We establish that stability is necessary and sufficient for learning, even in the General Learning Setting where uniform convergence conditions are not necessary for learning, and where learning might only be possible with a non-ERM learning rule. This goes beyond previous work on the relationship between stability and learnability, which focused on supervised classification and regression, whe...

Optimization has always played a central role in machine learning and advances in the field of optimization and mathematical programming have greatly influenced machine learning models. However the connection between optimization and learning is much deeper : one can phrase statistical and online learning problems directly as corresponding optimization problems. In this dissertation I take this...

In this lecture, we introduce the notion of the growth function corresponding to a hypothesis class. This is the key notion that allows us to prove the learnability of infinite hypothesis classes.

Korean has locative construction as other languages do such as English. Although L2 acquisition of locative construction has been examined in L2 English research, few experimental investigations of Korean L2 acquisition have been conducted. The current study focused on the syntactic alternation among Figure Framed sentence, Ground Framed sentence, Figure only sentence and Ground only sentence. ...

Much of the work in inductive learning considers languages that represent hypotheses using some restricted form of propositional logic; an important research problem is extending propo-sitional learning algorithms to use more expressive rst-order representations. Further, it is desirable for these algorithms to have solid theoretical foundations, so that their behavior is reliable and predictab...

There is much debate over the degree to which language learning is governed by innate language-specific biases, or acquired through cognition-general principles. Here we examine the probabilistic language acquisition hypothesis on three levels: We outline a theoretical result showing that probabilistic learning in the limit is possible for a very general class of languages. We then describe a p...

In any learnability setting, hypotheses are conjectured from some hypothesis space. Studied herein are the influence on learnability of the presence or absence of certain control structures in the hypothesis space. First presented are control structure characterizations of some rather specific but illustrative learnability results. The presence of these control structures is thereby shown essen...

The problem of characterizing learnability is the most basic question of learning theory. A fundamental and long-standing answer, formally proven for supervised classification and regression, is that learnability is equivalent to uniform convergence, and that if a problem is learnable, it is learnable via empirical risk minimization. Furthermore, for the problem of binary classification, unifor...

This paper explores the simplicity of learned neural networks under various settings: learned on real vs random data, varying size/architecture and using large minibatch size vs small minibatch size. The notion of simplicity used here is that of learnability i.e., how accurately can the prediction function of a neural network be learned from labeled samples from it. While learnability is differ...

Efficient learnability using the state merging algorithm is known for a subclass of probabilistic automata termed μ-distinguishable. In this paper, we prove that state merging algorithms can be extended to efficiently learn a larger class of automata. In particular, we show learnability of a subclass which we call μ2-distinguishable. Using an analog of the Myhill-Nerode theorem for probabilisti...