1 4 A Probabilistic Model | Machine Learning

A probabilistic model is a set of probability distributions, p(xjθ).
I We pick the distribution family p(·), but don’t know the parameter θ.
Example: Model data with a Gaussian distribution p(xjθ), θ = fµ; Σg.
The i.i.d. assumption
Assume data is independent and identically distributed (iid). This is written
xi
iid
∼ p(xjθ); i = 1; : : : ; n:
Writing the density as p(xjθ), then the joint density decomposes as
p(x1; : : : ; xnjθ) =
nYi=1
p(xijθ)
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