Anomaly Detection
1.1 Gaussian distribution
1.2 Estimating parameters for a Gaussian
$$\mu {i} = \dfrac {1}{m}\sum{j=1}^{m}x _{i}^{(j)}$$
$$\sigma {i}^{2} = \dfrac{1}{m}\sum{j=1}^{m}(x _{i}^{(j)} - \mu _{i})^2$$
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| mu = sum(X)/m;
sigma2 = sum((X-mu).^2)/m;
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我以为这些方程出了问题，因为概率最高的区域没有显示为 pdf 游的红色椭圆。
调试了一下，我发现高斯分布等值线的中心颜色是黄色的，在无 Retina 屏幕上几乎看不到。 😂😂😂
1.3 Selecting the threshold, ε
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| p = (pval < epsilon);
tp = sum((p == 1) & (yval == 1));
fp = sum((p == 1) & (yval == 0));
fn = sum((p == 0) & (yval == 1));
prec = tp/(tp+fp);
rec = tp/(tp+fn);
F1 = 2*prec*rec/(prec+rec);
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Recommender Systems
2.1 Movie ratings dataset
2.2.1 Collaborative filtering cost function
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| tmp = X*Theta' .* R - Y;
J = sum(sum(tmp.^2))/2;
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2.2.2 Collaborative filtering gradient
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| X_grad = tmp*Theta;
Theta_grad = tmp'*X;
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2.2.3 Regularized cost function
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| J = J + lambda/2*(sum(sum(Theta.^2))) + lambda/2*(sum(sum(X.^2)));
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2.2.4 Regularized gradient
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| X_grad = X_grad + lambda*X;
Theta_grad = Theta_grad + lambda*Theta;
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