Week 9

Density Estimation(异常检测)

Problem Motivation

• Density Estimation Algotithm

• Anomaly detection example

Gaussian Distribution(高斯分布或正态分布)

The formula for the Gaussian density is: $$ p(x) = \frac{1}{\sqrt{2\pi}\sigma}\exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right) $$

• Gaussian distribution example

  

• Parameter estimation

  

Algorithm

• Anomaly detection example

  

Building an Anomaly Detection System

Developing and Evaluating an Anomaly Detection System

• the important of real-number evaluation

  

• Aircraft engines motivating example

  

• Alogorithm evaluation

  

Anomaly Detection vs. Supervised Learning

Choosing What Features to Use

• Non-gaussian features

  

• Error analysis for anomaly detection

  

• Monitoring computers in a data center

  

Multivariate Gaussian Distribution(Optional)

Multivariate Gaussian Distribution

• Motivating example:Monitoring machines in a data center

  

• Multivariate Gaussian(Normal)distribution

  

• Multivariate Gaussian(Normal) examples

  

  

  

  

  

  

Anomaly Detection using the Multivariate Gaussian Distribution

• Multivariate Gaussian (Normal) distribution

  

• Anomaly detection with the multivariate Gaussian

  

• Relationship to original model

  

• Original model vs. Multivariate Gaussian

  

Predicting Movie Ratings

Problem Formulation

• Example : Predicting movie ratings

Content Based Recommendations

• Content-based recommender systems

  

• Problem formulation

  

• Optimization objective

  

• Optimization algorithm

  

Collaborative Filtering

Collaborative Filtering

• Problem motivation

  

• Optimization algorithm

  

• Collaborative filtering

  

Collaborative Filtering Algorithm

• Collaborative filtering optimization objective

  

• Collaborative filtering algorithm

  

Low Rank Matrix Factorization(低秩矩阵分解)

Vectorization: Low Rank Matrix Factorization

• Collaborative filtering

  

• Finding related movies

  

Implementational Detail: Mean Normalization

• Users who have not reated any movies

  

• Mean Normalizatio