Merge pull request #32 from sth4nth/master

extracted demos

README.md

@@ -10,7 +10,7 @@ The goal of the code are as follows:
 2. Efficient: utilizing matlab vectorization trick as much as possible to make the function fast. Many functions are even comparable with C implementation. Usually, functions in this package are orders faster than matlab builtin functions which provide same functionality (such as kmeans). If anyone found any matlab implementation which is faster than mine, I am happy to further optimize.
 3. Robust: many numerical stability techniques are applied, such as probability computation in log scale to avoid numerical underflow and overflow, square root form update of symetric matrix, etc.
 4. Easy to learn: the code is heavily commented. Reference formulas in PRML book are indicated for corresponding code lines.
-5. Practical: the package is designed not only for users to learn the algorithms in the book, but also to facilitate ML reseearch. Many functions in this package are already among the top downloads in Matlab [file exchange](http://www.mathworks.com/matlabcentral/fileexchange/?term=authorid%3A49739) site and widely used.
+5. Practical: the package is designed not only for users to learn the algorithms in the book, but also to facilitate ML research. Many functions in this package are already among the top downloads in Matlab [file exchange](http://www.mathworks.com/matlabcentral/fileexchange/?term=authorid%3A49739) site and widely used.
 
 License
 -------

TODO.txt

@@ -1,4 +1,5 @@
 TODO: 
 ch08: BP
 ch10: EP
-
+ch13: LDS stability
+ch05: MLP bias

chapter02/logGauss.m

@@ -1,21 +1,27 @@
-function y = logGauss(X, mu, Sigma)
+function y = logGauss(X, mu, sigma)
 % Compute log pdf of a Gaussian distribution.
 % Input:
 %   X: d x n data matrix
 %   mu: d x 1 mean vector of Gaussian
-%   Sigma: d x d covariance matrix of Gaussian
+%   sigma: d x d covariance matrix of Gaussian
 % Output:
 %   y: 1 x n probability density in logrithm scale y=log p(x)
 % Written by Mo Chen ([email protected]).
 [d,k] = size(mu);
-assert(all(size(Sigma)==d) && k==1)   % one mu and one dxd Sigma
-X = bsxfun(@minus,X,mu);
-[R,p]= chol(Sigma);
-if p ~= 0
-    error('ERROR: Sigma is not PD.');
-end
-Q = R'\X;
-q = dot(Q,Q,1);  % quadratic term (M distance)
-c = d*log(2*pi)+2*sum(log(diag(R)));   % normalization constant
-y = -0.5*(c+q);
-
+if all(size(sigma)==d) && k==1   % one mu and one dxd sigma
+    X = bsxfun(@minus,X,mu);
+    [R,p]= chol(sigma);
+    if p ~= 0
+        error('ERROR: sigma is not PD.');
+    end
+    Q = R'\X;
+    q = dot(Q,Q,1);  % quadratic term (M distance)
+    c = d*log(2*pi)+2*sum(log(diag(R)));   % normalization constant
+    y = -0.5*(c+q);
+elseif size(sigma,1)==1 && size(sigma,2)==size(mu,2) % k mu and (k or one) scalar sigma
+    X2 = repmat(dot(X,X,1)',1,k);
+    D = bsxfun(@plus,X2-2*X'*mu,dot(mu,mu,1));
+    q = bsxfun(@times,D,1./sigma);  % M distance
+    c = d*(log(2*pi)+2*log(sigma));          % normalization constant
+    y = -0.5*bsxfun(@plus,q,c);
+end

chapter05/mlpPred.m

@@ -0,0 +1,16 @@
+function y = mlpPred(model, X)
+% Multilayer perceptron prediction
+% Input:
+%   model: model structure
+%   X: d x n data matrix
+% Ouput:
+%   Y: p x n response matrix
+% Written by Mo Chen ([email protected]).
+W = model.W;
+L = length(W)+1;
+Z = cell(L);
+Z{1} = X;
+for l = 2:L
+    Z{l} = sigmoid(W{l-1}'*Z{l-1});
+end
+y = Z{L};

chapter10/rvmRegVb.m

@@ -20,6 +20,8 @@
     c0 = prior.c;
     d0 = prior.d;
 end
+idx = (1:m)';
+dg = sub2ind([m,m],idx,idx);
 I = eye(m);
 xbar = mean(X,2);
 tbar = mean(t,2);
@@ -36,11 +38,12 @@
 
 a = a0+1/2;
 c = c0+n/2;
-Ealpha = 1e-4;
-Ebeta = 1e-4;
+Ealpha = 1e-2;
+Ebeta = 1e-2;
 for iter = 2:maxiter
 %     q(w)
-    invS = diag(Ealpha)+Ebeta*XX;
+    invS = Ebeta*XX;
+    invS(dg) = invS(dg)+Ealpha;
     U = chol(invS);
     Ew = Ebeta*(U\(U'\Xt));
     KLw = -sum(log(diag(U)));        

chapter13/LDS/TODO.txt

@@ -0,0 +1,2 @@
+(1) test against matlab implementation of kalman filter
+(2) simplify ldsEm with less parameters (G=diag(g), S=I)