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Table 1:
Density Estimation Experiment Results, with Details about the Data Sets.
Number ofSet SizesDifference NLL:Difference NLL:Difference NLL:
Data SetInputs(Train,Valid,Test)RBMRBM MultinomialRBForest
adult 123 5000;1414;26,147 4.18 0.11 4.15 0.11 4.12 0.11 
connect-4 126 16,000;4000;47,557 0.75 0.04 −1.72 0.05 0.59 0.04 
dna 180 1400;600;1186 1.29 0.72 1.45 0.67 1.39 0.73 
mushrooms 112 2000;500;5624 −0.69 0.13 −0.69 0.11 0.042 0.12 
nips-0-12 500 400;100;1240 12.65 1.55 11.25 1.55 12.61 1.55 
ocr-letter 128 32,152;10,000;10,000 −2.49 0.44 0.99 0.43 3.78 0.43 
rcv1 150 40,000;10,000;15,0000 −1.29 0.16 −0.044 0.16 0.56 0.16 
web 300 14,000;3188;32,561 0.78 0.30 0.018 0.31 −0.15 0.31 
Number ofSet SizesDifference NLL:Difference NLL:Difference NLL:
Data SetInputs(Train,Valid,Test)RBMRBM MultinomialRBForest
adult 123 5000;1414;26,147 4.18 0.11 4.15 0.11 4.12 0.11 
connect-4 126 16,000;4000;47,557 0.75 0.04 −1.72 0.05 0.59 0.04 
dna 180 1400;600;1186 1.29 0.72 1.45 0.67 1.39 0.73 
mushrooms 112 2000;500;5624 −0.69 0.13 −0.69 0.11 0.042 0.12 
nips-0-12 500 400;100;1240 12.65 1.55 11.25 1.55 12.61 1.55 
ocr-letter 128 32,152;10,000;10,000 −2.49 0.44 0.99 0.43 3.78 0.43 
rcv1 150 40,000;10,000;15,0000 −1.29 0.16 −0.044 0.16 0.56 0.16 
web 300 14,000;3188;32,561 0.78 0.30 0.018 0.31 −0.15 0.31 

Notes: The comparison is made by looking at the difference between the test set average NLL of the MoB with that of the standard RBM, the RBM with multinomial groups and RBForest (i.e. the RBM, RBM multinomial or RBForest outperform the MoB if this difference is positive). The 95% confidence intervals were estimated based on a two-sample t-test statistic. The italics in the table mean that the MoB is a better density estimator, that is, it has a significantly lower test average NLL. Bold means that the corresponding Boltzmann machine is the better estimator.

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