added mukh and pikh

basic-ml.tex

@@ -112,6 +112,8 @@
 
 % prior probabilities
 \newcommand{\pik}[1][k]{\pi_{#1}} % pi_k, prior
+\newcommand{\pih}{\hat{\pi}} % pi hat, estimated prior (binary classification)
+\newcommand{\pikh}[1][k]{\hat{\pi}_{#1}} % pi_k hat, estimated prior
 \newcommand{\lpik}[1][k]{\log \pi_{#1}} % log pi_k, log of the prior
 \newcommand{\pit}{\pi(\thetav)} % Prior probability of parameter theta
 
@@ -137,6 +139,7 @@
 % probababilistic
 \newcommand{\bayesrulek}[1][k]{\frac{\P(\xv | y= #1) \P(y= #1)}{\P(\xv)}} % Bayes rule
 \newcommand{\muk}[1][k]{\bm{\mu_{#1}}} % mean vector of class-k Gaussian (discr analysis)
+\newcommand{\mukh}[1][k]{\bm{\hat{\mu}_{#1}}} % estimated mean vector of class-k Gaussian (discr analysis)
 
 % residual and margin
 \newcommand{\eps}{\epsilon} % residual, stochastic
@@ -158,10 +161,12 @@
 \newcommand{\Lxyit}{L\left(\yi, \fxit\right)} % loss of observation with f parameterized
 \newcommand{\Lxym}{L\left(\yi, f\left(\bm{\tilde{x}}^{(i)} ~|~ \thetav\right)\right)} % loss of observation with f parameterized
 \newcommand{\Lpixy}{L\left(y, \pix\right)} % loss in classification
+\newcommand{\Lpiy}{L\left(y, \pi\right)} % loss in classification
 \newcommand{\Lpiv}{L\left(y, \piv\right)} % loss in classification
 \newcommand{\Lpixyi}{L\left(\yi, \pixii\right)} % loss of observation in classification
 \newcommand{\Lpixyt}{L\left(y, \pixt\right)} % loss with pi parameterized
 \newcommand{\Lpixyit}{L\left(\yi, \pixit\right)} % loss of observation with pi parameterized
+\newcommand{\Lhy}{L\left(y, h\right)} % L(y, h), loss function on discrete classes
 \newcommand{\Lhxy}{L\left(y, \hx\right)} % L(y, h(x)), loss function on discrete classes
 \newcommand{\Lr}{L\left(r\right)} % L(r), loss defined on residual (reg) / margin (classif)
 \newcommand{\lone}{|y - \fx|} % L1 loss