Dasgupta S. The sample complexity of learning fixed-structure Bayesian networks. Machine Learn 1997;29:165--80. Home/Search Document Not in Database Summary Related Articles Check |
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Collective Mining of Bayesian Networks from Distributed.. - Chen, Sivakumar.. (2002) (2 citations) (Correct)
....Let h and c be two possible (joint) distributions of the variables in a BN. For i = 1, 2, n, let h i (x i # i ) c i (x i # i ) be the corresponding conditional distribution at node i, where x i is the variable at node i and # i is the set of parents of node i. Following [15], define a distance dCP (P, c i , h i ) between h i and c i with respect to the true distribution P : dCP (P, c i , h i ) # i P (# i ) x i P (x i # i ) ln( c i (x i h i (x i ) 10) It is then easy to show that dKL (P, h) dKL (P, c) dCP (P, c i , h i ) 11) ....
....satisfies this requirement is called the sample complexity. This is usually referred to as the probably approximately correct (PAC) framework. Friedman and Yakhini [20] have examined the sample complexity of the maximum description length principle (MDL) based learning procedure for BNs. Dasgupta [15] gave a thorough analysis for the multinomial model with Boolean variables. Suppose the BN has n nodes and each node has at most k parents. Given # and #, an upper bound of sample complexity is N(#, #) 1 ln(1 3n #) ## ) 13) Equation (13) gives a relation between the ....
S. Dasgupta, "The sample complexity of learning fixed-structure Bayesian networks," Machine Learning, vol. 29, pp. 165--180, 1997.
Parameter Learning in Object Oriented Bayesian Networks - Langseth, Bangsø (2001) (1 citation) (Correct)
....A [40, proposition 4.3.7] sup A # # # # f(x #) # # . Similar results for the maximal error of the estimated conditional distribution are derived in [39] These results have made the KL divergence the distance measure of choice in Bayesian network learning, see e.g. [11,14,18,23,32]. We have chosen to use the empirical KL divergence D( #f)instead of D(f# fN ) since the former is finite (with probability 1) and therefore simplifies the asymptotic expansion. Results similar to ours can be obtained for D(f# fN ) by use of bounded approximations [1] for the divergence ....
S. Dasgupta, The sample complexity of learning fixed-structure Bayesian networks, Machine Learning 29(2--3) (1997) 165--180.
Expressive Probability Models For Speech Recognition And.. - Russell (1999) (1 citation) (Correct)
....is O(2 d n) as opposed to O(2 d ) for the atomic distribution. This has at least two consequences: first, it becomes possible to represent models with many hundreds of variables; second, the amount of data required to learn such models grows roughly linearly with the number of variables [3]. Additional expressive power is needed to represent temporal processes. A temporal process involves an infinite number of random variables, hence temporal modellinglanguages involvesome kindof universal quantification over time. Hidden Markovmodels (HMMs) for example, are temporal models in ....
Sanjoy Dasgupta. The sample complexity of learning fixed-structure Bayesian networks. Machine Learning, 29:165--180, 1997.
How an Expert can use Imperfect Knowledge to Improve an.. - Greiner, Cheng, Darken (Correct)
.... of the dominant approaches, based on maximizing likelihood [Hec95] or finding independencies [GSSK87, CBL97] Section 3 shows how the error bars for an inference from a belief net varies with the sample size; this relates to the work on determining the sample complexity for learning belief nets [Hof93, FY96, Das97]. Of course, those papers dealt with the problem of identifying which of a given class of belief nets is best; by contrast, we are given a single belief net to evaluate. Also, while those other analyses are in terms of the Maximize Likelihood based approaches, some of our analyses are in terms ....
S. Dasgupta. The sample complexity of learning fixed-structure Bayesian networks. Machine Learning, 29:165--180, 1997.
Bayesian Applications of Belief Networks and.. - Antal, Fannes.. (2003) (Correct)
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Dasgupta S. The sample complexity of learning fixed-structure Bayesian networks. Machine Learn 1997;29:165--80.
Structural Extension to Logistic Regression: - Discriminative Parameter Learning (Correct)
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S. Dasgupta. The sample complexity of learning fixedstructure bayesian networks. Machine Learning, 29, 1997.
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