Difference between revisions of "Entropy Minimization for Semi-supervised Learning"
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<math> | <math> | ||
H(Y|X,Z; L_{n}) = -\frac{1}{n} \sum^{n}_{i=1} \sum^{K}_{k=1} P(Y=w_{k}|x_{i}, z_{i})\text{log}P(Y=w_{k}|x_{i},z_{i}) | H(Y|X,Z; L_{n}) = -\frac{1}{n} \sum^{n}_{i=1} \sum^{K}_{k=1} P(Y=w_{k}|x_{i}, z_{i})\text{log}P(Y=w_{k}|x_{i},z_{i}) | ||
+ | </math> | ||
+ | |||
+ | The posterior distribution is defined as | ||
+ | |||
+ | <math> | ||
+ | C(\mathbf{\theta}, \lambda; L_{n}) = -\frac{1}{n} \sum^{n}_{i=1} \sum^{K}_{k=1} P(Y=w_{k}|x_{i}, z_{i})\text{log}P(Y=w_{k}|x_{i},z_{i}) | ||
</math> | </math> |
Revision as of 20:23, 8 October 2010
Minimum entropy regularization can be applied to any model of posterior distribution.
The learning set is denoted , where : If is labeled as , then and for ; if is unlabeled, then for .
The conditional entropy of class labels conditioned on the observed variables:
The posterior distribution is defined as