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Chapter 1 Probability Concepts
, 2011
"... This chapter reviews basic probability concepts that are necessary for the modeling and statistical analysis of financial data. 1.1 Random Variables We start with the basic definition of a random variable: Definition 1 A Random variable X is a variable that can take on a given set of values, called ..."
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This chapter reviews basic probability concepts that are necessary for the modeling and statistical analysis of financial data. 1.1 Random Variables We start with the basic definition of a random variable: Definition 1 A Random variable X is a variable that can take on a given set of values, called
KINDERGARTEN STUDENTS ’ UNDERSTANDING OF PROBABILITY CONCEPTS
"... This study explored kindergarten students ’ intuitive strategies and understandings in probabilities. The paper aims to provide an in depth insight into the levels of probability understanding across four constructs, as proposed by Jones (1997), for kindergarten students. Qualitative evidence from t ..."
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students develop a sound awareness of probability concepts and appropriately use these concepts in solving problems has been recognized in recent curriculum documents (e.g., National Council of Teachers of Mathematics, 2000). These recommendations adopt the position that young students,
1.1 The Bayesian Probability Concept
"... Abstract: Bayesian networks (BN) are a valid method to analyze causal dependencies with uncertainties and to calculate inferences based on evidences. This paper describes a method to enable domain experts to configure and use large causal Bayesian networks without the help of BN experts. For this th ..."
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benefit the method allows to generate and use large BN (with hundred of nodes) without excessive effort. Obviously in this approach probabilities are used in a special way. To motivate this, Bayesian probability concept is discussed before introducing the method. The method is illustrated by the example
The Evolution of Social and Economic Networks
 JOURNAL OF ECONOMIC THEORY 106, 265–295
, 2002
"... We examine the dynamic formation and stochastic evolution of networks connecting individuals. The payoff to an individual from an economic or social activity depends on the network of connections among individuals. Over time individuals form and sever links connecting themselves to other individuals ..."
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Cited by 889 (37 self)
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individuals based on the improvement that the resulting network offers them relative to the current network. In addition to intended changes in the network there is a small probability of unintended changes or errors. Predictions can be made regarding the likelihood that the stochastic process will lead
The strength of weak learnability
 MACHINE LEARNING
, 1990
"... This paper addresses the problem of improving the accuracy of an hypothesis output by a learning algorithm in the distributionfree (PAC) learning model. A concept class is learnable (or strongly learnable) if, given access to a Source of examples of the unknown concept, the learner with high prob ..."
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Cited by 871 (26 self)
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probability is able to output an hypothesis that is correct on all but an arbitrarily small fraction of the instances. The concept class is weakly learnable if the learner can produce an hypothesis that performs only slightly better than random guessing. In this paper, it is shown that these two notions
Bayesian Interpolation
 NEURAL COMPUTATION
, 1991
"... Although Bayesian analysis has been in use since Laplace, the Bayesian method of modelcomparison has only recently been developed in depth. In this paper, the Bayesian approach to regularisation and modelcomparison is demonstrated by studying the inference problem of interpolating noisy data. T ..."
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Cited by 728 (17 self)
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. The concepts and methods described are quite general and can be applied to many other problems. Regularising constants are set by examining their posterior probability distribution. Alternative regularisers (priors) and alternative basis sets are objectively compared by evaluating the evidence for them
Guaranteed minimumrank solutions of linear matrix equations via nuclear norm minimization,”
 SIAM Review,
, 2010
"... Abstract The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and col ..."
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Cited by 562 (20 self)
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with overwhelming probability, provided the codimension of the subspace is Ω(r(m + n) log mn), where m, n are the dimensions of the matrix, and r is its rank. The techniques used in our analysis have strong parallels in the compressed sensing framework. We discuss how affine rank minimization generalizes this pre
Solving multiclass learning problems via errorcorrecting output codes
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 1995
"... Multiclass learning problems involve nding a de nition for an unknown function f(x) whose range is a discrete set containing k>2values (i.e., k \classes"). The de nition is acquired by studying collections of training examples of the form hx i;f(x i)i. Existing approaches to multiclass l ..."
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Cited by 726 (8 self)
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learning problems include direct application of multiclass algorithms such as the decisiontree algorithms C4.5 and CART, application of binary concept learning algorithms to learn individual binary functions for each of the k classes, and application of binary concept learning algorithms with distributed
LEARNING PROBABILITY CONCEPTS USING MICROSOFT EXCEL
"... The difficulties encountered by students of all ages in understanding probability and randomness have been widely documented. This paper describes an attempt to teach probability concepts at secondary school level using widely available spreadsheet software. The 10PLUS (Ten Probability Lessons Using ..."
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The difficulties encountered by students of all ages in understanding probability and randomness have been widely documented. This paper describes an attempt to teach probability concepts at secondary school level using widely available spreadsheet software. The 10PLUS (Ten Probability Lessons
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