Difference between revisions of "Entropy Minimization for Semi-supervised Learning"
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<math> | <math> | ||
− | C(\theta, \lambda; L_{n}) = L(\theta; \mathcal{L}_{n}) - \lambda H(Y|X,Z; \mathcal{L}_{n}) | + | \begin{eqnarray} |
+ | C(\theta, \lambda; L_{n}) & = & L(\theta; \mathcal{L}_{n}) - \lambda H(Y|X,Z; \mathcal{L}_{n}) | ||
+ | & = & \sum^{n}_{i=1} \text{log}(\sum^{K}_{k=1} z_{ik}P(Y^{i}=w_{k}|X^{i})) | ||
+ | \end{eqnarray} | ||
</math> | </math> |
Revision as of 20:27, 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
Failed to parse (unknown function "\begin{eqnarray}"): {\displaystyle \begin{eqnarray} C(\theta, \lambda; L_{n}) & = & L(\theta; \mathcal{L}_{n}) - \lambda H(Y|X,Z; \mathcal{L}_{n}) & = & \sum^{n}_{i=1} \text{log}(\sum^{K}_{k=1} z_{ik}P(Y^{i}=w_{k}|X^{i})) \end{eqnarray} }