Convergence of Random Variables
... As seen from the above definition, this notion concerns itself with the convergence of a sequence of probabilities! At the first glance, it may seem that the notions of almost sure convergence and convergence in probability are the same. But the two definitions actually tell very different stories! ...
... As seen from the above definition, this notion concerns itself with the convergence of a sequence of probabilities! At the first glance, it may seem that the notions of almost sure convergence and convergence in probability are the same. But the two definitions actually tell very different stories! ...
Lower Bounds on Learning Random Structures with
... For a concept class that does not have polynomially bounded representations, the polynomial p has an additional parameter size(f ) bounding the length of the representation of the target concept f . For a randomized learning algorithm A we require that A return an -good hypothesis h with at least a ...
... For a concept class that does not have polynomially bounded representations, the polynomial p has an additional parameter size(f ) bounding the length of the representation of the target concept f . For a randomized learning algorithm A we require that A return an -good hypothesis h with at least a ...
Optimal Information Transmission
... Returning to our doctor-patient example, there now arises the question: For a doctor not knowing the patient’s preference between the two kinds of uncertainty resolution, how should she send to him a piece of information on his health condition such that both of their utility levels are maximized in ...
... Returning to our doctor-patient example, there now arises the question: For a doctor not knowing the patient’s preference between the two kinds of uncertainty resolution, how should she send to him a piece of information on his health condition such that both of their utility levels are maximized in ...
Notes #1 - Department of Computer Science
... Now define a distinguishing circuit Dn for G as follows: On input a1 , a2 , · · · , al(n) , Dn computes An (a1 , a2 , · · · , ai−1 ), and accepts if this equals ai . Then p(n) = the probability that Dn accepts G(s) for random s = pred(n), and r(n) = the probability that Dn accepts a random string = ...
... Now define a distinguishing circuit Dn for G as follows: On input a1 , a2 , · · · , al(n) , Dn computes An (a1 , a2 , · · · , ai−1 ), and accepts if this equals ai . Then p(n) = the probability that Dn accepts G(s) for random s = pred(n), and r(n) = the probability that Dn accepts a random string = ...
Corpus-based estimates of word association predict - clic
... 0010-0285/Ó 2014 Elsevier Inc. All rights reserved. ...
... 0010-0285/Ó 2014 Elsevier Inc. All rights reserved. ...
Chapter 1 Probability, Percent, Rational Number Equivalence
... The mathematics emphasized in this chapter reflects the importance in today’s society of being able to understand basic concepts of probability. References to probability are all around us,including weather forecasting. Suppose you have some outdoor plans made for a particular day and the weather re ...
... The mathematics emphasized in this chapter reflects the importance in today’s society of being able to understand basic concepts of probability. References to probability are all around us,including weather forecasting. Suppose you have some outdoor plans made for a particular day and the weather re ...
Mathematical model of conflict and cooperation with non
... [5] Salam,K.M.M., Takahashi, K. “Mathematical model of conflict with nonannihilating multi-opponent”, Journal of Interdisciplinary Mathematics in ...
... [5] Salam,K.M.M., Takahashi, K. “Mathematical model of conflict with nonannihilating multi-opponent”, Journal of Interdisciplinary Mathematics in ...
Combinatorial Probability
... A straight must start with a card that is 5 or higher, 10 possibilities. Once the values are decided on, suits can be assigned in 45 ways. This counting regards a straight flush as a straight. If you want to exclude straight flushes, suits can be assigned in 45 − 4 ways. (f) full house: 13 · C4,3 · ...
... A straight must start with a card that is 5 or higher, 10 possibilities. Once the values are decided on, suits can be assigned in 45 ways. This counting regards a straight flush as a straight. If you want to exclude straight flushes, suits can be assigned in 45 − 4 ways. (f) full house: 13 · C4,3 · ...
The Robustness-Performance Tradeoff in Markov Decision Processes
... the real parameters, so that the performance of the solution under nominal parameters may provide important information for predicting the performance under the true parameters. Finally, there is a certain tradeoff relationship between the worst-case performance and the nominal performance, that is ...
... the real parameters, so that the performance of the solution under nominal parameters may provide important information for predicting the performance under the true parameters. Finally, there is a certain tradeoff relationship between the worst-case performance and the nominal performance, that is ...
Probability box
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A probability box (or p-box) is a characterization of an uncertain number consisting of both aleatoric and epistemic uncertainties that is often used in risk analysis or quantitative uncertainty modeling where numerical calculations must be performed. Probability bounds analysis is used to make arithmetic and logical calculations with p-boxes.An example p-box is shown in the figure at right for an uncertain number x consisting of a left (upper) bound and a right (lower) bound on the probability distribution for x. The bounds are coincident for values of x below 0 and above 24. The bounds may have almost any shapes, including step functions, so long as they are monotonically increasing and do not cross each other. A p-box is used to express simultaneously incertitude (epistemic uncertainty), which is represented by the breadth between the left and right edges of the p-box, and variability (aleatory uncertainty), which is represented by the overall slant of the p-box.