Entropy and information theory
Entropy and information theory
Elements of information theory
Elements of information theory
Spikes: exploring the neural code
Spikes: exploring the neural code
Multiple Protein Structure Alignment by Deterministic Annealing
CSB '03 Proceedings of the IEEE Computer Society Conference on Bioinformatics
Information-theoretic co-clustering
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
Information-theoretic tools for mining database structure from large data sets
SIGMOD '04 Proceedings of the 2004 ACM SIGMOD international conference on Management of data
Learning Hidden Variable Networks: The Information Bottleneck Approach
The Journal of Machine Learning Research
Protein structure alignment by deterministic annealing
Bioinformatics
Multivariate information bottleneck
Neural Computation
Derivation of natural stimulus feature set using a data-driven model
ICCS'03 Proceedings of the 2003 international conference on Computational science
Characterizing the fine structure of a neural sensory code through information distortion
Journal of Computational Neuroscience
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Information-based distortion methods have been used successfully in the analysis of neural coding problems. These approaches allow the discovery of neural symbols and the corresponding stimulus space of a neuron or neural ensemble quantitatively, while making few assumptions about the nature of either the code or of relevant stimulus features. The neural codebook is derived by quantizing sensory stimuli and neural responses into a small set of clusters, and optimizing the quantization to minimize an information distortion function. The method of annealing has been used to solve the corresponding high-dimensional nonlinear optimization problem. The annealing solutions undergo a series of bifurcations, which we study using bifurcation theory in the presence of symmetries. In this contribution we describe these symmetry breaking bifurcations in detail, and indicate some of the consequences of the form of the bifurcations. In particular, we show that the annealing solutions break symmetry at pitchfork bifurcations, and that subcritical branches can exist. Thus, at a subcritical bifurcation, there are local information distortion solutions which are not found by the method of annealing. Since the annealing procedure is guaranteed to converge to a local solution eventually, the subcritical branch must turn and become optimal at some later saddle-node bifurcation, which we have shown occur generically for this class of problems. This implies that the rate distortion curve, while convex for noninformation-based distortion measures, is not convex for information-based distortion methods.