• Bernoulli
  • Volume 24, Number 4A (2018), 2429-2460.

Adaptive confidence sets for matrix completion

Alexandra Carpentier, Olga Klopp, Matthias Löffler, and Richard Nickl

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In the present paper, we study the problem of existence of honest and adaptive confidence sets for matrix completion. We consider two statistical models: the trace regression model and the Bernoulli model. In the trace regression model, we show that honest confidence sets that adapt to the unknown rank of the matrix exist even when the error variance is unknown. Contrary to this, we prove that in the Bernoulli model, honest and adaptive confidence sets exist only when the error variance is known a priori. In the course of our proofs, we obtain bounds for the minimax rates of certain composite hypothesis testing problems arising in low rank inference.

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Bernoulli, Volume 24, Number 4A (2018), 2429-2460.

Received: August 2016
Revised: January 2017
First available in Project Euclid: 26 March 2018

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Zentralblatt MATH identifier

adaptivity confidence sets low rank recovery matrix completion minimax hypothesis testing unknown variance


Carpentier, Alexandra; Klopp, Olga; Löffler, Matthias; Nickl, Richard. Adaptive confidence sets for matrix completion. Bernoulli 24 (2018), no. 4A, 2429--2460. doi:10.3150/17-BEJ933.

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