SGD for matrix factorization, NMF, and cold start slides

42 Pages·2016·1.6 MB·English

by  Emily Fox

Case Study 4: Collaborative Filtering
Collaborative Filtering
Matrix Completion
Alternating Least Squares
Machine Learning for Big Data
CSE547/STAT548, University of Washington
Sham Kakade
May 19, 2016
©Sham Kakade 2016 1
Collaborative Filtering
• Goal: Find movies of interest to a user based on
movies watched by the user and others
• Methods: matrix factorization
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Women on the Verge of a
Nervous Breakdown
The Celebration
City of God
What do I
recommend???
Wild Strawberries
La Dolce Vita
©Sham Kakade 2016 3
Netflix Prize
• Given 100 million ratings on a scale of 1
to 5, predict 3 million ratings to highest
accuracy
• 17770 total movies
• 480189 total users
• Over 8 billion total ratings
• How to fill in the blanks?
©Sham Kakade 2016 Figures from Ben Re4cht
Matrix Completion Problem
X known for black cells
ij
X unknown for white cells
X = ij
RoRwows si ninddeexx umseorsvies
CCoolluummnns sin idnedxe mxo uviseesrs
• Filling missing data?
©Sham Kakade 2016 5
Interpreting Low-Rank Matrix Completion
(aka Matrix Factorization)
R’
X = L
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Identifiability of Factors
R’
X = L
• If r is described by L , R what happens if we redefine the “topics” as
uv u v
• Then,
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Matrix Completion via Rank Minimization
• Given observed values:
• Find matrix
• Such that:
• But…
• Introduce bias:
• Two issues:
©Sham Kakade 2016 8
Approximate Matrix Completion
• Minimize squared error:
– (Other loss functions are possible)
• Choose rank k:
• Optimization problem:
©Sham Kakade 2016 9
Coordinate Descent for Matrix Factorization
• Fix movie factors, optimize for user factors
• First observation:
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