On the Teachability of Randomized Learners

The present paper introduces a new model for teaching {em randomized learners}. Our new model, though based on the classical teaching dimension model, allows to study the influence of various parameters such as the learner\u27s memory size, its ability to provide or to not provide feedback, and the influence of the order in which examples are presented. Furthermore, within the new model it is possible to investigate new aspects of teaching like teaching from positive data only or teaching with inconsistent teachers. Furthermore, we provide characterization theorems for teachability from positive data for both ordinary teachers and inconsistent teachers with and without feedback

A Trichotomy for Transductive Online Learning

We present new upper and lower bounds on the number of learner mistakes in the `transductive' online learning setting of Ben-David, Kushilevitz and Mansour (1997). This setting is similar to standard online learning, except that the adversary fixes a sequence of instances $x_1,\dots,x_n$ to be labeled at the start of the game, and this sequence is known to the learner. Qualitatively, we prove a trichotomy, stating that the minimal number of mistakes made by the learner as $n$ grows can take only one of precisely three possible values: $n$, $\Theta\left(\log (n)\right)$, or $\Theta(1)$. Furthermore, this behavior is determined by a combination of the VC dimension and the Littlestone dimension. Quantitatively, we show a variety of bounds relating the number of mistakes to well-known combinatorial dimensions. In particular, we improve the known lower bound on the constant in the $\Theta(1)$ case from $\Omega\left(\sqrt{\log(d)}\right)$ to $\Omega(\log(d))$ where $d$ is the Littlestone dimension. Finally, we extend our results to cover multiclass classification and the agnostic setting

Generalization Bounds: Perspectives from Information Theory and PAC-Bayes

A fundamental question in theoretical machine learning is generalization. Over the past decades, the PAC-Bayesian approach has been established as a flexible framework to address the generalization capabilities of machine learning algorithms, and design new ones. Recently, it has garnered increased interest due to its potential applicability for a variety of learning algorithms, including deep neural networks. In parallel, an information-theoretic view of generalization has developed, wherein the relation between generalization and various information measures has been established. This framework is intimately connected to the PAC-Bayesian approach, and a number of results have been independently discovered in both strands. In this monograph, we highlight this strong connection and present a unified treatment of generalization. We present techniques and results that the two perspectives have in common, and discuss the approaches and interpretations that differ. In particular, we demonstrate how many proofs in the area share a modular structure, through which the underlying ideas can be intuited. We pay special attention to the conditional mutual information (CMI) framework; analytical studies of the information complexity of learning algorithms; and the application of the proposed methods to deep learning. This monograph is intended to provide a comprehensive introduction to information-theoretic generalization bounds and their connection to PAC-Bayes, serving as a foundation from which the most recent developments are accessible. It is aimed broadly towards researchers with an interest in generalization and theoretical machine learning.Comment: 222 page

Pharmacovigilance Decision Support : The value of Disproportionality Analysis Signal Detection Methods, the development and testing of Covariability Techniques, and the importance of Ontology

The cost of adverse drug reactions to society in the form of deaths, chronic illness, foetal malformation, and many other effects is quite significant. For example, in the United States of America, adverse reactions to prescribed drugs is around the fourth leading cause of death. The reporting of adverse drug reactions is spontaneous and voluntary in Australia. Many methods that have been used for the analysis of adverse drug reaction data, mostly using a statistical approach as a basis for clinical analysis in drug safety surveillance decision support. This thesis examines new approaches that may be used in the analysis of drug safety data. These methods differ significantly from the statistical methods in that they utilize co variability methods of association to define drug-reaction relationships. Co variability algorithms were developed in collaboration with Musa Mammadov to discover drugs associated with adverse reactions and possible drug-drug interactions. This method uses the system organ class (SOC) classification in the Australian Adverse Drug Reaction Advisory Committee (ADRAC) data to stratify reactions. The text categorization algorithm BoosTexter was found to work with the same drug safety data and its performance and modus operandi was compared to our algorithms. These alternative methods were compared to a standard disproportionality analysis methods for signal detection in drug safety data including the Bayesean mulit-item gamma Poisson shrinker (MGPS), which was found to have a problem with similar reaction terms in a report and innocent by-stander drugs. A classification of drug terms was made using the anatomical-therapeutic-chemical classification (ATC) codes. This reduced the number of drug variables from 5081 drug terms to 14 main drug classes. The ATC classification is structured into a hierarchy of five levels. Exploitation of the ATC hierarchy allows the drug safety data to be stratified in such a way as to make them accessible to powerful existing tools. A data mining method that uses association rules, which groups them on the basis of content, was used as a basis for applying the ATC and SOC ontologies to ADRAC data. This allows different views of these associations (even very rare ones). A signal detection method was developed using these association rules, which also incorporates critical reaction terms.Doctor of Philosoph