I'm currently self studying these notes and in this slide it says that naively marginalizing over all unobserved variables requires an exponential number of computations. Does anyone know why it is exponential?
Complexity of exact inference on graphical models
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$\begingroup$
probability
statistics
random-variables
statistical-inference
1 Answers
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Suppose $W=(W_1,\ldots,W_n)$, where each $W_i$ is binary. Then $W$ can take on $2^n$ different values, so the sum $\sum_w P(Y,e,w)$ is over $2^n$ terms.