Probabilistic Horn abduction and Bayesian networks
... Determining what is in a system from observations (diagnosis and recognition) is an important part of AI. There have been many logic-based proposals as to what is a diagnosis 17, 57, 13, 45, 12]. One problem with all of these proposals is that for any diagnostic problem of a reasonable size there a ...
... Determining what is in a system from observations (diagnosis and recognition) is an important part of AI. There have been many logic-based proposals as to what is a diagnosis 17, 57, 13, 45, 12]. One problem with all of these proposals is that for any diagnostic problem of a reasonable size there a ...
Metric Embeddings with Relaxed Guarantees.
... slack parameter , a much more flexible and powerful alternative would be to have a single embedding of the metric with the property that, for some (slowly growing) function D(·), it achieved distortion D() on all but an fraction of distance pairs, for all > 0. We call such an embedding gracefu ...
... slack parameter , a much more flexible and powerful alternative would be to have a single embedding of the metric with the property that, for some (slowly growing) function D(·), it achieved distortion D() on all but an fraction of distance pairs, for all > 0. We call such an embedding gracefu ...
Lecture 5
... where we have applied (2.8) with fk = 1{Xn−k a). Therefore P(τa ≤ n, Xn < a) = P(τa ≤ n, Xn > a) = P(Xn > a), which then implies (2.9). Remark. The proof of Theorem 2.3 shows that a discrete ...
... where we have applied (2.8) with fk = 1{Xn−k a). Therefore P(τa ≤ n, Xn < a) = P(τa ≤ n, Xn > a) = P(Xn > a), which then implies (2.9). Remark. The proof of Theorem 2.3 shows that a discrete ...
Advanced Topics in Markov chains
... If F, FkS(k ≥ 0) are σ-fields, then we say that Fk ↑ F if Fk ⊂ Fk+1 (k ≥ 0) and F = σ( k≥0 Fk ). Note that this is the same as saying that (Fk )k≥0 is a filtration and F = F∞ , as we have defined it above. Similarly, if F, T Fk (k ≥ 0) are σ-fields, then we say that Fk ↓ F if Fk ⊃ Fk+1 (k ≥ 0) and F ...
... If F, FkS(k ≥ 0) are σ-fields, then we say that Fk ↑ F if Fk ⊂ Fk+1 (k ≥ 0) and F = σ( k≥0 Fk ). Note that this is the same as saying that (Fk )k≥0 is a filtration and F = F∞ , as we have defined it above. Similarly, if F, T Fk (k ≥ 0) are σ-fields, then we say that Fk ↓ F if Fk ⊃ Fk+1 (k ≥ 0) and F ...
Plausibility Measures: A User`s Guide
... For a plausibility measure Pl with a domain D where subtraction makes sense, it is possible to define a dual notion Pld by taking Pld (A) = Pl(W ) ? Pl(A), where A is the complement of A. For example, the dual of a belief function is called a plausibility function [Shafer 1976] and the dual of a pos ...
... For a plausibility measure Pl with a domain D where subtraction makes sense, it is possible to define a dual notion Pld by taking Pld (A) = Pl(W ) ? Pl(A), where A is the complement of A. For example, the dual of a belief function is called a plausibility function [Shafer 1976] and the dual of a pos ...
A Quantitative Version of the Gibbard-Satterthwaite theorem for Three Alternatives
... Since the preliminary version of this paper [FKN08] appeared in FOCS’08, three follow-up works generalized its results to more than three alternatives, under various additional constraints. The first follow-up work is by Xia and Conitzer [XC08], who use similar techniques to show that a random manip ...
... Since the preliminary version of this paper [FKN08] appeared in FOCS’08, three follow-up works generalized its results to more than three alternatives, under various additional constraints. The first follow-up work is by Xia and Conitzer [XC08], who use similar techniques to show that a random manip ...
Mansour`s Conjecture is True for Random DNF Formulas
... Applying recent work on sandwiching polynomials, our results imply that a t−O(log 1/ǫ) -biased distribution fools the above subclasses of DNF formulas. This gives pseudorandom generators for these subclasses with shorter seed length than all previous work. ...
... Applying recent work on sandwiching polynomials, our results imply that a t−O(log 1/ǫ) -biased distribution fools the above subclasses of DNF formulas. This gives pseudorandom generators for these subclasses with shorter seed length than all previous work. ...
1st grade Math Master List - Montezuma
... numbers in any form, using tools strategically. (CCSS: 7.EE.3) 2.2b Apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies. (CCSS: 7.EE.3) 2.2c Use variabl ...
... numbers in any form, using tools strategically. (CCSS: 7.EE.3) 2.2b Apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies. (CCSS: 7.EE.3) 2.2c Use variabl ...
PDF
... enough to force there to be a function on * such that Pl "# Pl %e Pl " for disjoint sets and ; we say that determines decomposition for Pl. In fact, the axiom DECOMP which results from replacing all occurrences of & in DECOMP by is already enough to force there to be a f ...
... enough to force there to be a function on * such that Pl "# Pl %e Pl " for disjoint sets and ; we say that determines decomposition for Pl. In fact, the axiom DECOMP which results from replacing all occurrences of & in DECOMP by is already enough to force there to be a f ...
pdf
... Pl ~ by taking Pl ~& Pl +!N Pl $ , where is the complement of . For example, the dual of a belief function is called a plausibility function [Shafer 1976] and the dual of a possibility measure is a necessity measure [Dubois and Prade 1990]; a probability distribution is its own dua ...
... Pl ~ by taking Pl ~& Pl +!N Pl $ , where is the complement of . For example, the dual of a belief function is called a plausibility function [Shafer 1976] and the dual of a possibility measure is a necessity measure [Dubois and Prade 1990]; a probability distribution is its own dua ...
T R ECHNICAL ESEARCH
... fully describes this scale invariance is quite arcane. At the other extreme is the scale invariance associated with stochastic and diffusion processes. In this realm, scale invariance departs from the visual and wends its way into the abstract where the probabilistic nature of sample paths becomes t ...
... fully describes this scale invariance is quite arcane. At the other extreme is the scale invariance associated with stochastic and diffusion processes. In this realm, scale invariance departs from the visual and wends its way into the abstract where the probabilistic nature of sample paths becomes t ...
Proof - PhilPapers
... that his conjunctive forks are simple Bayesian networks. Indeed they were the first Bayesian networks to be introduced. Reichenbach went further and formulated what he called (1956, p. 157f.), the principle of the common cause. This states that, if A and B are correlated, then either A causes B , o ...
... that his conjunctive forks are simple Bayesian networks. Indeed they were the first Bayesian networks to be introduced. Reichenbach went further and formulated what he called (1956, p. 157f.), the principle of the common cause. This states that, if A and B are correlated, then either A causes B , o ...
Interval Estimation - Caltech High Energy Physics
... The general situation can be described as follows: Suppose we sample random variables X from a probability distribution f (x; θ, ν), depending on parameters θ and ν. The parameter space is here divided into two subsets. The first set, denoted θ, represents parameters that are of interest to learn ab ...
... The general situation can be described as follows: Suppose we sample random variables X from a probability distribution f (x; θ, ν), depending on parameters θ and ν. The parameter space is here divided into two subsets. The first set, denoted θ, represents parameters that are of interest to learn ab ...
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.