Completed
Monotone regression: problem definition
Class Central Classrooms beta
YouTube videos curated by Class Central.
Classroom Contents
Nonnegative Polynomials, Nonconvex Polynomial Optimization, and Applications to Learning
Automatically move to the next video in the Classroom when playback concludes
- 1 Intro
- 2 Optimizing over nonnegative polynomials
- 3 1. Shape-constrained regression
- 4 2. Difference of Convex (DC) programming Problems of the form min fo (x)
- 5 Monotone regression: problem definition
- 6 NP-hardness and SOS relaxation
- 7 Approximation theorem
- 8 Numerical experiments (1/2) • Low noise environment
- 9 Difference of Convex (dc) decomposition
- 10 Existence of dc decomposition (2/3)
- 11 Convex-Concave Procedure (CCP)
- 12 Picking the "best" decomposition for CCP
- 13 Undominated decompositions (1/2)
- 14 Comparing different decompositions (1/2)
- 15 Main messages • Optimization over nonnegative polynomials has many applications Powerful SDP/SOS-based relaxations available.
- 16 Uniqueness of dc decomposition
