refined doc for ch13 LDS

TODO.txt

@@ -3,7 +3,7 @@ extract demos
 modify linPred to use Sigma instead of U and modify related regression functions
 chapter10/12: prediction functions for VB
 chapter07: rvm seq bug
-chapter13/common/other: refine doc
+common/other: refine doc
 chapter13: refine ldsRnd
 chapter05: MLP
 chapter08: BP, EP

chapter09/mixGaussRnd.m

@@ -1,5 +1,5 @@
 function [X, z, model] = mixGaussRnd(d, k, n)
-% Sampling form a Gaussian mixture distribution.
+% Genarate samples form a Gaussian mixture model.
 % Input:
 %   d: dimension of data
 %   k: number of components

chapter13/LDS/kalmanFilter.m

@@ -1,5 +1,12 @@
 function [mu, V, llh] = kalmanFilter(X, model)
 % Kalman filter 
+% Input:
+%   X: d x n data matrix
+%   model: model structure
+% Output:
+%   mu: q x n matrix of latent mean mu_t=E[z_t] w.r.t p(z_t|x_{1:t})
+%   V: q x q x n latent covariance U_t=cov[z_t] w.r.t p(z_t|x_{1:t})
+%   llh: loglikelihood
 % Written by Mo Chen ([email protected]).
 A = model.A; % transition matrix 
 G = model.G; % transition covariance

chapter13/LDS/kalmanSmoother.m

@@ -1,5 +1,14 @@
 function [nu, U, Ezz, Ezy, llh] = kalmanSmoother(X, model)
-% Kalman smoother
+% Kalman smoother (forward-backward algorithm for linear dynamic system)
+% Input:
+%   X: d x n data matrix
+%   model: model structure
+% Output:
+%   nu: q x n matrix of latent mean mu_t=E[z_t] w.r.t p(z_t|x_{1:T})
+%   U: q x q x n latent covariance U_t=cov[z_t] w.r.t p(z_t|x_{1:T})
+%   Ezz: q x q matrix E[z_tz_t^T]
+%   Ezy: q x q matrix E[z_tz_{t-1}^T]
+%   llh: loglikelihood
 % Written by Mo Chen ([email protected]).
 A = model.A; % transition matrix 
 G = model.G; % transition covariance

chapter13/LDS/ldsEm.m

@@ -1,5 +1,11 @@
 function [model, llh] = ldsEm(X, model)
-% EM algorithm for parameter estimation of LDS
+% EM algorithm for parameter estimation of linear dynamic system.
+% Input:
+%   X: d x n data matrix
+%   model: prior model structure
+% Output:
+%   model: trained model structure
+%   llh: loglikelihood
 % Written by Mo Chen ([email protected]).
 tol = 1e-4;
 maxIter = 100;
@@ -9,11 +15,11 @@
     [nu, U, Ezz, Ezy, llh(iter)] = kalmanSmoother(X, model);
     if llh(iter)-llh(iter-1) < tol*abs(llh(iter-1)); break; end   % check likelihood for convergence
 %     M-step 
-    model = mStep(X, nu, U, Ezz, Ezy);
+    model = maximization(X, nu, U, Ezz, Ezy);
 end
 llh = llh(2:iter);
 
-function model = mStep(X ,nu, U, Ezz, Ezy)
+function model = maximization(X ,nu, U, Ezz, Ezy)
 n = size(X,2);
 mu0 = nu(:,1);
 P0 = U(:,:,1);

chapter13/LDS/ldsRnd.m

@@ -1,5 +1,13 @@
-function [X, model] = ldsRnd(d, k, n )
-
+function [X, model] = ldsRnd(d, k, n)
+% Generate  a data sequence from linear dynamic system.
+% Input:
+%   d: dimension of data
+%   k: dimension of latent variable
+%   n: number of data
+% Output:
+%   X: d x n data matrix
+%   model: model structure
+% Written by Mo Chen ([email protected]).
 A = randn(k,k);
 G = iwishrnd(eye(k),k);
 C = randn(d,k);