On Minimax Estimation in the Presence of Side Information About Remote Data

Ahlswede, Rudolf; Burnashev, M. V.

doi:10.1214/aos/1176347496

Cited by 35 publications

(45 citation statements)

References 10 publications

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“…The present work generalizes to the nonparametric setting the case considered by Ahlswede and Burnashev [7], namely when R 1 = ∞. To the best of the author's knowledge, this paper is the first to consider the problem of nonparametric learning from compressed observations with side information.…”

Section: A Related Workmentioning

confidence: 73%

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Learning From Compressed Observations

Raginsky

2007

2007 IEEE Information Theory Workshop

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Abstract-The problem of statistical learning is to construct a predictor of a random variable Y as a function of a related random variable X on the basis of an i.i.d. training sample from the joint distribution of (X, Y ). Allowable predictors are drawn from some specified class, and the goal is to approach asymptotically the performance (expected loss) of the best predictor in the class. We consider the setting in which one has perfect observation of the X-part of the sample, while the Y -part has to be communicated at some finite bit rate. The encoding of the Y -values is allowed to depend on the X-values. Under suitable regularity conditions on the admissible predictors, the underlying family of probability distributions and the loss function, we give an information-theoretic characterization of achievable predictor performance in terms of conditional distortion-rate functions. The ideas are illustrated on the example of nonparametric regression in Gaussian noise.

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Section: A Related Workmentioning

confidence: 73%

“…First of all, it would be of interest to derive informationtheoretic lower bounds on the generalization performance of rate-constrained learning algorithms. In particular, just as Ahlswede and Burnashev had done in the parametric case [7], we could study the asymptotics of the ninimax excess risk…”

Section: Discussion and Future Workmentioning

confidence: 99%

Learning From Compressed Observations

Raginsky

2007

2007 IEEE Information Theory Workshop

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“…The existing work on statistical inference (hypothesis testing and estimation in [4] and [3]) under communication constraints uses a "one shot" side information. It seems important to introduce and analyze interactive models.…”

Section: Other Problemsmentioning

confidence: 99%

Estimating with Randomized Encoding the Joint Empirical Distribution in a Correlated Source

Ahlswede

Zhang²

2006

Lecture Notes in Computer Science

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“…Функция Б(т\\ро) является U-вы-пуклой по г и монотонно возрастающей при г ^ ро-Поэтому 7 должно удовлетворять условию 0 < 7 < -^CPIIIPO)-Д ЛЯ таких j величина г (7) определяется как единственный корень (для ро ^ т) уравнения (4).…”

Section: известный входной блокunclassified