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What is PAC learning model in machine learning?
Probably approximately correct (PAC) learning is a theoretical framework for analyzing the generalization error of a learning algorithm in terms of its error on a training set and some measure of complexity. The goal is typically to show that an algorithm achieves low generalization error with high probability.
What is agnostic PAC learning?
Agnostic PAC Learning. • Definition: A learner that doesn’t assume that. contains an error free hypothesis and that simply. finds the hypothesis with minimum training error is. often called an agnostic learner.
What is PAC theory?
In computational learning theory, probably approximately correct (PAC) learning is a framework for mathematical analysis of machine learning. It was proposed in 1984 by Leslie Valiant.
What is mistake bound model?
Definition 1 An algorithm A is said to learn C in the mistake bound model if for any concept c ∈ C, and for any ordering of examples consistent with c, the total number of mistakes ever made by A is bounded by p(n,size(c)), where p is a polynomial.
Are disjunctions PAC learnable?
There are at most 2n monotone conjunctions, so by Theorem 1 the class of monotone conjunctions is learnable in the PAC model. Non-monotone conjunctions, disjunctions, k-CNF, k-DNF. There are at most 2O(nk) k-CNFs, so for constant k, by Theorem 1 the class of k-CNFs is learnable in the PAC model.
What is PAC algorithm?
When is a hypothesis class PAC learnable?
What does this mean? The definition states that a hypothesis class is PAC learnable if there exists a function m_H and an algorithm that for any labeling function f, distribution D over the domain of inputs X, delta and epsilon that with m ≥ m_H produces a hypothesis h such that with probability 1- delta it yields a true error lower than epsilon.
How is PAC learnability changed in data science?
Notice the changes in the definition with regards to the definition of PAC learnability. By introducing the data-labels distribution D we allow for the fact that the true error of the learned hypothesis is going to be less or equal to the error of the optimal hypothesis plus a factor epsilon.
How to calculate lower bound for PAC learning?
Based on these parameters we could calculate how many samples we need to achieve such accuracy and we arrived at the following lower bound for the samples: This can be fit into the general PAC learning framework, the following formal definition was given from the book Understanding Machine Learning:
Why is it called Agnostic PAC learning?
So why is it called Agnostic PAC learning? Well, the word agnostic comes from the fact that the learning is agnostic towards the data-labels distribution — this means that it is going to learn the best labeling function f by making no assumptions about the data-labels distribution. What changes in this case?