545,273 research outputs found
Communication-constrained hypothesis testing: Optimality, robustness, and reverse data processing inequalities
We study hypothesis testing under communication constraints, where each
sample is quantized before being revealed to a statistician. Without
communication constraints, it is well known that the sample complexity of
simple binary hypothesis testing is characterized by the Hellinger distance
between the distributions. We show that the sample complexity of simple binary
hypothesis testing under communication constraints is at most a logarithmic
factor larger than in the unconstrained setting and this bound is tight. We
develop a polynomial-time algorithm that achieves the aforementioned sample
complexity. Our framework extends to robust hypothesis testing, where the
distributions are corrupted in the total variation distance. Our proofs rely on
a new reverse data processing inequality and a reverse Markov inequality, which
may be of independent interest. For simple -ary hypothesis testing, the
sample complexity in the absence of communication constraints has a logarithmic
dependence on . We show that communication constraints can cause an
exponential blow-up leading to sample complexity even for adaptive
algorithms.Comment: To appear in IEEE Transactions on Information Theor
Distributed Hypothesis Testing with Privacy Constraints
We revisit the distributed hypothesis testing (or hypothesis testing with
communication constraints) problem from the viewpoint of privacy. Instead of
observing the raw data directly, the transmitter observes a sanitized or
randomized version of it. We impose an upper bound on the mutual information
between the raw and randomized data. Under this scenario, the receiver, which
is also provided with side information, is required to make a decision on
whether the null or alternative hypothesis is in effect. We first provide a
general lower bound on the type-II exponent for an arbitrary pair of
hypotheses. Next, we show that if the distribution under the alternative
hypothesis is the product of the marginals of the distribution under the null
(i.e., testing against independence), then the exponent is known exactly.
Moreover, we show that the strong converse property holds. Using ideas from
Euclidean information theory, we also provide an approximate expression for the
exponent when the communication rate is low and the privacy level is high.
Finally, we illustrate our results with a binary and a Gaussian example
Optimal high-dimensional and nonparametric distributed testing under communication constraints
We derive minimax testing errors in a distributed framework where the
data is split over multiple machines and their communication to a central machine is limited to b bits. We investigate both the d- and infinite-dimensional
signal detection problem under Gaussian white noise. We also derive distributed testing algorithms reaching the theoretical lower bounds.
Our results show that distributed testing is subject to fundamentally different phenomena that are not observed in distributed estimation. Among our
findings, we show that testing protocols that have access to shared randomness can perform strictly better in some regimes than those that do not. We
also observe that consistent nonparametric distributed testing is always possible, even with as little as 1-bit of communication and the corresponding
test outperforms the best local test using only the information available at
a single local machine. Furthermore, we also derive adaptive nonparametric
distributed testing strategies and the corresponding theoretical lower bound
Simple Binary Hypothesis Testing under Local Differential Privacy and Communication Constraints
We study simple binary hypothesis testing under both local differential
privacy (LDP) and communication constraints. We qualify our results as either
minimax optimal or instance optimal: the former hold for the set of
distribution pairs with prescribed Hellinger divergence and total variation
distance, whereas the latter hold for specific distribution pairs. For the
sample complexity of simple hypothesis testing under pure LDP constraints, we
establish instance-optimal bounds for distributions with binary support;
minimax-optimal bounds for general distributions; and (approximately)
instance-optimal, computationally efficient algorithms for general
distributions. When both privacy and communication constraints are present, we
develop instance-optimal, computationally efficient algorithms that achieve the
minimum possible sample complexity (up to universal constants). Our results on
instance-optimal algorithms hinge on identifying the extreme points of the
joint range set of two distributions and , defined as
,
where is the set of channels characterizing the constraints.Comment: 1 figur
On Power Allocation for Distributed Detection with Correlated Observations and Linear Fusion
We consider a binary hypothesis testing problem in an inhomogeneous wireless
sensor network, where a fusion center (FC) makes a global decision on the
underlying hypothesis. We assume sensors observations are correlated Gaussian
and sensors are unaware of this correlation when making decisions. Sensors send
their modulated decisions over fading channels, subject to individual and/or
total transmit power constraints. For parallel-access channel (PAC) and
multiple-access channel (MAC) models, we derive modified deflection coefficient
(MDC) of the test statistic at the FC with coherent reception.We propose a
transmit power allocation scheme, which maximizes MDC of the test statistic,
under three different sets of transmit power constraints: total power
constraint, individual and total power constraints, individual power
constraints only. When analytical solutions to our constrained optimization
problems are elusive, we discuss how these problems can be converted to convex
ones. We study how correlation among sensors observations, reliability of local
decisions, communication channel model and channel qualities and transmit power
constraints affect the reliability of the global decision and power allocation
of inhomogeneous sensors
Model-Driven End-to-End Learning for Integrated Sensing and Communication
Integrated sensing and communication (ISAC) is envisioned to be one of the pillars of 6G. However, 6G is also expected to be severely affected by hardware impairments. Under such impairments, standard model-based approaches might fail if they do not capture the underlying reality. To this end, data-driven methods are an alternative to deal with cases where imperfections cannot be easily modeled. In this paper, we propose a model-driven learning architecture for joint single- target multi-input multi-output (MIMO) sensing and multi-input single-output (MISO) communication. We compare it with a standard neural network approach under complexity constraints. Results show that under hardware impairments, both learning methods yield better results than the model-based standard baseline. If complexity constraints are further introduced, model- driven learning outperforms the neural-network-based approach. Model-driven learning also shows better generalization performance for new unseen testing scenario
Bayesian Design of Tandem Networks for Distributed Detection With Multi-bit Sensor Decisions
We consider the problem of decentralized hypothesis testing under
communication constraints in a topology where several peripheral nodes are
arranged in tandem. Each node receives an observation and transmits a message
to its successor, and the last node then decides which hypothesis is true. We
assume that the observations at different nodes are, conditioned on the true
hypothesis, independent and the channel between any two successive nodes is
considered error-free but rate-constrained. We propose a cyclic numerical
design algorithm for the design of nodes using a person-by-person methodology
with the minimum expected error probability as a design criterion, where the
number of communicated messages is not necessarily equal to the number of
hypotheses. The number of peripheral nodes in the proposed method is in
principle arbitrary and the information rate constraints are satisfied by
quantizing the input of each node. The performance of the proposed method for
different information rate constraints, in a binary hypothesis test, is
compared to the optimum rate-one solution due to Swaszek and a method proposed
by Cover, and it is shown numerically that increasing the channel rate can
significantly enhance the performance of the tandem network. Simulation results
for -ary hypothesis tests also show that by increasing the channel rates the
performance of the tandem network significantly improves
Communication Complexity of Distributed Statistical Algorithms
This paper constructs bounds on the minimax risk under loss functions when statistical estimation is performed in a distributed environment and with communication constraints. We treat this problem using techniques from information theory and communication complexity. In many cases our bounds rely crucially on metric entropy conditions and the classical reduction from estimation to testing. A number of examples exhibit how bounds on the minimax risk play out in practice. We also study distributed statistical estimation problems in the context of PAC-learnability and derive explicit algorithms for solving classical problems. We study the communication complexity of these algorithms
Testing Against Independence with an Eavesdropper
We study a distributed binary hypothesis testing (HT) problem with
communication and security constraints, involving three parties: a remote
sensor called Alice, a legitimate decision centre called Bob, and an
eavesdropper called Eve, all having their own source observations. In this
system, Alice conveys a rate R description of her observation to Bob, and Bob
performs a binary hypothesis test on the joint distribution underlying his and
Alice's observations. The goal of Alice and Bob is to maximise the exponential
decay of Bob's miss-detection (type II-error) probability under two
constraints: Bob's false alarm-probability (type-I error) probability has to
stay below a given threshold and Eve's uncertainty (equivocation) about Alice's
observations should stay above a given security threshold even when Eve learns
Alice's message. For the special case of testing against independence, we
characterise the largest possible type-II error exponent under the described
type-I error probability and security constraints.Comment: submitted to ITW 202
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