6,535 research outputs found
Model Order Selection Rules For Covariance Structure Classification
The adaptive classification of the interference covariance matrix structure
for radar signal processing applications is addressed in this paper. This
represents a key issue because many detection architectures are synthesized
assuming a specific covariance structure which may not necessarily coincide
with the actual one due to the joint action of the system and environment
uncertainties. The considered classification problem is cast in terms of a
multiple hypotheses test with some nested alternatives and the theory of Model
Order Selection (MOS) is exploited to devise suitable decision rules. Several
MOS techniques, such as the Akaike, Takeuchi, and Bayesian information criteria
are adopted and the corresponding merits and drawbacks are discussed. At the
analysis stage, illustrating examples for the probability of correct model
selection are presented showing the effectiveness of the proposed rules
Representation Learning: A Review and New Perspectives
The success of machine learning algorithms generally depends on data
representation, and we hypothesize that this is because different
representations can entangle and hide more or less the different explanatory
factors of variation behind the data. Although specific domain knowledge can be
used to help design representations, learning with generic priors can also be
used, and the quest for AI is motivating the design of more powerful
representation-learning algorithms implementing such priors. This paper reviews
recent work in the area of unsupervised feature learning and deep learning,
covering advances in probabilistic models, auto-encoders, manifold learning,
and deep networks. This motivates longer-term unanswered questions about the
appropriate objectives for learning good representations, for computing
representations (i.e., inference), and the geometrical connections between
representation learning, density estimation and manifold learning
Regularization and Bayesian Learning in Dynamical Systems: Past, Present and Future
Regularization and Bayesian methods for system identification have been
repopularized in the recent years, and proved to be competitive w.r.t.
classical parametric approaches. In this paper we shall make an attempt to
illustrate how the use of regularization in system identification has evolved
over the years, starting from the early contributions both in the Automatic
Control as well as Econometrics and Statistics literature. In particular we
shall discuss some fundamental issues such as compound estimation problems and
exchangeability which play and important role in regularization and Bayesian
approaches, as also illustrated in early publications in Statistics. The
historical and foundational issues will be given more emphasis (and space), at
the expense of the more recent developments which are only briefly discussed.
The main reason for such a choice is that, while the recent literature is
readily available, and surveys have already been published on the subject, in
the author's opinion a clear link with past work had not been completely
clarified.Comment: Plenary Presentation at the IFAC SYSID 2015. Submitted to Annual
Reviews in Contro
Bayesian Regression of Piecewise Constant Functions
We derive an exact and efficient Bayesian regression algorithm for piecewise
constant functions of unknown segment number, boundary location, and levels. It
works for any noise and segment level prior, e.g. Cauchy which can handle
outliers. We derive simple but good estimates for the in-segment variance. We
also propose a Bayesian regression curve as a better way of smoothing data
without blurring boundaries. The Bayesian approach also allows straightforward
determination of the evidence, break probabilities and error estimates, useful
for model selection and significance and robustness studies. We discuss the
performance on synthetic and real-world examples. Many possible extensions will
be discussed.Comment: 27 pages, 18 figures, 1 table, 3 algorithm
Perfectly Secure Steganography: Capacity, Error Exponents, and Code Constructions
An analysis of steganographic systems subject to the following perfect
undetectability condition is presented in this paper. Following embedding of
the message into the covertext, the resulting stegotext is required to have
exactly the same probability distribution as the covertext. Then no statistical
test can reliably detect the presence of the hidden message. We refer to such
steganographic schemes as perfectly secure. A few such schemes have been
proposed in recent literature, but they have vanishing rate. We prove that
communication performance can potentially be vastly improved; specifically, our
basic setup assumes independently and identically distributed (i.i.d.)
covertext, and we construct perfectly secure steganographic codes from public
watermarking codes using binning methods and randomized permutations of the
code. The permutation is a secret key shared between encoder and decoder. We
derive (positive) capacity and random-coding exponents for perfectly-secure
steganographic systems. The error exponents provide estimates of the code
length required to achieve a target low error probability. We address the
potential loss in communication performance due to the perfect-security
requirement. This loss is the same as the loss obtained under a weaker order-1
steganographic requirement that would just require matching of first-order
marginals of the covertext and stegotext distributions. Furthermore, no loss
occurs if the covertext distribution is uniform and the distortion metric is
cyclically symmetric; steganographic capacity is then achieved by randomized
linear codes. Our framework may also be useful for developing computationally
secure steganographic systems that have near-optimal communication performance.Comment: To appear in IEEE Trans. on Information Theory, June 2008; ignore
Version 2 as the file was corrupte
Perfectly Secure Steganography: Capacity, Error Exponents, and Code Constructions
An analysis of steganographic systems subject to the following perfect
undetectability condition is presented in this paper. Following embedding of
the message into the covertext, the resulting stegotext is required to have
exactly the same probability distribution as the covertext. Then no statistical
test can reliably detect the presence of the hidden message. We refer to such
steganographic schemes as perfectly secure. A few such schemes have been
proposed in recent literature, but they have vanishing rate. We prove that
communication performance can potentially be vastly improved; specifically, our
basic setup assumes independently and identically distributed (i.i.d.)
covertext, and we construct perfectly secure steganographic codes from public
watermarking codes using binning methods and randomized permutations of the
code. The permutation is a secret key shared between encoder and decoder. We
derive (positive) capacity and random-coding exponents for perfectly-secure
steganographic systems. The error exponents provide estimates of the code
length required to achieve a target low error probability. We address the
potential loss in communication performance due to the perfect-security
requirement. This loss is the same as the loss obtained under a weaker order-1
steganographic requirement that would just require matching of first-order
marginals of the covertext and stegotext distributions. Furthermore, no loss
occurs if the covertext distribution is uniform and the distortion metric is
cyclically symmetric; steganographic capacity is then achieved by randomized
linear codes. Our framework may also be useful for developing computationally
secure steganographic systems that have near-optimal communication performance.Comment: To appear in IEEE Trans. on Information Theory, June 2008; ignore
Version 2 as the file was corrupte
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