Maximum A Posteriori (MAP)

Learn how to solve maximum a posteriori (MAP) using the gradient-solving method.

Limitation of MLE

Imagine NN coin tosses where xi{H,T}  i=1,2,...,Nx_i \in \{H, T\} \ \forall \ i=1,2, ..., N denotes the outcome of the ithi^{th} toss. Let pp be the probability of the outcome being heads (HH) and 1p1-p be the probability of the outcome being tails (TT) . The negative log-likelihood of the observed tosses D={x1,x2,...,xN}D = \{x_1, x_2, ..., x_N\} can be written as follows:

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