5 results
7 - Understanding Phase Transitions via Mutual Information and MMSE
- Edited by Miguel R. D. Rodrigues, University College London, Yonina C. Eldar, Weizmann Institute of Science, Israel
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- Book:
- Information-Theoretic Methods in Data Science
- Published online:
- 22 March 2021
- Print publication:
- 08 April 2021, pp 197-228
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Summary
The ability to understand and solve high-dimensional inference problems is essential for modern data science. This chapter examines high-dimensional inference problems through the lens of information theory and focuses on the standard linear model as a canonical example that is both rich enough to be practically useful and simple enough to be studied rigorously. In particular, this model can exhibit phase transitions where an arbitrarily small change in the model parameters can induce large changes in the quality of estimates. For this model, the performance of optimal inference can be studied using the replica method from statistical physics but, until recently, it was not known whether the resulting formulas were actually correct. In this chapter, we present a tutorial description of the standard linear model and its connection to information theory. We also describe the replica prediction for this model and outline the authors’ recent proof that it is exact.
6 - The capacity of finite-state channels in the high-noise regime
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- By Henry D. Pfister, Texas A&M University
- Edited by Brian Marcus, University of British Columbia, Vancouver, Karl Petersen, University of North Carolina, Chapel Hill, Tsachy Weissman, Stanford University, California
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- Book:
- Entropy of Hidden Markov Processes and Connections to Dynamical Systems
- Published online:
- 05 June 2011
- Print publication:
- 26 May 2011, pp 179-222
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Summary
Abstract. This article considers the derivative of the entropy rate of a hidden Markov process with respect to the observation probabilities. The main result is a compact formula for the derivative that can be evaluated easily using Monte Carlo methods. It is applied to the problem of computing the capacity of a finite-state channel (FSC) and, in the high-noise regime, the formula has a simple closed-form expression that enables series expansion of the capacity of an FSC. This expansion is evaluated for a binary-symmetric channel under a (0, 1) run-length-limited constraint and an intersymbol-interference channel with Gaussian noise.
Introduction
The hidden Markov process
A hidden Markov process (HMP) is a discrete-time finite-state Markov chain (FSMC) observed through a memoryless channel. The HMP has become ubiquitous in statistics, computer science, and electrical engineering because it approximates many processes well using a dependency structure that leads to many efficient algorithms. While the roots of the HMP lie in the “grouped Markov chains” of Harris [20] and the “functions of a finite-state Markov chain” of Blackwell [8], the HMP first appears (in full generality) as the output process of a finite-state channel (FSC) [9]. The statistical inference algorithm of Baum and Petrie [5], however, cemented the HMP's place in history and is responsible for great advances in fields such as speech recognition and biological sequence analysis [22, 24]. An exceptional survey of HMPs, by Ephraim and Merhav, gives a nice summary of what is known in this area [12].
Contributors
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- By Rose Teteki Abbey, K. C. Abraham, David Tuesday Adamo, LeRoy H. Aden, Efrain Agosto, Victor Aguilan, Gillian T. W. Ahlgren, Charanjit Kaur AjitSingh, Dorothy B E A Akoto, Giuseppe Alberigo, Daniel E. Albrecht, Ruth Albrecht, Daniel O. Aleshire, Urs Altermatt, Anand Amaladass, Michael Amaladoss, James N. Amanze, Lesley G. Anderson, Thomas C. Anderson, Victor Anderson, Hope S. Antone, María Pilar Aquino, Paula Arai, Victorio Araya Guillén, S. Wesley Ariarajah, Ellen T. Armour, Brett Gregory Armstrong, Atsuhiro Asano, Naim Stifan Ateek, Mahmoud Ayoub, John Alembillah Azumah, Mercedes L. García Bachmann, Irena Backus, J. Wayne Baker, Mieke Bal, Lewis V. Baldwin, William Barbieri, António Barbosa da Silva, David Basinger, Bolaji Olukemi Bateye, Oswald Bayer, Daniel H. Bays, Rosalie Beck, Nancy Elizabeth Bedford, Guy-Thomas Bedouelle, Chorbishop Seely Beggiani, Wolfgang Behringer, Christopher M. Bellitto, Byard Bennett, Harold V. Bennett, Teresa Berger, Miguel A. 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Yee, Viktor Yelensky, Yeo Khiok-Khng, Gustav K. K. Yeung, Angela Yiu, Amos Yong, Yong Ting Jin, You Bin, Youhanna Nessim Youssef, Eliana Yunes, Robert Michael Zaller, Valarie H. Ziegler, Barbara Brown Zikmund, Joyce Ann Zimmerman, Aurora Zlotnik, Zhuo Xinping
- Edited by Daniel Patte, Vanderbilt University, Tennessee
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- The Cambridge Dictionary of Christianity
- Published online:
- 05 August 2012
- Print publication:
- 20 September 2010, pp xi-xliv
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CRESST
- E. Pécontal, T. Buchert, Ph. Di Stefano, Y. Copin, G. Angloher, M. Bauer, I. Bavykina, A. Bento, A. Brown, C. Bucci, C. Ciemniak, C. Coppi, G. Deuter, F. von Feilitzsch, D. Hauff, S. Henry, P. Huff, J. Imber, S. Ingleby, C. Isaila, J. Jochum, M. Kiefer, M. Kimmerle, H. Kraus, J.-C. Lanfranchi, R.F. Lang, B. Majorovits, M. Malek, R. McGowan, V.B. Mikhailik, E. Pantic, F. Petricca, S. Pfister, W. Potzel, F. Pröbst, W. Rau, S. Roth, K. Rottler, C. Sailer, K. Schäffner, J. Schmaler, S. Scholl, W. Seidel, L. Stodolsky, A.J.B. Tolhurst, I. Usherov, W. Westphal
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- Journal:
- European Astronomical Society Publications Series / Volume 36 / 2009
- Published online by Cambridge University Press:
- 30 May 2009, pp. 231-236
- Print publication:
- 2009
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The CRESST-II direct Dark Matter search is located in the Gran Sasso underground laboratories, Italy. CaWO4 crystals are used as scintillating targets for WIMP (weakly interacting massive particle) interactions. They are operated as cryogenic calorimeters in combination with a second cryogenic detector used to measure the scintillation light produced in the target crystal. For each particle interaction, the combination of phonon and light signals provides an event by event discrimination which allows to distinguish known particles (alphas, betas, gammas, neutrons) from the expected signal of WIMPs. A major upgrade of the setup comprises modifications of the shielding, installation of a muon-veto, and new read out electronics, as well as a new detector-support structure to accommodate up to 33 detector modules, i.e. 10 kg of target mass. The experiment was thereafter successfully commissioned in 2007. Data obtained during this commissioning phase from 2 detector modules are presented here. Combining the data collected with these two detector modules with data from one single module obtained during the CRESST-I phase, the experiment could already place a limit of ~6 × 10-7 pb for the spin independent WIMP-nucleon scattering cross section at a WIMP mass of ~60 GeV/c2.
EURECA – The Future of Cryogenic Dark Matter Detection in Europe
- E. Pécontal, T. Buchert, Ph. Di Stefano, Y. Copin, H. Kraus, E. Armengaud, M. Bauer, I. Bavykina, A. Benoit, A. Bento, J. Blümer, L. Bornschein, A. Broniatowski, G. Burghart, P. Camus, A. Chantelauze, M. Chapellier, G. Chardin, C. Ciemniak, C. Coppi, N. Coron, O. Crauste, F.A. Danevich, M. De Jésus, P. de Marcillac, E. Daw, X. Defay, G. Deuter, J. Domange, P. Di Stefano, G. Drexlin, L. Dumoulin, K. Eitel, F. von Feilitzsch, D. Filosofov, P. Gandit, E. Garcia, J. Gascon, G. Gerbier, J. Gironnet, H. Godfrin, S. Grohmann, M. Gros, M. Hannewald, D. Hauff, F. Haug, S. Henry, P. Huff, J. Imber, S. Ingleby, C. Isaila, J. Jochum, A. Juillard, M. Kiefer, M. Kimmerle, H. Kluck, V.V. Kobychev, V. Kozlov, V.M. Kudovbenko, V.A. Kudryavtsev, T. Lachenmaier, J.-C. Lanfranchi, R.F. Lang, P. Loaiza, A. Lubashevsky, M. Malek, S. Marnieros, R. McGowan, V. Mikhailik, A. Monfardini, X.-F. Navick, T. Niinikoski, A.S. Nikolaiko, L. Oberauer, E. Olivieri, Y. Ortigoza, E. Pantic, P. Pari, B. Paul, G. Perinic, F. Petricca, S. Pfister, C. Pobes, D.V. Poda, R.B. Podviyanuk, O.G. Polischuk, W. Potzel, F. Pröbst, J. Puimedon, M. Robinson, S. Roth, K. Rottler, S. Rozov, C. Sailer, A. Salinas, V. Sanglard, M.L. Sarsa, K. Schäffner, S. Scholl, S. Scorza, A. Smolnikov, W. Seidel, S. Semikh, M. Stern, L. Stodolsky, M. Teshima, V. Tomasello, A. Torrento, L. Torres, V.I. Tretyak, J.A. Villar, M.A. Verdier, I. Usherov, J. Wolf, E. Yakushev
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- Journal:
- European Astronomical Society Publications Series / Volume 36 / 2009
- Published online by Cambridge University Press:
- 30 May 2009, pp. 249-255
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- 2009
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EURECA (European Underground Rare Event Calorimeter Array) is an astro-particle physics facility aiming to directly detect galactic dark matter. The Laboratoire Souterrain de Modane has been selected as host laboratory. The EURECA collaboration unites CRESST, EDELWEISS and the Spanish-French experiment ROSEBUD, thus concentrating and focussing effort on cryogenic detector research in Europe into a single facility. EURECA will use a target mass of up to one ton, enough to explore WIMP – nucleon scalar scattering cross sections in the region of 10-9 – 10-10 picobarn. A major advantage of EURECA is the planned use of more than just one target material (multi target experiment for WIMP identification).