Adaptive confidence sets for matrix completion.

被引：10

作者：

Carpentier, Alexandra ^{[1
]}

Klopp, Olga ^{[2
,3
]}

Loeffler, Matthias ^{[4
]}

Nickl, Richard ^{[4
]}

机构：

[1] Univ Potsdam, Inst Math, Neuen Palais 10, D-14469 Potsdam, Germany

[2] Univ Paris Ouest, CREST, 200 Ave Republ Nanterre, Nanterre, France

[3] Univ Paris Ouest, MODALX, 200 Ave Republ Nanterre, Nanterre, France

[4] Univ Cambridge, Stat Lab, Ctr Math Sci, Wilberforce Rd, Cambridge CB3 0WB, England

来源：

BERNOULLI | 2018年 / 24卷 / 4A期

基金：

欧洲研究理事会; 英国工程与自然科学研究理事会;

关键词：

adaptivity; confidence sets; low rank recovery; matrix completion; minimax hypothesis testing; unknown variance; NORM; INEQUALITIES; INFERENCE; BOUNDS;

D O I：

10.3150/17-BEJ933

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：2429 / 2460

页数：32

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