#computational learning theory

[p01ym47h-blog]

Scott Aaronson on Philosophical Progress - Machine Intelligence Research Institute

In order to bear results, philosophical questions need to be formulated or broken down in such a way that they can be worked upon mathematically and computationally. The philosophy community has known this for some time. To me, a philosophy novice, this is new and pleasing.

A discussion a year ago with my older brother weighing the importance of philosophy, a quick read of the wonderful, and highly accessible Logicomix (thank you Thorup), and the post above, an interview with Scott Aaronson, helped me realize my perception of philosophy was flawed. I believed the entire field consisted of Hume, Kant, Locke, Mill, Aristotle, Plato, and other premodern philosophers. When in reality, mathematicians and logicians of the 19th and 20th centuries drove philosophy toward analytical rigor. Frege, Cantor, Russel, Gödel, Von Neumann, Turing, and others, pushed philosophy toward provability. Without mathematical rigor, philosophical questions remain intractable. And even if mathematics, at its axiomatic core, is a human defined, incomplete system, moving philosophy towards a rigorous, mathematical framework is still beneficial. But maybe I need to be slapped a little harder in the face by Gödel's incompleteness.

It will be exciting to watch the progress of computational learning theory in coming years. Just how far can we push machine learning?

[woodvavb027-blog]

An Introduction to Computational Learning Theory

An Introduction to Computational Learning Theory Emphasizing issues of computational efficiency, Michael Kearns and Umesh Vazirani introduce a number of central topics in computational learning theory for researchers and students in artificial intelligence, neural networks, theoretical computer science, and statistics.Computational learning theory is a new and rapidly expanding area of research that examines formal models of induction with the goals of discovering the common methods underlying efficient learning algorithms and identifying the computational impediments to learning.Each topic in the book has been chosen to elucidate a general principle, which is explored in a precise formal setting. Intuition has been emphasized in the presentation to make the material accessible to the nontheoretician while still providing precise arguments for the specialist. This balance is the result of new proofs of established theorems, and new presentations of the standard proofs.The topics covered include the motivation, definitions, and fundamental results, both positive and negative, for the widely studied L. G. Valiant model of Probably Approximately Correct Learning; Occam's Razor, which formalizes a relationship between learning and data compression; the Vapnik-Chervonenkis dimension; the equivalence of weak and strong learning; efficient learning in the presence of noise by the method of statistical queries; relationships between learning and cryptography, and the resulting computational limitations on efficient learning; reducibility between learning problems; and algorithms for learning finite automata from active experimentation.

[lyalljbcw027-blog]

Computational Learning Theory: Third European Conference, EuroCOLT '97, Jerusalem, Israel, March 17 - 19, 1997, Proceedings (Lecture Notes in Computer ... / Lecture Notes in Artificial Intelligence)

Computational Learning Theory: Third European Conference, EuroCOLT '97, Jerusalem, Israel, March 17 - 19, 1997, Proceedings (Lecture Notes in Computer ... / Lecture Notes in Artificial Intelligence) This book constitutes the refereed proceedings of the Third European Conference on Computational Learning Theory, EuroCOLT'97, held in Jerusalem, Israel, in March 1997.The book presents 25 revised full papers carefully selected from a total of 36 high-quality submissions. The volume spans the whole spectrum of computational learning theory, with a certain emphasis on mathematical models of machine learning. Among the topics addressed are machine learning, neural nets, statistics, inductive inference, computational complexity, information theory, and theoretical physics.