Test Martingales, Bayes Factors and p-Values
... an obvious way to test P : you refute the quality of P ’s probabilities by making money against them. As Ville pointed out, the event that a test martingale tends to infinity has probability zero, and for every event of probability zero, there is a test martingale that tends to infinity if the event ...
... an obvious way to test P : you refute the quality of P ’s probabilities by making money against them. As Ville pointed out, the event that a test martingale tends to infinity has probability zero, and for every event of probability zero, there is a test martingale that tends to infinity if the event ...
Chapter 5
... 61. The ABCD football association is considering a Super Ten Football Conference. The top 10 football teams in the country, based on past records, would be members of the Super Ten Conference. Each team would play every other team in the conference during the season and the team winning the most gam ...
... 61. The ABCD football association is considering a Super Ten Football Conference. The top 10 football teams in the country, based on past records, would be members of the Super Ten Conference. Each team would play every other team in the conference during the season and the team winning the most gam ...
On The Learnability Of Discrete Distributions
... f0; 1gn and U is the uniform distribution, then KL(DjjU ) n (since we can always encode each output of U using n bits). Thus, the performance of the \random guessing" hypothesis has at worst Kullback-Leibler divergence n, and this will form our measuring stick for the performance of \weak learning ...
... f0; 1gn and U is the uniform distribution, then KL(DjjU ) n (since we can always encode each output of U using n bits). Thus, the performance of the \random guessing" hypothesis has at worst Kullback-Leibler divergence n, and this will form our measuring stick for the performance of \weak learning ...
results Kamprad
... compared to Leavers who also reported Excellent or Very good health when they retired. In contrast, if Previous Stayers report Pretty bad health at the time of exit, then they experience a higher risk of deteriorating health during the period of retirement as compared to Leavers that also reported p ...
... compared to Leavers who also reported Excellent or Very good health when they retired. In contrast, if Previous Stayers report Pretty bad health at the time of exit, then they experience a higher risk of deteriorating health during the period of retirement as compared to Leavers that also reported p ...
Phylogenetic Reconstruction with Insertions and Deletions Alexandr Andoni , Mark Braverman
... leaves of the tree correspond to the species which exist today. The root of the tree is their closest common ancestor, and each branching indicates a specification event, in which one species is extinct, and several new species are formed. The goal of phylogenetic reconstruction is to infer the tree ...
... leaves of the tree correspond to the species which exist today. The root of the tree is their closest common ancestor, and each branching indicates a specification event, in which one species is extinct, and several new species are formed. The goal of phylogenetic reconstruction is to infer the tree ...
Statistical Inference, Occam`s Razor, and Statistical Mechanics on
... latter problem, on which considerable ink has already been expended in the literature (Rissanen 1984, 1986; Barron 1985; Clarke and Barron 1990; Barron and Cover 1991; Wallace and Freeman 1987; Yamanishi 1995; MacKay 1992a, 1992b; Moody 1992; Murata et al. 1994). The first contribution is to cast Ba ...
... latter problem, on which considerable ink has already been expended in the literature (Rissanen 1984, 1986; Barron 1985; Clarke and Barron 1990; Barron and Cover 1991; Wallace and Freeman 1987; Yamanishi 1995; MacKay 1992a, 1992b; Moody 1992; Murata et al. 1994). The first contribution is to cast Ba ...
R u t c o r Research Sample width for multi-category
... which of the C different classes objects from X belong and, in supervised machine learning, it is arrived at on the basis of a sample, a set of objects from X together with their classifications in [C]. In [4], the notion of sample width for binary classifiers (C = 2) mapping from the real line X = ...
... which of the C different classes objects from X belong and, in supervised machine learning, it is arrived at on the basis of a sample, a set of objects from X together with their classifications in [C]. In [4], the notion of sample width for binary classifiers (C = 2) mapping from the real line X = ...
pdf
... come up with some (arbitrary) prior that expresses her subjective beliefs about the situation. It then makes sense to assess the consequences of ignoring information in terms of expected loss, where the expectation is taken with respect to the agent’s subjective prior. Good’s total evidence theorem, ...
... come up with some (arbitrary) prior that expresses her subjective beliefs about the situation. It then makes sense to assess the consequences of ignoring information in terms of expected loss, where the expectation is taken with respect to the agent’s subjective prior. Good’s total evidence theorem, ...
Coloring graphs from random lists of fixed size
... assignment L is called a list assignment for G and the sets L(v) are referred to as lists or color lists. If all lists have equal size k, then L is called a k-list assignment. We then want to find a proper vertex coloring ϕ of G, such that ϕ(v) ∈ L(v) for all v ∈ V (G). If such a coloring ϕ exists th ...
... assignment L is called a list assignment for G and the sets L(v) are referred to as lists or color lists. If all lists have equal size k, then L is called a k-list assignment. We then want to find a proper vertex coloring ϕ of G, such that ϕ(v) ∈ L(v) for all v ∈ V (G). If such a coloring ϕ exists th ...
Lecture 2
... A Two-class Classifier Let us first look at a single classifier for two classes with options set at certain values. The two-class situation is certainly the most common and occurs very frequently in practice. We will extend our analysis to more than two classes later. A natural criterion for judging ...
... A Two-class Classifier Let us first look at a single classifier for two classes with options set at certain values. The two-class situation is certainly the most common and occurs very frequently in practice. We will extend our analysis to more than two classes later. A natural criterion for judging ...
Connectivity Properties of Random Subgraphs of the Cube - IME-USP
... be fixed. Suppose X ⊂ ΓQn (x) and Y ⊂ ΓQn (y) are k-element sets of vertices. Then we define the properties L(x, y) = Lk (x, y), L(x, Y ) = Lk (x, Y ) = Lk (x, y, Y ), and L(X, Y ) = Lk (X, Y ) = Lk (x, y, X, Y ) as follows. (i ) We say that H has L(x, y) if there are k short, internally vertex-disj ...
... be fixed. Suppose X ⊂ ΓQn (x) and Y ⊂ ΓQn (y) are k-element sets of vertices. Then we define the properties L(x, y) = Lk (x, y), L(x, Y ) = Lk (x, Y ) = Lk (x, y, Y ), and L(X, Y ) = Lk (X, Y ) = Lk (x, y, X, Y ) as follows. (i ) We say that H has L(x, y) if there are k short, internally vertex-disj ...
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.