Intelligence Semantics

# The mathematical foundations of learning machines by Nils J Nilsson

By Nils J Nilsson

Read or Download The mathematical foundations of learning machines PDF

Similar intelligence & semantics books

An Introduction to Computational Learning Theory

Emphasizing problems with computational potency, Michael Kearns and Umesh Vazirani introduce a couple of critical issues in computational studying idea for researchers and scholars in synthetic intelligence, neural networks, theoretical desktop technology, and data. Computational studying idea is a brand new and quickly increasing region of analysis that examines formal versions of induction with the ambitions of studying the typical tools underlying effective studying algorithms and determining the computational impediments to studying.

Neural Networks and Learning Machines

For graduate-level neural community classes provided within the departments of machine Engineering, electric Engineering, and desktop technology.   Neural Networks and studying Machines, 3rd version is well known for its thoroughness and clarity. This well-organized and entirely up to date textual content continues to be the main entire therapy of neural networks from an engineering point of view.

Reaction-Diffusion Automata: Phenomenology, Localisations, Computation

Reaction-diffusion and excitable media are among so much exciting substrates. regardless of obvious simplicity of the actual methods concerned the media convey quite a lot of extraordinary styles: from objective and spiral waves to traveling localisations and desk bound respiring styles. those media are on the center of such a lot typical techniques, together with morphogenesis of residing beings, geological formations, anxious and muscular job, and socio-economic advancements.

Extra info for The mathematical foundations of learning machines

Example text

USING VERSION SPACES FOR LEARNING Chapter 4 Neural Networks In chapter two we de ned several important subsets of Boolean functions. Suppose we decide to use one of these subsets as a hypothesis set for supervised function learning. We next have the question of how best to implement the function as a device that gives the outputs prescribed by the function for arbitrary inputs. In this chapter we describe how networks of non-linear elements can be used to implement various input-output functions and how they can be trained using supervised learning methods.

The total squared error (over all patterns in a training set, , containing m patterns) is then: "= m X nX +1 i=1 j =1 (di ; xij wj )2 We want to choose the weights wj to minimize this squared error. One way to nd such a set of weights is to start with an arbitrary weight vector and move it along the negative gradient of " as a function of the weights. Since " is quadratic in the wj , we know that it has a global minimum, and thus this steepest descent procedure is guaranteed to nd the minimum. Each component of the gradient is the partial derivative of " with respect to one of the weights.

There is no closed-form expression for the number of linearly separable functions of n dimensions, but the following table gives the numbers for n up to 6. n 1 2 3 4 5 6 Boolean Linearly Separable Functions Functions 4 4 16 14 256 104 65,536 1,882 4:3 109 94,572 1:8 1019 15,028,134 Muroga, 1971] has shown that (for n > 1) there are no more than 2n2 linearly separable functions of n dimensions. 3 Summary The diagram in Fig. 6 shows some of the set inclusions of the classes of Boolean functions that we have considered.