A General Derivative Identity for the Conditional Expectation with Focus on the Exponential Family

Alex Dytso, Martina Cardone

Consider a pair of random vectors $(\mathbf{X},\mathbf{Y})$ and the conditional expectation operator $\mathbb{E}[\mathbf{X}|\mathbf{Y}=\mathbf{y}]$. This work studies analytic pro…