Elementary Stochastic Analysis-5
... Homogenous chains are stationary and so qij(n)’s are independent of the time parameter n: Π(n+1) = Π(n)Q (***) Π(0) is known and so Π(n) can be computed A general expression for Π(n) (transient probability), ztransform is used ...
... Homogenous chains are stationary and so qij(n)’s are independent of the time parameter n: Π(n+1) = Π(n)Q (***) Π(0) is known and so Π(n) can be computed A general expression for Π(n) (transient probability), ztransform is used ...
Betting Two Patterns against Each Other
... Suppose that each of two players selects a specific pattern and bets that, in a series of independent Bernoulli trials, the pattern appears sooner than the pattern chosen by his opponent, as investigated in [5]. We want to compute the probability of winning this game for each of the two players, the ...
... Suppose that each of two players selects a specific pattern and bets that, in a series of independent Bernoulli trials, the pattern appears sooner than the pattern chosen by his opponent, as investigated in [5]. We want to compute the probability of winning this game for each of the two players, the ...
On the Generalization Ability of Online Strongly
... convex programming algorithm for the SVM objective function — it repeatedly (and randomly) subsamples the training set in order to minimize the empirical SVM objective function. A corollary to this work essentially shows the convergence rate of P EGASOS (as a randomized optimization algorithm) is co ...
... convex programming algorithm for the SVM objective function — it repeatedly (and randomly) subsamples the training set in order to minimize the empirical SVM objective function. A corollary to this work essentially shows the convergence rate of P EGASOS (as a randomized optimization algorithm) is co ...
Improved Regret Bounds for Undiscounted Continuous
... results for RL with deterministic transitions in the discounted setting (Bernstein and Shimkin, 2010), as well as for RL with transition functions that are linear in state and action (Strehl and Littman, 2008; Brunskill et al., 2009; Abbasi-Yadkori and Szepesvári, 2011; Ibrahmi et al., 2012). More ...
... results for RL with deterministic transitions in the discounted setting (Bernstein and Shimkin, 2010), as well as for RL with transition functions that are linear in state and action (Strehl and Littman, 2008; Brunskill et al., 2009; Abbasi-Yadkori and Szepesvári, 2011; Ibrahmi et al., 2012). More ...
Why Dembski`s Design Inference Doesn`t Work
... became widely known in the early 1990s; much of that credibility has been based on the belief that a solid theoretical foundation has been laid for Intelligent Design in William Dembski’s 1998 book, The Design Inference. This article challenges that belief by questioning some of Dembski’s assumption ...
... became widely known in the early 1990s; much of that credibility has been based on the belief that a solid theoretical foundation has been laid for Intelligent Design in William Dembski’s 1998 book, The Design Inference. This article challenges that belief by questioning some of Dembski’s assumption ...
Continued misinterpretation of confidence intervals
... generates confidence intervals, and is said to have a confidence coefficient of X % if, in repeated sampling, X % of intervals would contain the true parameter value for all values of the true value (Neyman, 1937). The idea of a confidence procedure is conceptually very clear. The confidence coeffic ...
... generates confidence intervals, and is said to have a confidence coefficient of X % if, in repeated sampling, X % of intervals would contain the true parameter value for all values of the true value (Neyman, 1937). The idea of a confidence procedure is conceptually very clear. The confidence coeffic ...
The Average-Case Complexity of Counting Distinct Elements
... of distinct elements in the stream. An algorithm A is said to -approximate F0 if it outputs an estimate F̃0 for which Pr[|F̃0 − F0 | < F0 ] > 2/3, where the probability is over the coin tosses of A. The 2/3 probability can be amplified by taking the median of several independent estimates. We cons ...
... of distinct elements in the stream. An algorithm A is said to -approximate F0 if it outputs an estimate F̃0 for which Pr[|F̃0 − F0 | < F0 ] > 2/3, where the probability is over the coin tosses of A. The 2/3 probability can be amplified by taking the median of several independent estimates. We cons ...
Lecture 7: graphical models and belief propagation
... The likelihood term P (~y |~x) describes how a rendered scene ~x generates observations ~y . The prior probability, P (~x), tells the probability of any given scene ~x occuring. We often ignore the denominator, P (~y ), called the evidence, as it is constant with respect to the variables we seek to ...
... The likelihood term P (~y |~x) describes how a rendered scene ~x generates observations ~y . The prior probability, P (~x), tells the probability of any given scene ~x occuring. We often ignore the denominator, P (~y ), called the evidence, as it is constant with respect to the variables we seek to ...
Error Probability Bounds for Balanced Binary Relay Trees , Student Member, IEEE
... resources consumed in having each sensor transmit directly to the fusion center might be regarded as excessive. Energy consumption can be reduced by setting up a directed tree, rooted at the fusion center. In this tree structure, measurements are summarized by leaf sensor nodes and sent to their par ...
... resources consumed in having each sensor transmit directly to the fusion center might be regarded as excessive. Energy consumption can be reduced by setting up a directed tree, rooted at the fusion center. In this tree structure, measurements are summarized by leaf sensor nodes and sent to their par ...
Cascading Failures: Extreme Properties of Large Blackouts in the Electric Grid
... The risk of a bad day has gone from $0.00 to more than $4,000. The risk of a very bad day, in which the factory produces 1000 or more defective units is only slightly smaller at about $3,900. The powerlaw probability function causes the bulk of the risk to be associated with the infrequent, but larg ...
... The risk of a bad day has gone from $0.00 to more than $4,000. The risk of a very bad day, in which the factory produces 1000 or more defective units is only slightly smaller at about $3,900. The powerlaw probability function causes the bulk of the risk to be associated with the infrequent, but larg ...
Slides
... – Too much work to list the complete set of antecedents or consequents to ensure an exceptionless rule. – Too hard to use such rules. ...
... – Too much work to list the complete set of antecedents or consequents to ensure an exceptionless rule. – Too hard to use such rules. ...
Communication Complexity of Set Disjointness
... The gap between the deterministic (and thus probabilistic) upper bound of Theorem 1.1 and probabilistic lower bound of Theorem 1.2 for DISJnk naturally raises the question what is the probabilistic complexity for k = o(n). In this paper we prove that the lower bound is tight for all k, and in partic ...
... The gap between the deterministic (and thus probabilistic) upper bound of Theorem 1.1 and probabilistic lower bound of Theorem 1.2 for DISJnk naturally raises the question what is the probabilistic complexity for k = o(n). In this paper we prove that the lower bound is tight for all k, and in partic ...
here
... which approaches 1 as n becomes large. We generalize Condorcet’s model by presenting it as a game with incomplete information in the following way: Let I = {1, 2, . . ., n} be a set of jurors and let D be the defendant. There are two states of nature: g – in which D is guilty, and z – in which D is ...
... which approaches 1 as n becomes large. We generalize Condorcet’s model by presenting it as a game with incomplete information in the following way: Let I = {1, 2, . . ., n} be a set of jurors and let D be the defendant. There are two states of nature: g – in which D is guilty, and z – in which D is ...
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.