The sample complexity of pattern classication
... ((x1 y1) : : : (xm ym)) of length m and a real number > 0, dene the error estimate er^ z (h) = m1 jfi : yih(xi) < gj : This estimate counts the proportion of examples that are not correctly classied with a margin of . Let H be a class of real-valued functions dened on X . For > 0, a sequ ...
... ((x1 y1) : : : (xm ym)) of length m and a real number > 0, dene the error estimate er^ z (h) = m1 jfi : yih(xi) < gj : This estimate counts the proportion of examples that are not correctly classied with a margin of . Let H be a class of real-valued functions dened on X . For > 0, a sequ ...
Tossing a Biased Coin
... algorithm, but the only source of randomness available might be a biased coin. We can obtain a sequence of bits with the Multi-Level strategy in the following way: we flip the biased coin a large number of times. Then we run through each of the levels, producing a bit for each heads-tails or tails-h ...
... algorithm, but the only source of randomness available might be a biased coin. We can obtain a sequence of bits with the Multi-Level strategy in the following way: we flip the biased coin a large number of times. Then we run through each of the levels, producing a bit for each heads-tails or tails-h ...
Naive Bayesian Classifier
... In our example, for the attribute-value pair student = yes of X, we need to count the number of customers who are students, and for which buy = yes (which contributes to P (X|buy = yes)) and the number of customers who are students and for which buy = no (which contributes to P (X|buy = no)). But wh ...
... In our example, for the attribute-value pair student = yes of X, we need to count the number of customers who are students, and for which buy = yes (which contributes to P (X|buy = yes)) and the number of customers who are students and for which buy = no (which contributes to P (X|buy = no)). But wh ...
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... classifiers with small error probability. One can, however, do even better than to derive classifiers from good regression estimators. One of the goals of this paper is to investigate consistency properties of an RBF-estimate of m and of the classifier derived from it, and of an RBF classifier based ...
... classifiers with small error probability. One can, however, do even better than to derive classifiers from good regression estimators. One of the goals of this paper is to investigate consistency properties of an RBF-estimate of m and of the classifier derived from it, and of an RBF classifier based ...
Reasoning System
... • Reasoning is a process of thinking; reasoning is logically arguing; reasoning ...
... • Reasoning is a process of thinking; reasoning is logically arguing; reasoning ...
Probability-Possibility Transformations, Triangular Fuzzy Sets
... has already been proposed in the past [9], [15], [25], [31]. More recent results have been obtained by Lasserre [26], Mauris et al. [27], [29] and applied to the problem of representing physical measurements. This paper further explores the connection between this probability-possibility transformat ...
... has already been proposed in the past [9], [15], [25], [31]. More recent results have been obtained by Lasserre [26], Mauris et al. [27], [29] and applied to the problem of representing physical measurements. This paper further explores the connection between this probability-possibility transformat ...
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... Being able to predict the future is not always a good thing. Cassandra of Troy had the gift of foreseeing but was cursed by Apollo that her predictions would never be believed. Her warnings of the destruction of Troy were ignored and to simplify, let’s just say that things just didn’t go well for he ...
... Being able to predict the future is not always a good thing. Cassandra of Troy had the gift of foreseeing but was cursed by Apollo that her predictions would never be believed. Her warnings of the destruction of Troy were ignored and to simplify, let’s just say that things just didn’t go well for he ...
65. Gnedenko, Khinchin. Elementary probability
... Thirty five years have passed since the appearance of the first edition of this book written on the suggestion of the late Khinchin. After his death I have inserted various changes and additions. The book did not lose readers and I am pleased that some of them have accordingly been led to deep thoug ...
... Thirty five years have passed since the appearance of the first edition of this book written on the suggestion of the late Khinchin. After his death I have inserted various changes and additions. The book did not lose readers and I am pleased that some of them have accordingly been led to deep thoug ...
Ars Conjectandi
Ars Conjectandi (Latin for The Art of Conjecturing) is a book on combinatorics and mathematical probability written by Jakob Bernoulli and published in 1713, eight years after his death, by his nephew, Niklaus Bernoulli. The seminal work consolidated, apart from many combinatorial topics, many central ideas in probability theory, such as the very first version of the law of large numbers: indeed, it is widely regarded as the founding work of that subject. It also addressed problems that today are classified in the twelvefold way, and added to the subjects; consequently, it has been dubbed an important historical landmark in not only probability but all combinatorics by a plethora of mathematical historians. The importance of this early work had a large impact on both contemporary and later mathematicians; for example, Abraham de Moivre.Bernoulli wrote the text between 1684 and 1689, including the work of mathematicians such as Christiaan Huygens, Gerolamo Cardano, Pierre de Fermat, and Blaise Pascal. He incorporated fundamental combinatorial topics such as his theory of permutations and combinations—the aforementioned problems from the twelvefold way—as well as those more distantly connected to the burgeoning subject: the derivation and properties of the eponymous Bernoulli numbers, for instance. Core topics from probability, such as expected value, were also a significant portion of this important work.