Asymptotic theory of information-theoretic experimental design

Neural Computation

Volumn 17, Issue 7, 2005, Pages 1480-1507

  Paninski, Liam ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 18744390761     PISSN: 08997667     EISSN: None     Source Type: Journal    
DOI: 10.1162/0899766053723032     Document Type: Article

References (44)

1. Axelrod, S., Fine, S., Gilad-Bachrach, R., Mendelson, S., & Tishby, N. (2001). The information of observations and application for active learning with uncertainty (Tech. Rep.). Jerusalem: Leibniz Center, Hebrew University. Available online: cite-seer.nj.nec.com/axelrod01information.html.
2. Barron, A., Schervish, M., & Wasserman, L. (1999). The consistency of posterior distributions in nonparametric problems. Annals of Statistics, 27, 536-561.
3. Bell, R., & Cover, T. (1980). Competitive optimality of logarithmic investment. Mathematics of Operations Research, 5, 161-166.
4. Berger, J., Bernardo, J., & Mendoza, M. (1989). On priors that maximize expected information. In J. Klein & H. J. Lee (Eds.), Recent developments of statistics and its applications (pp. 1-20). Seoul: Freedom Academy.
5. Chaloner, K., & Verdinelli, I. (1995). Bayesian experimental design: A review. Statistical Science, 10, 273-304.
6. Chichilnisky, E. (2001). A simple white noise analysis of neuronal light responses. Network: Computation in Neural Systems, 12, 199-213.
7. Clarke, B., & Barron, A. (1990). Information-theoretic asymptotics of Bayes methods. IEEE Transactions on Information Theory, 36, 453-471.
8. Clarke, B., & Barron, A. (1994). Jeffreys' prior is asymptotically least favorable under entropy risk. Journal of Statistical Planning Inference, 41, 37-60.
9. Clyde, M., & Chaloner, K. (1996). The equivalence of constrained and weighted designs in multiple objective design problems. Journal of the American Statistical Association, 91, 1236-1244.
10. Cohn, D., Ghahramani, Z., & Jordan, M. (1996). Active learning with statistical models. Journal of Artificial Intelligence Research, 4, 129-145.
11. Cover, T., & Thomas, J. (1991). Elements of information theory. New York: Wiley.
12. Dayan, P., & Abbott, L. (2001). Theoretical neuroscience. Cambridge, MA: MIT Press.
13. Deignan, P., Meckl, P., Franchek, M., Abraham, J., & Jaliwala, S. (2000). using mutual information to pre-process input data for a virtual sensor. Paper presented at the American Control Conference 2000, Chicago.
14. Dembo, A., & Zeitouni, O. (1993). Large deviations techniques and applications. New York: Springer.
15. Denzler, J., & Brown, C. (2000). Optimal selection of camera parameters for state estimation of static systems: An information theoretic approach. (University of Rochester Tech. Rep. 732). Rochester, NY: University of Rochester.
16. Fedorov, V. (1972). Theory of optimal experiments. New York: Academic Press.
17. Foldiak, P. (2001). Stimulus optimisation in primary visual cortex. Neurocomputing, 38-40, 1217-1222.
18. Freund, Y., Seung, H. S., Shamir, E., & Tishby, N. (1997). Selective sampling using the query by committee algorithm. Machine Learning, 28(2-3), 133-168.
19. Kontsevich, L., & Tyler, C. (1999). Bayesian adaptive estimation of psychometric slope and threshold. Vision Research, 39, 2729-2737.
20. Lee, T., & Yu, S. (1998). An information-theoretic framework for understanding saccadic behaviors. In S. A. Solla, T. K. Leen, & K.-R. Muller (Eds.), Advances in neural information processing, 12. Cambridge, MA: MIT Press.
21. Lewis, A. (1996). Convex analysis on the Hermitian matrices. SIAM Journal on Optimization, 6, 164-177.
22. Lindley, D. (1956). On a measure of information provided by an experiment. Annals of Mathematical Statistics, 29, 986-1005.
23. Luttrell, S. (1985). The use of transinformation in the design of data sampling schemes for inverse problems. Inverse Problems, 1, 199-218.
24. Machens, C. (2002). Adaptive sampling by information maximization. Physical Review Letters, 88, 228104-228107.
25. Mackay, D. (1992). Information-based objective functions for active data selection. Neural Computation, 4, 589-603.
26. Mascaro, M., & Bradley, D. (2002). Optimized neuronal tuning algorithm for multichannel recording. Unpublished abstract. Available online: http://www. compscipreprints.com/.
27. Milman, V., & Schechtman, G. (1986). Asymptotic theory of finite dimensional normed spaces. Berlin: Springer-Verlag.
28. Nelken, I., Prut, Y., Vaadia, E., & Abeles, M. (1994). In search of the best stimulus: An optimization procedure for finding efficient stimuli in the cat auditory cortex. Hearing Research, 72, 237-253.
29. Nelson, J., & Movellan, J. (2000). Active inference in concept learning. In T. K. Leen, T. G. Dietterich, & V. Tresp (Eds.), Advances in neural information processing, 13. Cambridge, MA: MIT Press.
30. Parmigiani, G. (1998). Designing observation times for interval censored data. Sankhya A, 60, 446-458.
31. Parmigiani, G., & Berry, D. (1994). Applications of Lindley information measure to the design of clinical experiments. In A. F. M. Smith & P. Freeman (Eds.), Aspects of uncertainty: A tribute to D. V. Lindley (pp. 333-352). New York: Wiley.
32. Pelli, D. (1987). The ideal psychometric procedure. Investigative Ophthalmology and Visual Science (Suppl.), 28, 366.
33. Rudin, W. (1973). Functional analysis. New York: McGraw-Hill.
34. Sahani, M. (1997). Interactively exploring a neural code by active learning. Poster session presented at NIC97 meeting, Snowbird, Utah. Available online: http://www.gatsby.ucl.ac.uk/~maneesh/conferences/nic97/poster/home.html.
35. Schervish, M. (1995). Theory of statistics. New York: Springer-Verlag.
36. Scholl, H. R. (1998, June). Shannon optimal priors on i.i.d. statistical experiments converge weakly to Jeffreys' prior. Test, 7(no. 1). Available online: citeseer.nj.nec.com/104699.html.
37. Schwartz, L. (1967). On Bayes procedures. Z. Wahrsch. Verw. Gabiete, 4, 10-26.
38. Simoncelli, E., Paninski, L., Pillow, J., & Schwartz, O. (2004). Characterization of neural responses with stochastic stimuli. In M. Gazzaniga (Ed.), The cognitive neurosciences. (3rd ed.). Cambridge, MA: MIT Press.
39. Sollich, P. (1996). Learning from minimum entropy queries in a large committee machine. Physical Review E, 53, R2060-R2063.
40. Talagrand, M. (1995). Concentration of measure and isoperimetric inequalities in product spaces. Publ. Math. IHES, 81, 73-205.
41. Tzanakou, E., Michalak, R., & Harth, E. (1979). The alopex process: Visual receptive fields by response feedback. Biological Cybernetics, 35, 161-174.
42. van der Vaart, A. (1998). Asymptotic statistics. Cambridge: Cambridge University Press.
43. Watson, A., & Fitzhugh, A. (1990). The method of constant stimuli is inefficient. Perception and Psychophysics, 47, 87-91.
44. Watson, A., & Pelli, D. (1983). QUEST: A Bayesian adaptive psychophysical method. Perception and Psychophysics, 33, 113-120.