440 research outputs found
Quantized Estimation of Gaussian Sequence Models in Euclidean Balls
A central result in statistical theory is Pinsker's theorem, which
characterizes the minimax rate in the normal means model of nonparametric
estimation. In this paper, we present an extension to Pinsker's theorem where
estimation is carried out under storage or communication constraints. In
particular, we place limits on the number of bits used to encode an estimator,
and analyze the excess risk in terms of this constraint, the signal size, and
the noise level. We give sharp upper and lower bounds for the case of a
Euclidean ball, which establishes the Pareto-optimal minimax tradeoff between
storage and risk in this setting.Comment: Appearing at NIPS 201
Robust one-bit compressed sensing with partial circulant matrices
We present optimal sample complexity estimates for one-bit compressed sensing
problems in a realistic scenario: the procedure uses a structured matrix (a
randomly sub-sampled circulant matrix) and is robust to analog pre-quantization
noise as well as to adversarial bit corruptions in the quantization process.
Our results imply that quantization is not a statistically expensive procedure
in the presence of nontrivial analog noise: recovery requires the same sample
size one would have needed had the measurement matrix been Gaussian and the
noisy analog measurements been given as data
High-Rate Vector Quantization for the Neyman-Pearson Detection of Correlated Processes
This paper investigates the effect of quantization on the performance of the
Neyman-Pearson test. It is assumed that a sensing unit observes samples of a
correlated stationary ergodic multivariate process. Each sample is passed
through an N-point quantizer and transmitted to a decision device which
performs a binary hypothesis test. For any false alarm level, it is shown that
the miss probability of the Neyman-Pearson test converges to zero exponentially
as the number of samples tends to infinity, assuming that the observed process
satisfies certain mixing conditions. The main contribution of this paper is to
provide a compact closed-form expression of the error exponent in the high-rate
regime i.e., when the number N of quantization levels tends to infinity,
generalizing previous results of Gupta and Hero to the case of non-independent
observations. If d represents the dimension of one sample, it is proved that
the error exponent converges at rate N^{2/d} to the one obtained in the absence
of quantization. As an application, relevant high-rate quantization strategies
which lead to a large error exponent are determined. Numerical results indicate
that the proposed quantization rule can yield better performance than existing
ones in terms of detection error.Comment: 47 pages, 7 figures, 1 table. To appear in the IEEE Transactions on
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