Neural Network Learning: Theoretical Foundations by Martin Anthony

By Martin Anthony

This crucial paintings describes contemporary theoretical advances within the learn of synthetic neural networks. It explores probabilistic types of supervised studying difficulties, and addresses the major statistical and computational questions. Chapters survey learn on development class with binary-output networks, together with a dialogue of the relevance of the Vapnik Chervonenkis measurement, and of estimates of the measurement for a number of neural community types. additionally, Anthony and Bartlett improve a version of type via real-output networks, and exhibit the usefulness of class with a "large margin." The authors clarify the position of scale-sensitive types of the Vapnik Chervonenkis measurement in huge margin type, and in genuine prediction. Key chapters additionally speak about the computational complexity of neural community studying, describing quite a few hardness effects, and outlining effective, optimistic studying algorithms. The booklet is self-contained and available to researchers and graduate scholars in laptop technology, engineering, and arithmetic.

Show description

Read or Download Neural Network Learning: Theoretical Foundations PDF

Best computer vision & pattern recognition books

Markov Models for Pattern Recognition: From Theory to Applications

Markov types are used to unravel not easy trend popularity difficulties at the foundation of sequential facts as, e. g. , automated speech or handwriting reputation. This complete creation to the Markov modeling framework describes either the underlying theoretical strategies of Markov types - overlaying Hidden Markov versions and Markov chain versions - as used for sequential info and offers the recommendations essential to construct profitable structures for sensible purposes.

Cognitive Systems

Layout of cognitive structures for guidance to humans poses a tremendous problem to the fields of robotics and synthetic intelligence. The Cognitive platforms for Cognitive suggestions (CoSy) undertaking was once equipped to handle the problems of i) theoretical growth on layout of cognitive structures ii) equipment for implementation of platforms and iii) empirical reviews to extra comprehend the use and interplay with such structures.

Motion History Images for Action Recognition and Understanding

Human motion research and popularity is a comparatively mature box, but one that is frequently no longer good understood by way of scholars and researchers. the massive variety of attainable adaptations in human movement and visual appeal, digital camera perspective, and atmosphere, current huge demanding situations. a few vital and customary difficulties stay unsolved through the pc imaginative and prescient neighborhood.

Data Clustering: Theory, Algorithms, and Applications

Cluster research is an unmonitored technique that divides a collection of gadgets into homogeneous teams. This booklet starts off with uncomplicated info on cluster research, together with the class of information and the corresponding similarity measures, via the presentation of over 50 clustering algorithms in teams in line with a few particular baseline methodologies reminiscent of hierarchical, center-based, and search-based tools.

Additional resources for Neural Network Learning: Theoretical Foundations

Example text

This quantity can be thought of as the approximation error of the class H, since it describes how accurately the best function in H can approximate the relationship between x and y that is determined by the probability distribution P. (Note that we take an infimum rather than simply a minimum here because the set of values that erp ranges over t The functions in H have to be measurable, and they also have to satisfy some additional, fairly weak, measurability conditions for the subsequent quantities to be well-defined.

Fig. 1. The planes Pi, P2, and P3 (defined by points xi,X2,#3 € R) divide R2 into six cells. ,ra, where zf = (xj,—l). , zm} is linearly independent. To apply the lemma, we shall set d = n + 1. ,2 m } Q Kd has every subset of no more than d points linearly independent. , m, and define C(T) = CC I Rd - | J Pi 1 . 2 The growth function 33 P2 Fig. 2. Planes Pi, P 2 , and P in R3. The intersections of Pi and P 2 with P are shown as bold lines. 2) k=0 Proof First notice that linear independence of every subset of up to d points of T is equivalent to the condition that the intersection of any 1 < k < d linear subspaces Pi is a (d —fc)-dimensionallinear subspace (a '(d - A;)-plane').

For any fixed positive 5, this probability is less than 6 provided ra : as required. 4 is the presence of 1/e rather than the larger 1/e2. We shall see this difference arise in a number of contexts. The intuitive explanation of this improvement is that less data is needed to form an accurate estimate of a random quantity if its variance is smaller. 5 Remarks Learning with respect to a touchstone class It is often useful to weaken the requirement of a learning algorithm by asking only that (with high probability) eiP(L(z)) < optp(T) + e = inf erP(*) + c 26 The Pattern Classification Problem where T, called the touchstone class, is a subset of H.

Download PDF sample

Rated 4.13 of 5 – based on 40 votes