
Observational nonidentifiability, generalized likelihood and free energy
We study the parameter estimation problem in mixture models with observa...
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Maximum Likelihood Constraint Inference from Stochastic Demonstrations
When an expert operates a perilous dynamic system, ideal constraint info...
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Filtering Additive Measurement Noise with Maximum Entropy in the Mean
The purpose of this note is to show how the method of maximum entropy in...
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Likelihood Ratio Exponential Families
The exponential family is well known in machine learning and statistical...
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Metric properties of homogeneous and spatially inhomogeneous Fdivergences
In this paper I investigate the construction and the properties of the s...
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Optimal Entropy Compression and Purification in Quantum Bits
Global unitary transformations (optswaps) that optimally increase the bi...
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Discretizing Dynamics for Maximum Likelihood Constraint Inference
Maximum likelihood constraint inference is a powerful technique for iden...
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Neural computation from first principles: Using the maximum entropy method to obtain an optimal bitsperjoule neuron
Optimization results are one method for understanding neural computation from Nature's perspective and for defining the physical limits on neuronlike engineering. Earlier work looks at individual properties or performance criteria and occasionally a combination of two, such as energy and information. Here we make use of Jaynes' maximum entropy method and combine a larger set of constraints, possibly dimensionally distinct, each expressible as an expectation. The method identifies a likelihoodfunction and a sufficient statistic arising from each such optimization. This likelihood is a firsthitting time distribution in the exponential class. Particular constraint sets are identified that, from an optimal inference perspective, justify earlier neurocomputational models. Interactions between constraints, mediated through the inferred likelihood, restrict constraintset parameterizations, e.g., the energybudget limits estimation performance which, in turn, matches an axonal communication constraint. Such linkages are, for biologists, experimental predictions of the method. In addition to the related likelihood, at least one type of constraint set implies marginal distributions, and in this case, a Shannon bits/joule statement arises.
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