6 research outputs found
The Sample Complexity of Search over Multiple Populations
This paper studies the sample complexity of searching over multiple
populations. We consider a large number of populations, each corresponding to
either distribution P0 or P1. The goal of the search problem studied here is to
find one population corresponding to distribution P1 with as few samples as
possible. The main contribution is to quantify the number of samples needed to
correctly find one such population. We consider two general approaches:
non-adaptive sampling methods, which sample each population a predetermined
number of times until a population following P1 is found, and adaptive sampling
methods, which employ sequential sampling schemes for each population. We first
derive a lower bound on the number of samples required by any sampling scheme.
We then consider an adaptive procedure consisting of a series of sequential
probability ratio tests, and show it comes within a constant factor of the
lower bound. We give explicit expressions for this constant when samples of the
populations follow Gaussian and Bernoulli distributions. An alternative
adaptive scheme is discussed which does not require full knowledge of P1, and
comes within a constant factor of the optimal scheme. For comparison, a lower
bound on the sampling requirements of any non-adaptive scheme is presented.Comment: To appear, IEEE Transactions on Information Theor
A Linear Programming Approach to Sequential Hypothesis Testing
Under some mild Markov assumptions it is shown that the problem of designing
optimal sequential tests for two simple hypotheses can be formulated as a
linear program. The result is derived by investigating the Lagrangian dual of
the sequential testing problem, which is an unconstrained optimal stopping
problem, depending on two unknown Lagrangian multipliers. It is shown that the
derivative of the optimal cost function with respect to these multipliers
coincides with the error probabilities of the corresponding sequential test.
This property is used to formulate an optimization problem that is jointly
linear in the cost function and the Lagrangian multipliers and an be solved for
both with off-the-shelf algorithms. To illustrate the procedure, optimal
sequential tests for Gaussian random sequences with different dependency
structures are derived, including the Gaussian AR(1) process.Comment: 25 pages, 4 figures, accepted for publication in Sequential Analysi
Asymptotic Optimality Theory For Decentralized Sequential Multihypothesis Testing Problems
The Bayesian formulation of sequentially testing hypotheses is
studied in the context of a decentralized sensor network system. In such a
system, local sensors observe raw observations and send quantized sensor
messages to a fusion center which makes a final decision when stopping taking
observations. Asymptotically optimal decentralized sequential tests are
developed from a class of "two-stage" tests that allows the sensor network
system to make a preliminary decision in the first stage and then optimize each
local sensor quantizer accordingly in the second stage. It is shown that the
optimal local quantizer at each local sensor in the second stage can be defined
as a maximin quantizer which turns out to be a randomization of at most
unambiguous likelihood quantizers (ULQ). We first present in detail our results
for the system with a single sensor and binary sensor messages, and then extend
to more general cases involving any finite alphabet sensor messages, multiple
sensors, or composite hypotheses.Comment: 14 pages, 1 figure, submitted to IEEE Trans. Inf. Theor
Quick Search for Rare Events
Rare events can potentially occur in many applications. When manifested as
opportunities to be exploited, risks to be ameliorated, or certain features to
be extracted, such events become of paramount significance. Due to their
sporadic nature, the information-bearing signals associated with rare events
often lie in a large set of irrelevant signals and are not easily accessible.
This paper provides a statistical framework for detecting such events so that
an optimal balance between detection reliability and agility, as two opposing
performance measures, is established. The core component of this framework is a
sampling procedure that adaptively and quickly focuses the
information-gathering resources on the segments of the dataset that bear the
information pertinent to the rare events. Particular focus is placed on
Gaussian signals with the aim of detecting signals with rare mean and variance
values
Optimal sensor scheduling for multiple hypothesis testing
Bibliography: p. 72-73."September 1981""ONR-N00014-77-0532"Robert R. Tenney
A Unified Multi-Functional Dynamic Spectrum Access Framework: Tutorial, Theory and Multi-GHz Wideband Testbed
Dynamic spectrum access is a must-have ingredient for future sensors that are ideally cognitive. The goal of this paper is a tutorial treatment of wideband cognitive radio and radar—a convergence of (1) algorithms survey, (2) hardware platforms survey, (3) challenges for multi-function (radar/communications) multi-GHz front end, (4) compressed sensing for multi-GHz waveforms—revolutionary A/D, (5) machine learning for cognitive radio/radar, (6) quickest detection, and (7) overlay/underlay cognitive radio waveforms. One focus of this paper is to address the multi-GHz front end, which is the challenge for the next-generation cognitive sensors. The unifying theme of this paper is to spell out the convergence for cognitive radio, radar, and anti-jamming. Moore’s law drives the system functions into digital parts. From a system viewpoint, this paper gives the first comprehensive treatment for the functions and the challenges of this multi-function (wideband) system. This paper brings together the inter-disciplinary knowledge