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Unsupervised Learning: Difference between revisions
→EM Algorithm
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We will fix <math>\theta</math> and optimize wrt <math>Q</math>.<br> | We will fix <math>\theta</math> and optimize wrt <math>Q</math>.<br> | ||
Jensen's inequality holds with equality iff either the function is linear or if the random variable is degenerate.<br> | Jensen's inequality holds with equality iff either the function is linear or if the random variable is degenerate.<br> | ||
We will assume <math>\frac{P(x^{(i)}, z^{(i)}=j; \theta) | |||
}{Q^{(i)}_{(j)}}</math> is a constant.<br> | }{Q^{(i)}_{(j)}}</math> is a constant.<br> | ||
This implies <math>Q^{(i)}(j) = c * P(x^{(i)}, z^{(i)} = j ; \theta)</math>.<br> | This implies <math>Q^{(i)}(j) = c * P(x^{(i)}, z^{(i)} = j ; \theta)</math>.<br> | ||