|
|
Line 11: |
Line 11: |
| <math> | | <math> |
| H(Y|X,Z; L_{n}) = -\frac{1}{n} \sum^{n}_{i=1} \sum^{K}_{k=1} P(Y^{(i)}=w_{k}|X^{(i)}, Z^{(i)})\text{log}P(Y^{(i)}=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^{(i)}=w_{k}|X^{(i)}, Z^{(i)})\text{log}P(Y^{(i)}=w_{k}|X^{(i)},Z^{(i)}) |
| + | </math> |
| + | |
| + | Assuming that labels are missing at random, we have that |
| + | |
| + | <math> |
| + | P(Y^{(i)}=w_{k}|X^{(i)}, Z^{(i)}) = \frac{Z^{(i)_{k}}P(Y^{(i)}=w_{k}|X^{(i)})}{\sum^{K}_{k=1} Z^{(i)}_{l} P(Y^{(i)}=w_{k}|X^{(i)})} |
| </math> | | </math> |
| | | |
Revision as of 20:48, 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:
Assuming that labels are missing at random, we have that
The posterior distribution is defined as