# Andrew Ng Coursera Machine Learning(vII)

Posted by Kaiyuan Chen on September 3, 2017

## Anomaly detection

We model p(x) and p(x_test) < \eps, then flag anomaly

### Gaussian Distribution

x ~ N(\mu, \standard deviation^2)

p(x) = p(x1; mu1, sq1) * p(x2; m2, sq2) … = product of all p

Algorithm:

1. choose features that you might think indicative
2. fit parameters
3. compute p(x) the product(of two pdfs) is the result

#### Developing and evaluating an anomaly detection system

Assume we have some labelled data, of anomalous and non-anomalous examples, for training set, unlabeled and it’s ok to let anomalous to slip in then use labelled set to test cross validation and test

algorithm

1. fit model p(x) on training set
2. predict on cross validation / test example

evaluation metrics: big-four / precision, recall / F score

#### Choosing features

we use different features, like different order, log to make data distributed more Gaussian we choose feature that make usually large/small value in event of anomaly

### Recommender System

#### Content-based Recommender system

use a vector to describe the degree of class(like romance, action) we can treat every user as a linear regression problem to learn all users(all thetas) just add a summation to all linear regressions

#### Collaborative Filtering

feature learning: when we have a series of theta for every users, we can infer the features (which are how romantic a movie is)

##### algorithm

instead of switching between estimating x and estimating theta, we optimize a general equation such that

J(x, theta) = 1/2 * sum(theta*x - y)^2 + regulation term of theta + regulation term of x

1. initialize x and theta to small random values

#### low rank matrix factorization

we can have a matrix that contain all the predictive rating for users/movies and we compute it as X * Theta’

In mathematics, low-rank approximation is a minimization problem, in which the cost function measures the fit between a given matrix (the data) and an approximating matrix (the optimization variable), subject to a constraint that the approximating matrix has reduced rank.

we use Euclidean distance

##### Implementation Details

If we do predictive matrix and collaborative filtering directly, for a new user without any information will minimize J by setting every parameter to 0.

To solve this problem, we use mean normalization. we subtract average rating of every matrix and learn theta and x through this new matrix.