Physical Fuctuomatics (Tohoku University) 1 Physical Fluctuomatics Applied Stochastic Process 1st Review of probabilistic information processing Kazuyuki Tanaka Graduate School of Information Sciences [email protected]http://www.smapip.is.tohoku.ac.jp/~kazu/ Webpage: http://www.smapip.is.tohoku.ac.jp/~kazu/ PhysicalFluctuomatics/2010/
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Physical Fuctuomatics (Tohoku University) 1 Physical Fluctuomatics Applied Stochastic Process 1st Review of probabilistic information processing Kazuyuki.
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Physical Fuctuomatics (Tohoku University) 1
Physical FluctuomaticsApplied Stochastic Process
1st Review of probabilistic information processing
Kazuyuki TanakaGraduate School of Information Sciences
Kazuyuki Tanaka: Introduction of Image Processing by Probabilistic Models, Morikita Publishing Co., Ltd., 2006 (in Japanese) .Kazuyuki Tanaka: Mathematics of Statistical Inference by Bayesian Network, Corona Publishing Co., Ltd., 2009 (in Japanese).
Physical Fuctuomatics (Tohoku University) 3
References of the present lecture
K. Tanaka: Statistical-mechanical approach to image processing (Topical Review), Journal of Physics A: Mathematical and General, vol.35, no.37, pp.R81-R150, 2002.Y. Kabashima and D. Saad: Statistical mechanics of low-density parity-check codes (Topical Review), J. Phys. A, vol.37, no.6, pp.R1-R43, 2004. H. Nishimori: Statistical Physics of Spin Glasses and Information Processing, ---An Introduction, Oxford University Press, 2001.M. Opper and D. Saad D (eds): Advanced Mean Field Methods --- Theory and Practice, MIT Press, 2001.C. M. Bishop: Pattern Recognition and Machine Learning, Springer, 2006.M. J. Wainwright and M. I. Jordan: Graphical Models, Exponential Families, and Variational Inference, now Publishing Inc, 2008.M. Mezard, A. Montanari: Information, Physics, and Computation, Oxford University Press, 2009.
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Benefit of Information & Communications Technology
Ubiquitous ComputingUbiquitous Internet
Benefit of Information & Communications Technology
Demand for IntelligenceIt cannot be satisfied only with it being only cheap and being quick.
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Field of Information Processing
Information processing according to theoriesInformation processing according to theoriesInference from propositionsInference from propositions
Realization by progress of computational processing capacityRealization by progress of computational processing capacity
Information processing in real worldInformation processing in real worldDiversity of reason in phenomenon Diversity of reason in phenomenon Compete data is not necessarily obtained.Compete data is not necessarily obtained.It is difficult to extract and select some important It is difficult to extract and select some important
information from a lot of data. information from a lot of data. Uncertainty caused by the gap of knowing simply and Uncertainty caused by the gap of knowing simply and understanding actually.understanding actually.We hope to deal successfully with such uncertainty.We hope to deal successfully with such uncertainty.
Information processing for numerical calculationsDefinite Procedure has been given for each calculation.
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Computer for next generations
Required CapacityCapability to sympathize with a user ( Knowledge)Capability to put failure and experience to account in the next chance ( Learning )
How should we deal successfully with the uncertainty caused How should we deal successfully with the uncertainty caused by the gap of knowing simply and understanding actually?by the gap of knowing simply and understanding actually?
Formulation of knowledge and uncertainty
Realization of information processing data with uncertainty
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Computational model for information processing in data with uncertainty
Probabilistic InferenceProbabilistic model
with graphical structure ( Bayesian network )Medical diagnosis
Failure diagnosis Risk Management
Probabilistic information processing can give us unexpected capacity in a system constructed from many cooperating elements with randomness.
Inference system for data with uncertainty
modeling
Node is random variable.Arrow is conditional probability.
Mathematical expression of uncertainty=>Probability and Statistics
Graph with cycles
Important aspect
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Computational Model for Probabilistic Information Processing
Probabilistic Information Processing Probabilistic Model
Bayes Formula
Algorithm
Monte Carlo MethodMarkov Chain Monte Carlo
MethodRandomized AlgorithmGenetic Algorithm
Approximate MethodBelief PropagationMean Field Method
K. Tanaka: J. Phys. A, vol.35, 2002.A. S. Willsky: Proceedings of IEEE, vol.90, 2002.
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110218100
120219202
190202192
Average
192 202 190
202 219 120
100 218 110
192 202 190
202 173 120
100 218 110
Modeling of Probabilistic Image Processing based on Conventional Filters
Markov Random Filed Model Probabilistic Image Processing
The elements of such a digital array are called pixels.At each point, the intensity of light is represented as an integer number or a real number in the digital image data.
A sequence is formed by deciding the arrangement of bits.
A lot of elements have mutual relation of each otherSome physical concepts in Physical models are useful for the design of computational models in probabilistic information processing.
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Horizon of Computation in Probabilistic Information Processing
Compensation of expressing uncertainty using probability and statistics
It must be calculated by taking account of both events with high probability and events with low probability.
Computational Complexity
It is expected to break throw the computational complexity by introducing approximation algorithms.
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What is an important point in What is an important point in computational complexity? computational complexity?
How should we treat the calculation of the summation over 2N configuration?
FT, FT, FT,
21
1 2
,,,x x x
N
N
xxxf
}
}
}
;,,,
F){or Tfor(
F){or Tfor(
F){or Tfor(
;0
21
2
1
L
N
xxxfaa
x
x
x
a
N fold loops
If it takes 1 second in the case of N=10, it takes 17 minutes in N=20, 12 days in N=30 and 34 years in N=40.
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Why is a physical viewpoint effective in probabilistic information processing?
Matrials are constructed from a lot of molecules.(1023 molecules exist in 1 mol.)
Molecules have intermolecular forces of each other
1 2
,,, 21x x x
N
N
xxxf
Theoretical physicists always have to treat such multiple summation.
Development of Approximate Methods
Probabilistic information processing is also usually reduced to multiple summations or integrations.
Application of physical approximate methods to probabilistic information processing
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Academic Circulation
Academic Circulation
Academic Circulation between Physics and Information Sciences
Physics Information Sciences
Understanding and prediction of properties of materials and natural phenomena
Extraction and processing of information in data
Common ConceptStatistical Mechanical Informatics
Probabilistic Information Processing
Statistical Sciences
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Summary of the present lecture
Probabilistic information processingExamples of probabilistic information processingCommon concept in physics and information sciencesApplication of physical modeling and approximations
Future Lectures
Fundamental theory of probability and statisticsLinear model