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Testing goodness of fit of conditional density models with kernels

Jitkrittum, W; Kanagawa, H; Schölkopf, B; (2020) Testing goodness of fit of conditional density models with kernels. In: Peters, J and Sontag, D, (eds.) Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence. (pp. pp. 221-230). Proceedings of Machine Learning Research: Virtual. Green open access

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Abstract

We propose two nonparametric statistical tests of goodness of fit for conditional distributions: given a conditional probability density function p(y|x) and a joint sample, decide whether the sample is drawn from p(y|x)rx(x) for some density rx. Our tests, formulated with a Stein operator, can be applied to any differentiable conditional density model, and require no knowledge of the normalizing constant. We show that 1) our tests are consistent against any fixed alternative conditional model; 2) the statistics can be estimated easily, requiring no density estimation as an intermediate step; and 3) our second test offers an interpretable test result providing insight on where the conditional model does not fit well in the domain of the covariate. We demonstrate the interpretability of our test on a task of modeling the distribution of New York City's taxi drop-off location given a pick-up point. To our knowledge, our work is the first to propose such conditional goodness-of-fit tests that simultaneously have all these desirable properties.

Type: Proceedings paper
Title: Testing goodness of fit of conditional density models with kernels
Event: 36th Conference on Uncertainty in Artificial Intelligence
Open access status: An open access version is available from UCL Discovery
Publisher version: http://proceedings.mlr.press/v124/jitkrittum20a.ht...
Language: English
Additional information: © Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence, UAI 2020. All rights reserved. This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10125425
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