Write the equation for cross-entropy loss

What is the formula for calculating the mutual information between two discrete random variables X and Y?

I(X;Y) = ∑∑ P(x,y) log(P(x,y)/(P(x)P(y)))

Mutual information I(X;Y) = H(X) - H(X|Y) = H(Y) - H(Y|X)

Mutual information measures dependence between variables X and Y

Write the formula for KL divergence D_KL(P||Q)

D_KL(P||Q) = Σ P(x) log(P(x)/Q(x)) for all x in the support of P

Write the equation for sigmoid function σ(x) = 1/(1+e^-x)

σ(x) = 1 / (1 + e^-x)

Write the formula for covariance between X and Y

Cov(X, Y) = Σ((Xi - X̄)(Yi - Ȳ)) / (n - 1)

Write the formula for PageRank equation

Pr(A) = (1-d) + d * Σ(Pr(W)/L(W)) for all outbound links W leading to page A