Noga Alon ; Alon Gonen ; Elad Hazan ; Shay Moran - Boosting Simple Learners

theoretics:9253 - TheoretiCS, June 19, 2023, Volume 2 - https://doi.org/10.46298/theoretics.23.8
Boosting Simple LearnersArticle

Authors: Noga Alon ; Alon Gonen ; Elad Hazan ORCID; Shay Moran ORCID

    Boosting is a celebrated machine learning approach which is based on the idea of combining weak and moderately inaccurate hypotheses to a strong and accurate one. We study boosting under the assumption that the weak hypotheses belong to a class of bounded capacity. This assumption is inspired by the common convention that weak hypotheses are "rules-of-thumbs" from an "easy-to-learn class". (Schapire and Freund~'12, Shalev-Shwartz and Ben-David '14.) Formally, we assume the class of weak hypotheses has a bounded VC dimension. We focus on two main questions: (i) Oracle Complexity: How many weak hypotheses are needed to produce an accurate hypothesis? We design a novel boosting algorithm and demonstrate that it circumvents a classical lower bound by Freund and Schapire ('95, '12). Whereas the lower bound shows that $\Omega({1}/{\gamma^2})$ weak hypotheses with $\gamma$-margin are sometimes necessary, our new method requires only $\tilde{O}({1}/{\gamma})$ weak hypothesis, provided that they belong to a class of bounded VC dimension. Unlike previous boosting algorithms which aggregate the weak hypotheses by majority votes, the new boosting algorithm uses more complex ("deeper") aggregation rules. We complement this result by showing that complex aggregation rules are in fact necessary to circumvent the aforementioned lower bound. (ii) Expressivity: Which tasks can be learned by boosting weak hypotheses from a bounded VC class? Can complex concepts that are "far away" from the class be learned? Towards answering the first question we {introduce combinatorial-geometric parameters which capture expressivity in boosting.} As a corollary we provide an affirmative answer to the second question for well-studied classes, including half-spaces and decision stumps. Along the way, we establish and exploit connections with Discrepancy Theory.


    Volume: Volume 2
    Published on: June 19, 2023
    Accepted on: March 20, 2023
    Submitted on: March 27, 2022
    Keywords: Computer Science - Machine Learning,Statistics - Machine Learning
    Funding:
      Source : OpenAIRE Graph
    • Trade and Global Economic Shocks: A Network Perspective; Funder: National Science Foundation; Code: 2018267
    • Problems and Methods in Extremal Combinatorics; Funder: National Science Foundation; Code: 1855464
    • Modern Challenges in Learning Theory; Funder: European Commission; Code: 101039692

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