Principal Inertia Components and Applications

Calmon, Flávio P.; Makhdoumi, Ali; Médard, Muriel; Varia, Mayank; Christiansen, Mark M.; Duffy, Ken R.

doi:10.1109/tit.2017.2700857

Cited by 54 publications

(64 citation statements)

References 78 publications

(148 reference statements)

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“…which is 0 up for t between 0 and H(X Y ), and linear with slope 1 for t in the interval from H(X Y ) to H(X). It is also shown that G(t) in general is different from this lower bound, namely even in the neighborhood of t = 0 it is typically positive, because in [20] it is shown that the derivative at t = 0 is typically positive. However, this is not the case for the privacy funnel function G (n) (t) of X n Y n , as n → ∞.…”

Section: Privacy Funnelmentioning

confidence: 97%

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Convexity and Operational Interpretation of the Quantum Information Bottleneck Function

Datta

Hirche

Winter

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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In classical information theory, the information bottleneck method (IBM) can be regarded as a method of lossy data compression which focusses on preserving meaningful (or relevant) information. As such it has of late gained a lot of attention, primarily for its applications in machine learning and neural networks. A quantum analogue of the IBM has recently been defined, and an attempt at providing an operational interpretation of the so-called quantum IB function as an optimal rate of an information-theoretic task, has recently been made by Salek et al. The interpretation given by these authors is however incomplete, as its proof is based on the conjecture that the quantum IB function is convex. Our first contribution is the proof of this conjecture.Secondly, the expression for the rate function involves certain entropic quantities which occur explicitly in the very definition of the underlying information-theoretic task, thus making the latter somewhat contrived. We overcome this drawback by pointing out an alternative operational interpretation of it as the optimal rate of a bona fide information-theoretic task, namely that of quantum source coding with quantum side information at the decoder, which has recently been solved by Hsieh and Watanabe. We show that the quantum IB function characterizes the rate region of this task,We similarly show that the related privacy funnel function is concave (both in the classical and quantum case). However, we comment that it is unlikely that the quantum privacy funnel function can characterize the optimal asymptotic rate of an information theoretic task, since even its classical version lacks a certain essential additivity property.

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Section: Privacy Funnelmentioning

confidence: 97%

“…setting. Indeed, in [20] it is shown that the classical privacy funnel function is convex and obeys the piecewise linear lower bound…”

Section: Privacy Funnelmentioning

confidence: 99%

Convexity and Operational Interpretation of the Quantum Information Bottleneck Function

Datta

Hirche

Winter

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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“…Relying on the so-called principal inertia components (PICs) [70], Calmon et al [71] showed that if χ 2 (U ; V ) < for some 0 < < 1, then the minimum mean-squared error (MMSE) of reconstructing any zero-mean unit-variance function of U given V is lower bounded by 1 − , i.e., no function of U can be reconstructed with small MMSE given an observation of V . Thus, χ 2 -information measures an adversary's ability to reconstruct functions of U from V under an MMSE loss.…”

Section: F -Informationmentioning

confidence: 99%

On the Robustness of Information-Theoretic Privacy Measures and Mechanisms

Díaz

Wang

Calmon

et al. 2020

IEEE Trans. Inform. Theory

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Consider a data publishing setting for a dataset composed by both private and non-private features. The publisher uses an empirical distribution, estimated from n i.i.d. samples, to design a privacy mechanism which is applied to new fresh samples afterward. In this paper, we study the discrepancy between the privacy-utility guarantees for the empirical distribution, used to design the privacy mechanism, and those for the true distribution, experienced by the privacy mechanism in practice. We first show that, for any privacy mechanism, these discrepancies vanish at speed O(1/ √ n) with high probability. These bounds follow from our main technical results regarding the Lipschitz continuity of the considered information leakage measures. Then we prove that the optimal privacy mechanisms for the empirical distribution approach the corresponding mechanisms for the true distribution as the sample size n increases, thereby establishing the statistical consistency of the optimal privacy mechanisms. Finally, we introduce and study uniform privacy mechanisms which, by construction, provide privacy to all the distributions within a neighborhood of the estimated distribution and, thereby, guarantee privacy for the true distribution with high probability.

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“…Our strategy is based on identifying a family of analog mappings h(·) for which z corresponds to the scenario studied in Section III-B. To that aim, we use PIC-based analysis [16], which provides a decomposition of the statistical…”

Section: Quadratic Estimation Tasksmentioning

confidence: 99%

“…Our model-aware analysis characterizes the achievable accuracy in recovering the desired information under bit constraints for tasks which can be modeled as a linear function of the measurements as in, e.g., Rayleigh fading MIMO channel estimation [13]. Then, we show how the proposed approach can be extended to more involved tasks by utilizing the mathematical tool of principal inertia compoenents (PICs) [16]. Specifically, we show that PICs can facilitate identifying a proper transformation of the measurements from which the task can be treated as approximately linear, allowing to use the proposed task-based quantizer.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Task-Based Quantization With Application to Massive MIMO

Shlezinger

Eldar

Rodrigues

2019

IEEE Trans. Signal Process.

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Multiple-input multiple-output (MIMO) systems are required to communicate reliably at high spectral bands using a large number of antennas, while operating under strict power and cost constraints.In order to meet these constraints, future MIMO receivers are expected to operate with low resolution quantizers, namely, utilize a limited number of bits for representing their observed measurements, inherently distorting the digital representation of the acquired signals. The fact that MIMO receivers use their measurements for some task, such as symbol detection and channel estimation, other than recovering the underlying analog signal, indicates that the distortion induced by bit-constrained quantization can be reduced by designing the acquisition scheme in light of the system task, i.e., by task-based quantization.In this work we survey the theory and design approaches to task-based quantization, presenting modelaware designs as well as data-driven implementations. Then, we show how one can implement a task-based bit-constrained MIMO receiver, presenting approaches ranging from conventional hybrid receiver architectures to structures exploiting the dynamic nature of metasurface antennas. This survey narrows the gap between theoretical task-based quantization and its implementation in practice, providing concrete algorithmic and hardware design principles for realizing task-based MIMO receivers. N. Shlezinger and Y. C. Eldar are with the Faculty of Math and CS, the number of BS antennas grow arbitrarily large [1], [2]. An additional method to increase the network throughput is to explore the millimeter wave (mmWave) frequency range [3], thus overcoming the spectral congestion of traditional wireless bands. Such mmWave communications is particularly suitable for massive MIMO systems: The short wavelengths of mmWave signals allows packing a large number of antenna elements at a small physical size, and the massive number of elements facilitates directed beamforming which is essential at mmWave bands. While the theoretical gains of massive MIMO systems, particularly when combined with mmWave transmission, are clear, implementing such systems in practice under strict cost and power constraints is a challenging task. A major source of this increased cost are the analog-todigital convertor (ADC) components, which allow the analog signals observed by each antenna element to be processed in digital. The power consumption of an ADC is directly related to the signal bandwidth and the number of bits used for digital representation [4], [5]. Consequently, in massive MIMO systems, where the number of antennas and ADCs operating at high frequency bands is large, limiting the number of bits, thus operating under quantization constraints, is crucial to keep cost and power consumption feasible [3].Focusing on uplink communications, i.e., when the BS acts as the receiver, quantization constraints imply that the BS cannot process the channel output directly but rather only an inaccurate distorted digital representation of it. The distor...

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Principal Inertia Components and Applications

Cited by 54 publications

References 78 publications

Convexity and Operational Interpretation of the Quantum Information Bottleneck Function

Convexity and Operational Interpretation of the Quantum Information Bottleneck Function

On the Robustness of Information-Theoretic Privacy Measures and Mechanisms

Asymptotic Task-Based Quantization With Application to Massive MIMO

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