Fall 2010: STAT 598L: Probabilistic Graphical Models

# Additional (Unofficial) Errata for Probabilistic Graphical Models, first printing

## Chapter 2

• p. 40, exercise 2.9(b), likely the second condition should be $\left(\mathbf{X},\mathbf{Z}\ \perp \mathbf{W}\ \vert\ \mathbf{Y}\right)$, not $\left(\mathbf{X},\mathbf{Y}\ \perp \mathbf{W}\ \vert\ \mathbf{Y}\right)$.
• p. 41, exercise 2.17, should read $K=\left|Val\left(X\right)\right|.$
• p. 41, exercise 2.19(a), should read $I_P\left(X;Y\ \vert\ Z\right)=H_P\left(X\ \vert\ Z\right) - H_P\left(X\ \vert\ Y,Z\right).$

## Chapter 3

• p. 96, exercise 3.2c, confusing, probably should read something along the lines of ”… that is, can be written as $\sum_{i=1}^n\alpha_iX_i+\alpha_0$ where $Val\left(X_i\right)=\left\{0,1\right\}$ for $i=1,\dots,n.$
1. Conditional covariance is usually defined without integrating out the covariate, $Cov_p\left[X_i;X_j\ \vert\ \mathbf{Z}\right]=E_p\left[\left(X_i-E\left[X_i\ \vert\ \mathbf{Z}\right]\right)\left(X_j-E\left[X_j\ \vert\ \mathbf{Z}\right]\right)\right]$. If a covariate is to be integrated out, the expression for the first equation should then be $Cov_p\left[X_i;X_j\ \vert\ \mathbf{Z}\right] = E_{p\left(\mathbf{Z}\right)}E_{\left(X_i,X_j\ \vert\ \mathbf{Z}\right)}\left[\left(X_i-E\left[X_i\ \vert\ \mathbf{Z}\right]\right)\left(X_j-E\left[X_j\ \vert\ \mathbf{Z}\right]\right)\right]$.
2. Second equation should read $\rho_{i,j}=\frac{Cov_p\left[X_i;X_j\ \vert\ \mathcal{X}-\left\{X_i,X_j\right\}\right]}{\sqrtVar_p\left[X_i\ \vert\ \mathcal{X}-\left\{X_i,X_j\right\}\right]Var_p\left[X_j\ \vert\ \mathcal{X}-\left\{X_i,X_j\right\}\right]}}$.
3. Third equation should read $\rho_{i,j}=-\frac{J_{i,j}}{\sqrt{J_{i,i}J_{j,j}}}$.