson
(Home Page)

This tutorial first covers the basics of Venn predictors, including the special case of Venn-Abers predictors. After that, we consider Venn predictors in the context of trustworthiness. How to make decisions and recommendations from AI systems trustworthy is currently a key question for uptake and acceptance, often determining the success of such systems. Trustworthiness is also the ultimate goal of both Explainable AI (XAI) and Fairness, Accountability and Transparency (FAT).

"Conformal predictive distributions"

Paolo Toccaceli
(Home Page)

Predictive distributions (PD) can be informally seen a form of regression where, instead of a single value, the prediction is a probability distribution on the label space. While PDs tend to be associated primarily with Bayesian methods, the tutorial will introduce Conformal Predictive Distributions (CPD), which are instead formulated in a frequentist framework and as such do not require priors. CPD are closely related to Conformal Predictors, with which they share some properties. Some examples from real-world applications will illustrate the use of CPDs. A discussion of suitable metrics and diagnostic tools to evaluate probabilistic predictions will conclude the talk.

"Deep learning and Conformal Prediction"

Siamak Mehrkanoon
(Home Page)

Deep learning and artificial neural networks based models have significantly improved the state-of-the-art techniques in machine learning and data driven modeling, thanks to the increasing computing power as well as vast amount of available data. On the other hand, powerful kernel based models have also been successfully applied in different applications with well-established theoretical analysis. This tutorial aims at explaining synergies between neural networks, deep learning, kernel based methods and introducing some new models developed in this context.