2)" role="presentation" style="position: relative;"> xi∼N(μ,σ2) $x_i\sim N(\mu ,{\sigma }^2$

) $x_i \sim N(\mu,\sigma^2)$,
then $P(x)=\prod_{j=1}^n P(x_j;\mu,\sigma^2) < \xi$ is anomalous

3. Evaluation of Anomaly Detection Algorithm

Fit the model on training set and test the model on CV set/test set.
Precision/Recall/F1 Score
Use CV set to choose $\xi$

4. Comparison between Anomaly Detection and Supervised Learning

5. Other Features

$x ------->x^i/x^{\frac{1}{i} }$
$x ------->Log(x+i)$

(2) Recommendation Systems

1. Content Based Recommendations

For each user, learn a parameter $\theta$, use $\theta^T x$ to predict user’s favorites. $x_i$ represents the content of $i$-th movie.
This can be solved by linear regression

2. Collaborative Filtering Algorithm

Given $\theta$, Optimize $x$.
Similarly, this is a linear regression problem.

3. Vectorization

The predicted result is

4. Mean Normalization

What if $\theta^{(i)}=0$ ?
$\mu=average\sum\theta^{(i)}$, predict