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

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)))

Write the equation for cross-entropy loss

H(y, p) = -Σ(y_i * log(p_i)) for all i

How does the concept of information entropy, as described by Claude Shannon, contribute to understanding the complexity and unpredictability of communication systems?

Information entropy quantifies uncertainty and complexity in communication systems, aiding in efficient data encoding and transmission

Write the formula for covariance between X and Y

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

What integrated information theory (IIT) proposes — consciousness is identical to integrated information (Φ)

IIT posits consciousness equals integrated information (Φ)

How does the concept of "information entropy" in data compression algorithms represent the uncertainty and complexity of knowledge transfer in the novel "Cloud Atlas"?

Information entropy quantifies knowledge transfer uncertainty in "Cloud Atlas" through interconnected storylines' unpredictability