A Bayesian probability calculus for density matrices

Proceedings of the 22nd Conference on Uncertainty in Artificial Intelligence, UAI 2006

Volumn , Issue , 2006, Pages 503-511

  Warmuth, Manfred K ^a   Kuzmin, Dima ^a  

^a University of California Santa Cruz   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

A-DENSITY; BAYES RULE; BAYESIAN METHODS; BAYESIAN PROBABILITIES; DENSITY MATRIX; LOG LIKELIHOOD; MAP ESTIMATOR; QUANTUM PHYSICS; SYMMETRIC POSITIVE DEFINITE MATRICES; UPPER BOUND;

ARTIFICIAL INTELLIGENCE; BAYESIAN NETWORKS; CALCULATIONS; MATRIX ALGEBRA; QUANTUM THEORY;

PROBABILITY DISTRIBUTIONS;

EID: 80053217944     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (14)

1. M. Alexa. Linear combination of transformations. In SIGGRAPH '02: Proceedings of the 29th annual conference on Computer graphics and interactive techniques, pages 380-387, New York, NY, USA, 2002. ACM Press.
2. R. Bhatia. Matrix Analysis. Springer, Berlin, 1997.
3. N. J. Cerf and C. Adami. Quantum extension of conditional probability. Physical Review A, 60(2):893-897, August 1999. (Pubitemid 129690854)
4. C. M. Caves, C. A. Fuchs, K. K. Manne, and J. M. Renes. Gleason-type derivations of the quantum probability rule for generalized measurements. Foundations of Physics, 34:193 - 209, 2004.
5. R. P. Feynman. Statistical Mechanics: A Set of Lectures. Addison-Wesley, 1972.
6. A. Gleason. Measures on the closed sub-spaces of a Hilbert space. Indiana Univ. Math. J., 6:885-893, 1957.
7. A. S. Holevo. Statistical Structure of Quantum Theory, volume 67 of Lecture Notes in Physics. Monographs. Springer, Berlin, New York, 2001.
8. M.A. Nielsen and I.L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2000.
9. R. Schack, T. A. Brun, and C. M. Caves. Quantum Bayes rule. Physical Review A, 64(014305), 2001.
10. B. Simon. Functional Integration and Quantum Physics. Academic Press, New York, 1979.
11. K. Tsuda, G. Rätsch, and M. K. Warmuth. Matrix exponentiated gradient updates for on-line learning and Bregman projections. Journal of Machine Learning Research, 6:995-1018, June 2005.
12. M. K. Warmuth. Bayes rule for density matrices. In Advances in Neural Information Processing Systems 18 (NIPS 05). MIT Press, December 2005.
13. M. K. Warmuth and D. Kuzmin. Online variance minimization. In Proceedings of the 19th Annual Conference on Learning Theory (COLT06), 2006. To appear.
14. M. K. Warmuth and D. Kuzmin. Randomized PCA algorithms with regret bounds that are logarithmic in the dimension. Unpublished manuscript, 2006.