When conditional entropy H(X|Y) is zero, it means there is no remaining uncertainty or surprise about X once Y is known. This implies that X is a deterministic function of Y, so all information about X is completely contained within Y.
Conditions: X and Y are discrete random variables.
When conditional entropy H(X|Y) is zero, it means there is no remaining uncertainty or surprise about X once Y is known. This implies that X is a deterministic function of Y, so all information about X is completely contained within Y.
Conditions: X and Y are discrete random variables.
Conditional entropy is the difference between the joint entropy of X and Y and the marginal entropy of Y. This relationship is expressed by the entropy chain rule: H(X|Y) = H(X,Y)−H(Y).
Conditions: X and Y are discrete random variables with well-defined joint and marginal entropies.
Conditional entropy is the difference between the joint entropy of X and Y and the marginal entropy of Y. This relationship is expressed by the entropy chain rule: H(X|Y) = H(X,Y)−H(Y).
Conditions: X and Y are discrete random variables with well-defined joint and marginal entropies.
Conditional entropy H(X|Y) is bounded by 0≤H(X|Y) ≤ H(X) because learning the value of Y provides information that can only reduce or leave unchanged the average uncertainty about X; it cannot increase it on average.
Conditions: X and Y are discrete random variables.
Conditional entropy H(X|Y) is bounded by 0≤H(X|Y) ≤ H(X) because learning the value of Y provides information that can only reduce or leave unchanged the average uncertainty about X; it cannot increase it on average.
Conditions: X and Y are discrete random variables.
Conditional entropy H(X|Y) equals unconditional entropy H(X) if and only if the random variables X and Y are statistically independent. In this case, knowing Y provides no information about X, so the uncertainty remains unchanged.
Conditions: X and Y are discrete random variables.
Conditional entropy H(X|Y) equals unconditional entropy H(X) if and only if the random variables X and Y are statistically independent. In this case, knowing Y provides no information about X, so the uncertainty remains unchanged.
Conditions: X and Y are discrete random variables.
The exercise asks students to implement a Matlab function conditionalentropy(p) that computes the conditional entropy of X given Y from a 2D joint probability matrix p(x,y). It includes specific test cases to verify correctness, such as deterministic and uniform distributions.
Conditions: Input p is assumed to be a 2D joint probability array p(x,y).; Students may reuse existing entropy() and jointentropy() routines.
The exercise asks students to implement a Matlab function conditionalentropy(p) that computes the conditional entropy of X given Y from a 2D joint probability matrix p(x,y). It includes specific test cases to verify correctness, such as deterministic and uniform distributions.
Conditions: Input p is assumed to be a 2D joint probability array p(x,y).; Students may reuse existing entropy() and jointentropy() routines.