Final Exam: Advanced Math

WHAT YOU WILL LEARN

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  Recall the use of matrix operations to represent linear transformations
  

  define eigenvectors and eigenvalues
  

  define principal components and their uses
  

  recall the intuition behind principal component analysis
  

  define eigenvalues and eigenvectors
  

  mathematically compute principal components
  

  compute eigenvalues and eigenvectors
  

  perform principal component analysis
  

  build a baseline model using logistic regression
  

  build a logistic regression model using principal components
• 

  summarize the use cases of recommendation systems and the different techniques applied to build such models, with emphasis on the content-based filtering approach
  

  describe the use cases of recommendation systems and the different techniques applied to build such models, with emphasis on the content-based filtering approach
  

  summarize the intuition behind collaborative filtering, its main advantages, and how ratings matrices, the nearest neighbor approach, and latent factor analysis are involved
  

  describe the intuition behind collaborative filtering, its main advantages, and how ratings matrices, the nearest neighbor approach, and latent factor analysis are involved
  

  decompose a ratings matrix into its latent factors
  

  apply gradient descent to compute the factors of a ratings matrix
  

  compute a penalty for a large number of latent factors when computing the factors of a ratings matrix
  

  use numpy and pandas to define a ratings matrix that can be fed into a recommendation system
  

  implement the gradient descent algorithm to decompose a ratings matrix
  

  compute the predicted ratings given by users for various items by using matrix decomposition