fix chapter03

README.md

@@ -1,13 +1,16 @@
 Pattern Recognition and Machine Learning
 ===========
 
+This package contains the matlab implementation of the algorithms described in the book:
+Pattern Recognition and Machine Learning by C. Bishop (http://research.microsoft.com/en-us/um/people/cmbishop/prml/)
+
+
 License
 -------
 Currently Released Under GPLv3
 
 
 Contact
 -------
-sth4nth(CHEN, Mo) [username] at gmail dot com
+sth4nth at gmail dot com
 
-KuantKid(LI,Wei) [username] at gmail dot com

chapter01/nmi.m

@@ -1,5 +1,5 @@
 function z = nmi(x, y)
-% Compute nomalized mutual information I(x,y)/sqrt(H(x)*H(y)).
+% Compute normalized mutual information I(x,y)/sqrt(H(x)*H(y)).
 % x, y: two vectors of integers of the same length
 % Written by Mo Chen ([email protected]).
 assert(numel(x) == numel(y));
@@ -18,6 +18,8 @@
 Pxy = nonzeros(Mx'*My/n); %joint distribution of x and y
 Hxy = -dot(Pxy,log2(Pxy));
 
+
+% hacking, to elimative the 0log0 issue
 Px = nonzeros(mean(Mx,1));
 Py = nonzeros(mean(My,1));
 
@@ -31,3 +33,4 @@
 % normalized mutual information
 z = sqrt((MI/Hx)*(MI/Hy));
 z = max(0,z);
+

chapter01/nvi.m

@@ -1,5 +1,5 @@
 function z = nvi(x, y)
-% Compute nomalized variation information (1-I(x,y)/H(x,y)).
+% Compute normalized variation information (1-I(x,y)/H(x,y)).
 % x, y: two vectors of integers of the same length
 % Written by Mo Chen ([email protected]).
 assert(numel(x) == numel(y));

chapter03/demo.m

@@ -1,48 +1,25 @@
 % Done
 % demo for chapter 03
 clear; close all;
-n = 100;
-beta = 1e-1;
-X = rand(1,n);
-w = randn;
-b = randn;
-t = w'*X+b+beta*randn(1,n);
-x = linspace(min(X)-1,max(X)+1,n);   % test data
-
-% d = 1;
-% n = 200;
-% [X,t,model] = linRnd(d,n);
-% plotBand(X,t,2*model.sigma);
+d = 1;
+n = 200;
+[x,t,model] = linRnd(d,n);
+linPlot(model,x,t);
 %%
-model = linReg(X,t);
-y = linPred(model,x);
-figure;
-hold on;
-plot(X,t,'o');
-plot(x,y,'r-');
-hold off
+model = linReg(x,t);
+linPlot(model,x,t);
+fprintf('Press any key to continue. \n');
 pause
 %%
-[model,llh] = linRegEbEm(X,t);
-[y, sigma] = linPred(model,x,t);
+[model,llh] = linRegEbEm(x,t);
+linPlot(model,x,t);
 figure;
-hold on;
-plotBand(x,y,2*sigma);
-plot(X,t,'o');
-plot(x,y,'r-');
-hold off
-figure
 plot(llh);
-linPlot(model,x,t)
+fprintf('Press any key to continue. \n');
 pause
 %%
-[model,llh] = linRegEbFp(X,t);
+[model,llh] = linRegEbFp(x,t);
 [y, sigma] = linPred(model,x,t);
+linPlot(model,x,t);
 figure;
-hold on;
-plotBand(x,y,2*sigma);
-plot(X,t,'o');
-plot(x,y,'r-');
-hold off
-figure
 plot(llh);

chapter03/linPlot.m

@@ -1,13 +1,16 @@
 function linPlot(model, x, t)
+% Plot linear function and data
+% X: 1xn data
+% t: 1xn response
+% Written by Mo Chen ([email protected]).
 color = [255,228,225]/255; %pink
-[y,sigma] = linPred(model,x,t);
-h = 2*sigma;
-
+[x,idx] = sort(x);
+t = t(idx);
+[y,s] = linPred(model,x);
 figure;
 hold on;
-x = x(:);
-y = y(:);
-fill([x;flipud(x)],[y+h;flipud(y-h)],color);
+fill([x,fliplr(x)],[y+s,fliplr(y-s)],color);
+plot(x,t,'o');
 plot(x,y,'r-');
 hold off
 

chapter03/linPred.m

@@ -7,14 +7,16 @@
 w = model.w;
 w0 = model.w0;
 y = w'*X+w0;
-if nargin == 3
+if nargout > 1
     beta = model.beta;
     if isfield(model,'V')   % V*V'=inv(S) 3.54
         U = model.V'*bsxfun(@minus,X,model.xbar);
         sigma = sqrt(1/beta+dot(U,U,1));   % 3.59
     else
         sigma = sqrt(1/beta);
     end
-    p = exp(logGauss(t,y,sigma));
-%     p = exp(-0.5*(((t-y)./sigma).^2+log(2*pi))-log(sigma));
+    if nargin == 3 && nargout == 3
+        p = exp(logGauss(t,y,sigma));
+%         p = exp(-0.5*(((t-y)./sigma).^2+log(2*pi))-log(sigma));
+    end
 end

chapter03/linReg.m

@@ -21,6 +21,7 @@
 U = chol(S);
 w = U\(U'\(X*t'));  % 3.15 & 3.28
 w0 = tbar-dot(w,xbar);  % 3.19
-
+beta = 1/mean((t-w'*X).^2); % 3.21
 model.w = w;
 model.w0 = w0;
+model.beta = beta;

chapter03/linRnd.m

@@ -5,12 +5,12 @@
 %       X is generated form [0,1]
 %   d: dimension of data
 %   n: number of data
-beta = gamrnd(1,1);   % need statistcs toolbox
+beta = gamrnd(10,10);   % need statistcs toolbox
 X = rand(d,n);
 w = randn(d,1);
 w0 = randn(1,1);
-epsilon = randn(1,n)/beta;
-t = w'*X+w0+epsilon;
+err = randn(1,n)/sqrt(beta);
+t = w'*X+w0+err;
 
 model.w = w;
 model.w0 = w0;

helper/plotBand.m

@@ -7,4 +7,4 @@ function plotBand(x, y, h, color)
 x = x(:);
 y = y(:);
 h = h(:); 
-fill([x;flipud(x)],[y+h;flipud(y-h)],color);
+fill([x;flipud(x)]',[y+h;flipud(y-h)]',color);