Domain Adaptation H-Divergence
Tags: #machine learning #transfer learningEquation
$$d_{\mathcal{H}}(\mathcal{D},\mathcal{D}^{'})=2\sup_{h \in \mathcal{H}}|\Pr_{\mathcal{D}}[I(h)]-\Pr_{\mathcal{D}^{'}}[I(h)]|$$Latex Code
d_{\mathcal{H}}(\mathcal{D},\mathcal{D}^{'})=2\sup_{h \in \mathcal{H}}|\Pr_{\mathcal{D}}[I(h)]-\Pr_{\mathcal{D}^{'}}[I(h)]|
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Introduction
Equation
Latex Code
d_{\mathcal{H}}(\mathcal{D},\mathcal{D}^{'})=2\sup_{h \in \mathcal{H}}|\Pr_{\mathcal{D}}[I(h)]-\Pr_{\mathcal{D}^{'}}[I(h)]|
Explanation
The H-Divergence is defined as the superior of divengence between two probability Pr(D) and Pr(D^{'}) for any hypothesis h in all hypotheses class H. In this formulation, given domain X with two data distribution D and D^{'} over X, I(h) denotes the characteristic function(indicator function) on X, which means that for subset of x in I(h), h(x) = 1. You can check more detailed information of domain adaptation and H-divergence in this paper by Shai Ben-David, A theory of learning from different domains for more details.
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