We consider the following statistical estimation problem: given a family F of real valued functions over some domain X and an i.i.d. sample drawn from an unknown distribution P over X , find h ∈ F such that the expectation EP (h) is probably approximately equal to sup{EP (h) : h ∈ F}. This Expectation Maximization (EMX) problem captures many well studied learning problems; in fact, it is equiva...

We describe a quantum PAC learning algorithm for DNF formulae under the uniform distribution with a query complexity of Õ(s/ǫ+ s/ǫ), where s is the size of DNF formula and ǫ is the PAC error accuracy. If s and 1/ǫ are comparable, this gives a modest improvement over a previously known classical query complexity of Õ(ns/ǫ). We also show a lower bound of Ω(s logn/n) on the query complexity of any...

Stephen Crain (C) & Rosalind Thornton (T) have garnered a welldeserved reputation for their unwavering commitment to language learnability as a constraint not only on theories of child language and language development but also on experimental design and the interpretation of experimental findings. In his well-known defense of children’s early knowledge of syntactic constraints, Crain (1991) ar...

5.3 Approximating Stochastic Concepts by Functions ............................... 88 5.4 Classification Noise and Semi-Consistent Learning ..............................96 6. N on-U niform L earnab ility ...........................................................................98 6.1 The Notion of Non-Uniform L earnab ility ................................................98 6.2 Distribution-I...

This paper is concerned with learning categorial grammars in the model of Gold. We show that rigid and k-valued non-associative Lambek (NL) grammars are not learnable from well-bracketed sentences. In contrast to k-valued classical categorial grammars, k-valued Lambek grammars are not learnable from strings. This result was shown for several variants including the non-associative variant NL. Wh...

We study the problem of learning influence functions under incomplete observations of node activations. Incomplete observations are a major concern as most (online and real-world) social networks are not fully observable. We establish both proper and improper PAC learnability of influence functions under randomly missing observations. Proper PAC learnability under the Discrete-Time Linear Thres...

This paper investigates the effect of respondents’ age in relation to the experience of using mobile phone for sending text messages. The text entry factors considered in the study were speed, special character selections, case conversions, simplicity, learnability, menu traversals and audio feedback. One hundred and ten Malaysians aged between 17 – 39 years old were interviewed. Special charac...

This study examines the intergenerational transfer of human communication systems. It tests if human communication systems evolve to be easy to learn or easy to use (or both), and how population size affects learnability and usability. Using an experimental-semiotic task, we find that human communication systems evolve to be easier to use (production efficiency and reproduction fidelity), but h...

We study a fundamental question. What classes of hypotheses are learnable in the online learning model? The analogous question in the PAC learning model [12] was addressed by Vapnik and others [13], who showed that the VC dimension characterizes the learnability of a hypothesis class. In his influential work, Littlestone [9] studied the online learnability of hypothesis classes, but only in the...

We propose a mathematical model for learning the high-density areas of an unknown distribution from (unlabeled) random points drawn according to this distribution. While this type of a learning task has not been previously addressed in the Computational Learnability literature, we believe that this it a rather basic problem that appears in many practical learning scenarios. From a statistical t...