Open Access
A Tutorial Introduction
Bernhard Schölkopf,Alexander J. Smola +1 more
- pp 1-22
TLDR
This chapter contains sections titled: Data Representation and Similarity, A Simple Pattern Recognition Algorithm, Some Insights From Statistical Learning Theory, Hyperplane Classifiers, support Vector Classification, Support Vector Regression, Kernel Principal Component Analysis, Empirical Results and Implementations.Abstract:
This chapter contains sections titled: Data Representation and Similarity, A Simple Pattern Recognition Algorithm, Some Insights From Statistical Learning Theory, Hyperplane Classifiers, Support Vector Classification, Support Vector Regression, Kernel Principal Component Analysis, Empirical Results and Implementationsread more
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Journal ArticleDOI
Learning-Assisted Automated Reasoning with Flyspeck
Cezary Kaliszyk,Josef Urban +1 more
TL;DR: It is shown that 39 % of the 14185 theorems could be proved in a push-button mode (without any high-level advice and user interaction) in 30 seconds of real time on a fourteen-CPU workstation.
Journal ArticleDOI
Automated Reasoning in Higher-Order Logic using the TPTP THF Infrastructure
TL;DR: Key developments have been the specification of the THF language, the addition of higher-order problems to theTPTP, the development of the TPTP THF infrastructure, several ATP systems for higher- order logic, and the use of higher -order ATP in a range of domains.
Journal ArticleDOI
A Revision of the Proof of the Kepler Conjecture
TL;DR: The original Kepler conjecture was published in 2006 as mentioned in this paper, which states that no packing of congruent balls in three-dimensional Euclidean space has density greater than that of the face-centered cubic packing.
Book ChapterDOI
Formal Verification of Floating Point Trigonometric Functions
TL;DR: This paper describes in some depth the formal verification of the sin and cos functions, including the initial range reduction step, covering both pure mathematics and the detailed analysis of floating point rounding.
Book ChapterDOI
Canonical Big Operators
TL;DR: It is shown how these canonical big operations played a crucial enabling role in the study of various parts of linear algebra and multi-dimensional real analysis, as illustrated by the formal proofs of the properties of determinants, of the Cayley-Hamilton theorem and of Kantorovitch's theorem.