p. XII line-5: since p. 1-2: I blew this simple formula: should be α = −〈ξ, η〉/〈η, η〉. p. 2 I.1.1.4: The Riesz-Fischer Theorem is often stated this way today, but neither Riesz nor Fischer (who worked independently) phrased it in terms of completeness of the orthogonal system {e int}. If [a, b

We introduce a method of functionally classifying genes by using gene expression data from DNA microarray hybridization experiments. The method is based on the theory of support vector machines (SVMs). SVMs are considered a supervised computer learning method because they exploit prior knowledge

about Y through a ‘bottleneck ’ formed by a limited set of codewords ˜X. This constrained optimization problem can be seen as a generalization of rate distortion theory in which the distortion measure d(x, ˜x) emerges from the joint statistics of X and Y. This approach yields an exact set of self

perspective. These practical issues are then examined in the context of a case study in which TD(lambda) is applied to learning the game of backgammon from the outcome of self-play. This is apparently the first application of this algorithm to a complex nontrivial task. It is found that, with zero knowledge

When logic programming is based on the proof theory of intuitionistic logic, it is natural to allow implications in goals and in the bodies of clauses. Attempting to prove a goal of the form D ⊃ G from the context (set of formulas) Γ leads to an attempt to prove the goal G in the extended context Γ

is that good feature sets contain features that are highly correlated with the class, yet uncorrelated with each other. A feature evaluation formula, based on ideas from test theory, provides an operational definition of this hypothesis. CFS (Correlation based Feature Selection) is an algorithm that couples

learning theory (Bandura, 1977b, in press), self-directedness operates through a self system that comprises cognitive structures and subfunctions for perceiving, evaluating, motivating, and regulating behavior. An important, cognitively based source of self-motivation relies on the intervening processes

-to-one correspondence between the answer sets of the program and the models of the resulting propositional theory. In the worst case, there may be an exponential number of loops in a logic program. To address this problem, we propose an approach that adds loop formulas a few at a time, selectively. Based

at most k . 'Invariance for k--partial isomorphism' means having the same truth value at tuples of objects in any two models that are connected by a partial isomorphism in such a set. The precise sense of this is spelt out in the following proof. 21 Proof (Outline.) k-variable formulas

, watermarking, fingerprinting, steganography, and data embedding. In these applications, information is hidden within a host data set and is to be reliably communicated to a receiver. The host data set is intentionally corrupted, but in a covert way, designed to be imperceptible to a casual analysis. Next