A Homological Theory of Functions: Nonuniform Boolean Complexity Separation and VC Dimension Bound Via Algebraic Topology, and a Homological Farkas Lemma.
Greg YangPublished in: ITCS (2018)
Keyphrases
- vc dimension
- vapnik chervonenkis
- function classes
- vapnik chervonenkis dimension
- statistical learning theory
- upper bound
- worst case
- generalization bounds
- sample complexity
- concept classes
- lower bound
- distribution free
- sample size
- inductive inference
- covering numbers
- data dependent
- uniform convergence
- empirical risk minimization
- concept class
- theoretical framework
- compression scheme
- mind change complexity
- boolean functions
- real valued
- linear functions
- pac learning
- target function
- euclidean space
- learning problems
- risk bounds
- data sets
- image quality
- computational complexity
- reinforcement learning
- learning algorithm