By Balas K. Natarajan

ISBN-10: 0080510531

ISBN-13: 9780080510538

This is the 1st complete advent to computational studying concept. The authors uniform presentation of primary effects and their functions bargains AI researchers a theoretical viewpoint at the difficulties they examine. The booklet offers instruments for the research of probabilistic versions of studying, instruments that crisply classify what's and isn't successfully learnable. After a normal advent to Valiants PAC paradigm and the real idea of the Vapnik-Chervonenkis measurement, the writer explores particular subject matters akin to finite automata and neural networks. The presentation is meant for a wide audience--the authors skill to inspire and speed discussions for newbies has been praised by way of reviewers. every one bankruptcy comprises quite a few examples and workouts, in addition to an invaluable precis of significant effects. an exceptional creation to the realm, appropriate both for a primary path, or as an element in most cases computer studying and complex AI classes. additionally a huge reference for AI researchers.

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**Additional info for Machine Learning. A Theoretical Approach**

**Example text**

If/ = Σ*, EXAMPLE(O) returns nothing. 12. Let F be a class of concepts on a finite domain X. For each fe F, a discriminant o f / i s a set of examples such that/is the only concept i n / that is consistent with the set. A discriminant of minimum cardinality is denoted by D (/*). Assume F is finite. Prove or disprove each of the following assertions: (a)Forall/eF, \D(f)\

Now, / is defined on at most I r I variables and, hence, g is defined on at most max {I r I, Λ } < Irl + n variables. Hence, the binary encoding of g is of length o' (Irl +wn)log(lr I + nm) . Also, g can be constructed in time polynomial in I r I, n, and m. It follows that R is strongly closed under exception. A random polynomial-time fitting that is Occam is a random polynomialtime Occam fitting. 3 Occam's Razor 61 definition here. 2 without the restriction of polynomial dimension. 4 Let F be a class of concepts with a polynomial-time computable representation R.

1 x eS" In the above, Pr {f(xm)} is the probability that f(xm) is the sequence of examples obtained by m calls of EXAMPLE. 1) gives us m Σ Pr />(/·ΔΨ(ε,δ,η,/(*"*))) > ε Pr[f(x ))<5. m x eSm Summing both sides of the above over all / i n G, we get Σ feG Σ Pr / ? (/*ΔΨ(ε,δ,Λ,/(χ ,η )))>ε Pr lf(xm)} < Σ δ. m m x eS Flipping the order of the sums in the above, we get Σ m ΣΡτ m x eS P(fAW(ei5,n,f(xm)))>z Pr [f(xm)} < Σ δ. 4) feG It is convenient to define a switch function Θ : {true, false} ->N as follows.

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