Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distribution Regression with Sliced Wasserstein Kernels   The problem of learning functions over spaces of probabilities - or
distribution regression - is gaining significant interest in the machine
learning community. A key challenge behind this problem is to identify a
suitable representation capturing all relevant properties of the underlying
functional mapping. A principled approach to distribution regression is
provided by kernel mean embeddings, which lifts kernel-induced similarity on
the input domain at the probability level. This strategy effectively tackles
the two-stage sampling nature of the problem, enabling one to derive estimators
with strong statistical guarantees, such as universal consistency and excess
risk bounds. However, kernel mean embeddings implicitly hinge on the maximum
mean discrepancy (MMD), a metric on probabilities, which may fail to capture
key geometrical relations between distributions. In contrast, optimal transport
(OT) metrics, are potentially more appealing, as documented by the recent
literature on the topic. In this work, we propose the first OT-based estimator
for distribution regression. We build on the Sliced Wasserstein distance to
obtain an OT-based representation. We study the theoretical properties of a
kernel ridge regression estimator based on such representation, for which we
prove universal consistency and excess risk bounds. Preliminary experiments
complement our theoretical findings by showing the effectiveness of the
proposed approach and compare it with MMD-based estimators.

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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: math
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex