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Regression
- 1. Regression CS294 Practical Machine Learning Romain Thibaux 09/18/06
- 8. Linear regression 0 10 20 30 40 0 10 20 30 20 22 24 26 Temperature 0 10 20 0 20 40 [start Matlab demo lecture2.m] Given examples Predict given a new point
- 9. Linear regression 0 20 0 20 40 Temperature 0 10 20 30 40 0 10 20 30 20 22 24 26 Prediction Prediction
- 10. Ordinary Least Squares (OLS) 0 20 0 Error or “residual” Prediction Observation Sum squared error
- 11. Minimize the sum squared error Sum squared error Linear equation Linear system
- 12. Alternative derivation n d Solve the system (it’s better not to invert the matrix)
- 13. LMS Algorithm (Least Mean Squares) where Online algorithm
- 14. Beyond lines and planes everything is the same with still linear in 0 10 20 0 20 40
- 15. Geometric interpretation [Matlab demo] 0 10 20 0 100 200 300 400 -10 0 10 20
- 16. Ordinary Least Squares [summary] n d Let For example Let Minimize by solving Given examples Predict
- 17. Probabilistic interpretation 0 20 0 Likelihood
- 18. Assumptions vs. Reality Voltage Intel sensor network data Temperature 0 1 2 3 4 5 6 7 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
- 19. Overfitting 0 2 4 6 8 10 12 14 16 18 20 -15 -10 -5 0 5 10 15 20 25 30 [Matlab demo] Degree 15 polynomial
- 20. Ridge Regression (Regularization) 0 2 4 6 8 10 12 14 16 18 20 -10 -5 0 5 10 15 Effect of regularization (degree 19) with “small” Minimize by solving
- 21. Probabilistic interpretation Likelihood Prior Posterior
- 23. Errors in Variables (Total Least Squares) 0 0
- 24. Sensitivity to outliers High weight given to outliers Influence function 0 10 20 30 40 0 10 20 30 5 10 15 20 25 Temperature at noon
- 25. L 1 Regression Linear program Influence function
- 26. Kernel Regression 0 2 4 6 8 10 12 14 16 18 20 -10 -5 0 5 10 15 Kernel regression (sigma=1)
- 27. Spline Regression Regression on each interval 5200 5400 5600 5800 50 60 70
- 28. Spline Regression With equality constraints 5200 5400 5600 5800 50 60 70
- 29. Spline Regression With L 1 cost 5200 5400 5600 5800 50 60 70
- 30. 0 1 2 0 #requests per minute Time (days) 5000 Heteroscedasticity
- 31. MARS Multivariate Adaptive Regression Splines … on the board…
Hinweis der Redaktion
- Figure 1: scatter(1:20,10+(1:20)+2*randn(1,20),'k','filled'); a=axis; a(3)=0; axis(a);
- Figure 1: scatter(1:20,10+(1:20)+2*randn(1,20),'k','filled'); a=axis; a(3)=0; axis(a);
- Figure 1: scatter(1:20,10+(1:20)+2*randn(1,20),'k','filled'); a=axis; a(3)=0; axis(a);
- Link with perceptron
- A linear program is fast, but much slower than solving a linear system
- Link with kNN