ECCC-Report TR17-155https://eccc.weizmann.ac.il/report/2017/155Comments and Revisions published for TR17-155en-usMon, 06 Nov 2017 03:26:42 +0200
Revision 1
| Proofs of Proximity for Distribution Testing |
Alessandro Chiesa,
Tom Gur
https://eccc.weizmann.ac.il/report/2017/155#revision1Distribution testing is an area of property testing that studies algorithms that receive few samples from a probability distribution D and decide whether D has a certain property or is far (in total variation distance) from all distributions with that property. Most natural properties of distributions, however, require a large number of samples to test, which motivates the question of whether there are natural settings wherein fewer samples suffice.
We initiate a study of proofs of proximity for properties of distributions. In their basic form, these proof systems consist of a tester that not only has sample access to a distribution but also explicit access to a proof string that depends on the distribution. We refer to these as NP distribution testers, or MA distribution testers if the tester is a probabilistic algorithm. We also study the more general notion of IP distribution testers, in which the tester interacts with an all-powerful untrusted prover.
We investigate the power and limitations of proofs of proximity for distributions and chart a landscape that, surprisingly, is significantly different from that of proofs of proximity for functions. Our main results include showing that MA distribution testers can be quadratically stronger than standard distribution testers, but no stronger than that; in contrast, IP distribution testers can be exponentially stronger than standard distribution testers, but when restricted to public coins they can be at best quadratically stronger.Mon, 06 Nov 2017 03:26:42 +0200https://eccc.weizmann.ac.il/report/2017/155#revision1
Paper TR17-155
| Proofs of Proximity for Distribution Testing |
Alessandro Chiesa,
Tom Gur
https://eccc.weizmann.ac.il/report/2017/155Distribution testing is an area of property testing that studies algorithms that receive few samples from a probability distribution D and decide whether D has a certain property or is far (in total variation distance) from all distributions with that property. Most natural properties of distributions, however, require a large number of samples to test, which motivates the question of whether there are natural settings wherein fewer samples suffice.
We initiate a study of proofs of proximity for properties of distributions. In their basic form, these proof systems consist of a tester that not only has sample access to a distribution but also explicit access to a proof string that depends on the distribution. We refer to these as NP distribution testers, or MA distribution testers if the tester is a probabilistic algorithm. We also study the more general notion of IP distribution testers, in which the tester interacts with an all-powerful untrusted prover.
We investigate the power and limitations of proofs of proximity for distributions and chart a landscape that, surprisingly, is significantly different from that of proofs of proximity for functions. Our main results include showing that MA distribution testers can be quadratically stronger than standard distribution testers, but no stronger than that; in contrast, IP distribution testers can be exponentially stronger than standard distribution testers, but when restricted to public coins they can be at best quadratically stronger.Fri, 13 Oct 2017 12:24:00 +0300https://eccc.weizmann.ac.il/report/2017/155