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Documents authored by Tino, Peter

Document
DOI: 10.4230/DagSemProc.10302.4
One-shot Learning of Poisson Distributions in fast changing environments

Authors: Peter Tino

Published in: Dagstuhl Seminar Proceedings, Volume 10302, Learning paradigms in dynamic environments (2010)

Abstract
In Bioinformatics, Audic and Claverie were among the first to systematically study the influence of random fluctuations and sampling size on the reliability of digital expression profile data. For a transcript representing a small fraction of the library and a large number N of clones, the probability of observing x tags of the same gene will be well-approximated by the Poisson distribution parametrised by its mean (and variance) m>0, where the unknown parameter m signifies the number of transcripts of the given type (tag) per N clones in the cDNA library. On an abstract level, to determine whether a gene is differentially expressed or not, one has two numbers generated from two distinct Poisson distributions and based on this (extremely sparse) sample one has to decide whether the two Poisson distributions are identical or not. This can be used e.g. to determine equivalence of Poisson photon sources (up to time shift) in gravitational lensing. Each Poisson distribution is represented by a single measurement only, which is, of course, from a purely statistical standpoint very problematic. The key instrument of the Audic-Claverie approach is a distribution P over tag counts y in one library informed by the tag count x in the other library, under the null hypothesis that the tag counts are generated from the same but unknown Poisson distribution. P is obtained by Bayesian averaging (infinite mixture) of all possible Poisson distributions with mixing proportions equal to the posteriors (given x) under the flat prior over m. We ask: Given that the tag count samples from SAGE libraries are *extremely* limited, how useful actually is the Audic-Claverie methodology? We rigorously analyse the A-C statistic P that forms a backbone of the methodology and represents our knowledge of the underlying tag generating process based on one observation. We show will that the A-C statistic P and the underlying Poisson distribution of the tag counts share the same mode structure. Moreover, the K-L divergence from the true unknown Poisson distribution to the A-C statistic is minimised when the A-C statistic is conditioned on the mode of the Poisson distribution. Most importantly (and perhaps rather surprisingly), the expectation of this K-L divergence never exceeds 1/2 bit! This constitutes a rigorous quantitative argument, extending the previous empirical Monte Carlo studies, that supports the wide spread use of Audic-Claverie method, even though by their very nature, the SAGE libraries represent very sparse samples.
Cite as

Peter Tino. One-shot Learning of Poisson Distributions in fast changing environments. In Learning paradigms in dynamic environments. Dagstuhl Seminar Proceedings, Volume 10302, pp. 1-9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{tino:DagSemProc.10302.4,
  author =	{Tino, Peter},
  title =	{{One-shot Learning of Poisson Distributions in fast changing environments}},
  booktitle =	{Learning paradigms in dynamic environments},
  pages =	{1--9},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10302},
  editor =	{Barbara Hammer and Pascal Hitzler and Wolfgang Maass and Marc Toussaint},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10302.4},
  URN =		{urn:nbn:de:0030-drops-27998},
  doi =		{10.4230/DagSemProc.10302.4},
  annote =	{Keywords: Audic-Claverie statistic, Bayesian averaging, information theory, one-shot learning, Poisson distribution}
}
Document
DOI: 10.4230/DagSemProc.09081.5
Estimating Time Delay in Gravitationally Lensed Fluxes

Authors: Peter Tino, Juan C. Cuevas-Tello, and Somak Raychaudhury

Published in: Dagstuhl Seminar Proceedings, Volume 9081, Similarity-based learning on structures (2009)

Abstract
We study the problem of estimating the time delay between two signals representing delayed, irregularly sampled and noisy versions of the same underlying pattern. We propose a kernel-based technique in the context of an astronomical problem, namely estimating the time delay between two gravitationally lensed signals from a distant quasar. We test the algorithm on several artificial data sets, and also on real astronomical observations. By carrying out a statistical analysis of the results we present a detailed comparison of our method with the most popular methods for time delay estimation in astrophysics. Our method yields more accurate and more stable time delay estimates. Our methodology can be readily applied to current state-of-the-art optical monitoring data in astronomy, but can also be applied in other disciplines involving similar time series data.
Cite as

Peter Tino, Juan C. Cuevas-Tello, and Somak Raychaudhury. Estimating Time Delay in Gravitationally Lensed Fluxes. In Similarity-based learning on structures. Dagstuhl Seminar Proceedings, Volume 9081, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{tino_et_al:DagSemProc.09081.5,
  author =	{Tino, Peter and Cuevas-Tello, Juan C. and Raychaudhury, Somak},
  title =	{{Estimating Time Delay in Gravitationally Lensed Fluxes}},
  booktitle =	{Similarity-based learning on structures},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9081},
  editor =	{Michael Biehl and Barbara Hammer and Sepp Hochreiter and Stefan C. Kremer and Thomas Villmann},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09081.5},
  URN =		{urn:nbn:de:0030-drops-20378},
  doi =		{10.4230/DagSemProc.09081.5},
  annote =	{Keywords: Time series, kernel regression, statistical analysis, evolutionary algorithms, mixed representation}
}
Document
DOI: 10.4230/DagSemProc.08041.3
Equilibria of Iterative Softmax and Critical Temperatures for Intermittent Search in Self-Organizing Neural Networks

Authors: Peter Tino

Published in: Dagstuhl Seminar Proceedings, Volume 8041, Recurrent Neural Networks- Models, Capacities, and Applications (2008)

Abstract
Optimization dynamics using self-organizing neural networks (SONN) driven by softmax weight renormalization has been shown to be capable of intermittent search for high-quality solutions in assignment optimization problems. However, the search is sensitive to temperature setting in the softmax renormalization step. The powerful search occurs only at the critical temperature that depends on the problem size. So far the critical temperatures have been determined only by tedious trial-and-error numerical simulations. We offer a rigorous analysis of the search performed by SONN and derive analytical approximations to the critical temperatures. We demonstrate on a set of N-queens problems for a wide range of problem sizes N that the analytically determined critical temperatures predict the optimal working temperatures for SONN intermittent search very well.
Cite as

Peter Tino. Equilibria of Iterative Softmax and Critical Temperatures for Intermittent Search in Self-Organizing Neural Networks. In Recurrent Neural Networks- Models, Capacities, and Applications. Dagstuhl Seminar Proceedings, Volume 8041, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{tino:DagSemProc.08041.3,
  author =	{Tino, Peter},
  title =	{{Equilibria of Iterative Softmax and Critical Temperatures for Intermittent Search in Self-Organizing Neural Networks}},
  booktitle =	{Recurrent Neural Networks- Models, Capacities, and Applications},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8041},
  editor =	{Luc De Raedt and Barbara Hammer and Pascal Hitzler and Wolfgang Maass},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08041.3},
  URN =		{urn:nbn:de:0030-drops-14202},
  doi =		{10.4230/DagSemProc.08041.3},
  annote =	{Keywords: Recurrent self-organizing maps, symmetry breaking bifurcation, N-queens}
}
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