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Maximum entropy distributions on graphs
, 2013
"... Inspired by the problem of sensory coding in neuroscience, we study the maximum entropy distribution on weighted graphs with a given expected degree sequence. This distribution on graphs is characterized by independent edge weights parameterized by vertex potentials at each node. Using the general t ..."
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Cited by 5 (4 self)
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Inspired by the problem of sensory coding in neuroscience, we study the maximum entropy distribution on weighted graphs with a given expected degree sequence. This distribution on graphs is characterized by independent edge weights parameterized by vertex potentials at each node. Using the general theory of exponential family distributions, we prove the existence and uniqueness of the maximum likelihood estimator (MLE) of the vertex parameters. We also prove the consistency of the MLE from a single graph sample, extending the results of Chatterjee, Diaconis, and Sly for unweighted (binary) graphs. Interestingly, our extensions require an intricate study of the inverses of diagonally dominant positive matrices. Along the way, we derive analogues of the ErdősGallai criterion of graphical sequences for weighted graphs.
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, 2013
"... doi: 10.3389/fnint.2012.00126 Transsynaptic modality codes in the brain: possible involvement of synchronized spike timing, microRNAs, exosomes and epigenetic processes ..."
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doi: 10.3389/fnint.2012.00126 Transsynaptic modality codes in the brain: possible involvement of synchronized spike timing, microRNAs, exosomes and epigenetic processes
Article Estimating Functions of Distributions Defined over Spaces of Unknown Size
, 2013
"... entropy ..."
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How to take turns: the fly’s way to encode and decode rotational information
"... Running head: Neural code of spike trains. ..."
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"... In neuronal pathways that connect sensory with motor systems, an important transformation is the conversion of graded potentials into spikes. This transformation can occur within the receptor cells themselves if they have long axons but often occurs in second or ..."
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In neuronal pathways that connect sensory with motor systems, an important transformation is the conversion of graded potentials into spikes. This transformation can occur within the receptor cells themselves if they have long axons but often occurs in second or