50,338 research outputs found
Constrained Bayesian Active Learning of Interference Channels in Cognitive Radio Networks
In this paper, a sequential probing method for interference constraint
learning is proposed to allow a centralized Cognitive Radio Network (CRN)
accessing the frequency band of a Primary User (PU) in an underlay cognitive
scenario with a designed PU protection specification. The main idea is that the
CRN probes the PU and subsequently eavesdrops the reverse PU link to acquire
the binary ACK/NACK packet. This feedback indicates whether the probing-induced
interference is harmful or not and can be used to learn the PU interference
constraint. The cognitive part of this sequential probing process is the
selection of the power levels of the Secondary Users (SUs) which aims to learn
the PU interference constraint with a minimum number of probing attempts while
setting a limit on the number of harmful probing-induced interference events or
equivalently of NACK packet observations over a time window. This constrained
design problem is studied within the Active Learning (AL) framework and an
optimal solution is derived and implemented with a sophisticated, accurate and
fast Bayesian Learning method, the Expectation Propagation (EP). The
performance of this solution is also demonstrated through numerical simulations
and compared with modified versions of AL techniques we developed in earlier
work.Comment: 14 pages, 6 figures, submitted to IEEE JSTSP Special Issue on Machine
Learning for Cognition in Radio Communications and Rada
Probabilistic Numerics and Uncertainty in Computations
We deliver a call to arms for probabilistic numerical methods: algorithms for
numerical tasks, including linear algebra, integration, optimization and
solving differential equations, that return uncertainties in their
calculations. Such uncertainties, arising from the loss of precision induced by
numerical calculation with limited time or hardware, are important for much
contemporary science and industry. Within applications such as climate science
and astrophysics, the need to make decisions on the basis of computations with
large and complex data has led to a renewed focus on the management of
numerical uncertainty. We describe how several seminal classic numerical
methods can be interpreted naturally as probabilistic inference. We then show
that the probabilistic view suggests new algorithms that can flexibly be
adapted to suit application specifics, while delivering improved empirical
performance. We provide concrete illustrations of the benefits of probabilistic
numeric algorithms on real scientific problems from astrometry and astronomical
imaging, while highlighting open problems with these new algorithms. Finally,
we describe how probabilistic numerical methods provide a coherent framework
for identifying the uncertainty in calculations performed with a combination of
numerical algorithms (e.g. both numerical optimisers and differential equation
solvers), potentially allowing the diagnosis (and control) of error sources in
computations.Comment: Author Generated Postprint. 17 pages, 4 Figures, 1 Tabl
Foundational principles for large scale inference: Illustrations through correlation mining
When can reliable inference be drawn in the "Big Data" context? This paper
presents a framework for answering this fundamental question in the context of
correlation mining, with implications for general large scale inference. In
large scale data applications like genomics, connectomics, and eco-informatics
the dataset is often variable-rich but sample-starved: a regime where the
number of acquired samples (statistical replicates) is far fewer than the
number of observed variables (genes, neurons, voxels, or chemical
constituents). Much of recent work has focused on understanding the
computational complexity of proposed methods for "Big Data." Sample complexity
however has received relatively less attention, especially in the setting when
the sample size is fixed, and the dimension grows without bound. To
address this gap, we develop a unified statistical framework that explicitly
quantifies the sample complexity of various inferential tasks. Sampling regimes
can be divided into several categories: 1) the classical asymptotic regime
where the variable dimension is fixed and the sample size goes to infinity; 2)
the mixed asymptotic regime where both variable dimension and sample size go to
infinity at comparable rates; 3) the purely high dimensional asymptotic regime
where the variable dimension goes to infinity and the sample size is fixed.
Each regime has its niche but only the latter regime applies to exa-scale data
dimension. We illustrate this high dimensional framework for the problem of
correlation mining, where it is the matrix of pairwise and partial correlations
among the variables that are of interest. We demonstrate various regimes of
correlation mining based on the unifying perspective of high dimensional
learning rates and sample complexity for different structured covariance models
and different inference tasks
On the Equivalence between Herding and Conditional Gradient Algorithms
We show that the herding procedure of Welling (2009) takes exactly the form
of a standard convex optimization algorithm--namely a conditional gradient
algorithm minimizing a quadratic moment discrepancy. This link enables us to
invoke convergence results from convex optimization and to consider faster
alternatives for the task of approximating integrals in a reproducing kernel
Hilbert space. We study the behavior of the different variants through
numerical simulations. The experiments indicate that while we can improve over
herding on the task of approximating integrals, the original herding algorithm
tends to approach more often the maximum entropy distribution, shedding more
light on the learning bias behind herding
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