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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 30 / No. 1: Thirtieth AAAI Conference On Artificial Intelligence

Linear-Time Learning on Distributions with Approximate Kernel Embeddings

March 8, 2023

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Authors

Danica Sutherland

Carnegie Mellon University


Junier Oliva

Carnegie Mellon University


Barnabás Póczos

Carnegie Mellon University


Jeff Schneider

Carnegie Mellon University


DOI:

10.1609/aaai.v30i1.10308


Abstract:

Many interesting machine learning problems are best posed by considering instances that are distributions, or sample sets drawn from distributions. Most previous work devoted to machine learning tasks with distributional inputs has done so through pairwise kernel evaluations between pdfs (or sample sets). While such an approach is fine for smaller datasets, the computation of an N × N Gram matrix is prohibitive in large datasets. Recent scalable estimators that work over pdfs have done so only with kernels that use Euclidean metrics, like the L2 distance. However, there are a myriad of other useful metrics available, such as total variation, Hellinger distance, and the Jensen-Shannon divergence. This work develops the first random features for pdfs whose dot product approximates kernels using these non-Euclidean metrics. These random features allow estimators to scale to large datasets by working in a primal space, without computing large Gram matrices. We provide an analysis of the approximation error in using our proposed random features, and show empirically the quality of our approximation both in estimating a Gram matrix and in solving learning tasks in real-world and synthetic data.

Topics: AAAI

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HOW TO CITE:

Danica Sutherland|| Junier Oliva|| Barnabás Póczos|| Jeff Schneider Linear-Time Learning on Distributions with Approximate Kernel Embeddings Proceedings of the AAAI Conference on Artificial Intelligence, 30 (2016) .

Danica Sutherland|| Junier Oliva|| Barnabás Póczos|| Jeff Schneider Linear-Time Learning on Distributions with Approximate Kernel Embeddings AAAI 2016, .

Danica Sutherland|| Junier Oliva|| Barnabás Póczos|| Jeff Schneider (2016). Linear-Time Learning on Distributions with Approximate Kernel Embeddings. Proceedings of the AAAI Conference on Artificial Intelligence, 30, .

Danica Sutherland|| Junier Oliva|| Barnabás Póczos|| Jeff Schneider. Linear-Time Learning on Distributions with Approximate Kernel Embeddings. Proceedings of the AAAI Conference on Artificial Intelligence, 30 2016 p..

Danica Sutherland|| Junier Oliva|| Barnabás Póczos|| Jeff Schneider. 2016. Linear-Time Learning on Distributions with Approximate Kernel Embeddings. "Proceedings of the AAAI Conference on Artificial Intelligence, 30". .

Danica Sutherland|| Junier Oliva|| Barnabás Póczos|| Jeff Schneider. (2016) "Linear-Time Learning on Distributions with Approximate Kernel Embeddings", Proceedings of the AAAI Conference on Artificial Intelligence, 30, p.

Danica Sutherland|| Junier Oliva|| Barnabás Póczos|| Jeff Schneider, "Linear-Time Learning on Distributions with Approximate Kernel Embeddings", AAAI, p., 2016.

Danica Sutherland|| Junier Oliva|| Barnabás Póczos|| Jeff Schneider. "Linear-Time Learning on Distributions with Approximate Kernel Embeddings". Proceedings of the AAAI Conference on Artificial Intelligence, 30, 2016, p..

Danica Sutherland|| Junier Oliva|| Barnabás Póczos|| Jeff Schneider. "Linear-Time Learning on Distributions with Approximate Kernel Embeddings". Proceedings of the AAAI Conference on Artificial Intelligence, 30, (2016): .

Danica Sutherland|| Junier Oliva|| Barnabás Póczos|| Jeff Schneider. Linear-Time Learning on Distributions with Approximate Kernel Embeddings. AAAI[Internet]. 2016[cited 2023]; .


ISSN: 2374-3468


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