4,823 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
Active Anomaly Detection in Heterogeneous Processes
An active inference problem of detecting anomalies among heterogeneous
processes is considered. At each time, a subset of processes can be probed. The
objective is to design a sequential probing strategy that dynamically
determines which processes to observe at each time and when to terminate the
search so that the expected detection time is minimized under a constraint on
the probability of misclassifying any process. This problem falls into the
general setting of sequential design of experiments pioneered by Chernoff in
1959, in which a randomized strategy, referred to as the Chernoff test, was
proposed and shown to be asymptotically optimal as the error probability
approaches zero. For the problem considered in this paper, a low-complexity
deterministic test is shown to enjoy the same asymptotic optimality while
offering significantly better performance in the finite regime and faster
convergence to the optimal rate function, especially when the number of
processes is large. The computational complexity of the proposed test is also
of a significantly lower order.Comment: This work has been accepted for publication on IEEE Transactions on
Information Theor
Neural networks for gamma-hadron separation in MAGIC
Neural networks have proved to be versatile and robust for particle
separation in many experiments related to particle astrophysics. We apply these
techniques to separate gamma rays from hadrons for the MAGIC Cerenkov
Telescope. Two types of neural network architectures have been used for the
classi cation task: one is the MultiLayer Perceptron (MLP) based on supervised
learning, and the other is the Self-Organising Tree Algorithm (SOTA), which is
based on unsupervised learning. We propose a new architecture by combining
these two neural networks types to yield better and faster classi cation
results for our classi cation problem.Comment: 6 pages, 4 figures, to be published in the Proceedings of the 6th
International Symposium ''Frontiers of Fundamental and Computational
Physics'' (FFP6), Udine (Italy), Sep. 26-29, 200
Multiple Disorder Problems for Wiener and Compound Poisson Processes With Exponential Jumps
The multiple disorder problem consists of finding a sequence of stopping times which are as close as possible to the (unknown) times of "disorder" when the distribution of an observed process changes its probability characteristics. We present a formulation and solution of the multiple disorder problem for a Wiener and a compound Poisson process with exponential jumps. The method of proof is based on reducing the initial optimal switching problems to the corresponding coupled optimal stopping problems and solving the equivalent coupled free-boundary problems by means of the smooth- and continuous-fit conditions.Multiple disorder problem, Wiener process, compound Poisson process, optimal switching, coupled optimal stopping problem, (integro-differential) coupled free-boundary problem, smooth and continuous fit, Ito-Tanaka-Meyer formula.
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