From 314f4756103c28d362d10946aa820a78d216e007 Mon Sep 17 00:00:00 2001
From: sth4nth <sth4nth@gmail.com>
Date: Wed, 30 Jan 2019 14:17:00 +0800
Subject: [PATCH] tweak logistic regression

---
 chapter04/logitBin.m  | 15 +++++++--------
 chapter09/kmeansRnd.m |  2 +-
 2 files changed, 8 insertions(+), 9 deletions(-)

diff --git a/chapter04/logitBin.m b/chapter04/logitBin.m
index 80584a9..aa3eed7 100644
--- a/chapter04/logitBin.m
+++ b/chapter04/logitBin.m
@@ -1,16 +1,16 @@
-function [model, llh] = logitBin(X, y, lambda, eta)
+function [model, llh] = logitBin(X, y, lambda)
 % Logistic regression for binary classification optimized by Newton-Raphson method.
 % Input:
 %   X: d x n data matrix
-%   z: 1 x n label (0/1)
+%   y: 1 x n label (0/1)
 %   lambda: regularization parameter
-%   eta: step size
+%   alpha: step size
 % Output:
 %   model: trained model structure
 %   llh: loglikelihood
 % Written by Mo Chen (sth4nth@gmail.com).
 if nargin < 4
-    eta = 1e-1;
+    alpha = 1e-1;
 end
 if nargin < 3
     lambda = 1e-4;
@@ -20,18 +20,17 @@
 tol = 1e-4;
 epoch = 200;
 llh = -inf(1,epoch);
-h = 2*y-1;
 w = rand(d,1);
 for t = 2:epoch
     a = w'*X;
-    llh(t) = -(sum(log1pexp(-h.*a))+0.5*lambda*dot(w,w))/n; % 4.89
-    if llh(t)-llh(t-1) < tol; break; end
+    llh(t) = (dot(a,y)-sum(log1pexp(a))-0.5*lambda*dot(w,w))/n; % 4.90
+    if abs(llh(t)-llh(t-1)) < tol; break; end
     z = sigmoid(a);                     % 4.87
     g = X*(z-y)'+lambda*w;              % 4.96
     r = z.*(1-z);                       % 4.98
     Xw = bsxfun(@times, X, sqrt(r));
     H = Xw*Xw'+lambda*eye(d);           % 4.97
-    w = w-eta*(H\g); 
+    w = w-alpha*(H\g);                  % 4.92
 end
 llh = llh(2:t);
 model.w = w;
diff --git a/chapter09/kmeansRnd.m b/chapter09/kmeansRnd.m
index d48013f..b02f98f 100644
--- a/chapter09/kmeansRnd.m
+++ b/chapter09/kmeansRnd.m
@@ -10,7 +10,7 @@
 %   mu: d x k centers of clusters
 % Written by Mo Chen (sth4nth@gmail.com).
 alpha = 1;
-beta = nthroot(k,d); % in volume x^d there is k points: x^d=k
+beta = nthroot(k,d); % k points in volume x^d : x^d=k
 
 X = randn(d,n);
 w = dirichletRnd(alpha,ones(1,k)/k);