From data to constraints

@inproceedings{Mukhopadhyay2012FromDT,
  title={From data to constraints},
  author={Subhadeep Mukhopadhyay and Emanuel Parzen and Soumendra Nath Lahiri},
  year={2012}
}
Jaynes' Maximum Entropy (MaxEnt) inference starts with the assumption that we have a set of known constraints over the distribution. In statistical physics, we have a good intuition about the conserved macroscopic variables. It should not be surprising that in a real world applications, we have no idea about which coordinates to use for specifying the state of the system. In other words, we only observe empirical data and we have to take a decision on the constraints from the data. In an effort… 

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References

SHOWING 1-8 OF 8 REFERENCES
Nonparametric Statistical Data Modeling
TLDR
An approach to statistical data analysis which is simultaneously parametric and nonparametric is described, and density-quantile functions, autoregressive density estimation, estimation of location and scale parameters by regression analysis of the sample quantile function, and quantile-box plots are introduced.
Quantiles, Parametric-Select Density Estimations, and Bi-Information Parameter Estimators.
A quantile-based approach to statistical analysis and probability modeling of data is presented which formulates statistical inference problems as functional inference problems in which the
Quantile Based Variable Mining : Detection, FDR based Extraction and Interpretation
TLDR
A unified framework for high dimensional variable selection for classification problems is outlined and it is proposed that a key to accomplishing this unification is to think in terms of the quantile function and the comparison density.
Information Theory and an Extension of the Maximum Likelihood Principle
TLDR
The classical maximum likelihood principle can be considered to be a method of asymptotic realization of an optimum estimate with respect to a very general information theoretic criterion to provide answers to many practical problems of statistical model fitting.
Quantile Probability and Statistical Data Modeling
Quantile and conditional quantile statistical thinking, as I have innovated it in my research since 1976, is outlined in this comprehensive survey and introductory course in quantile data analysis.
Asymptotic properties of sample quantiles of discrete distributions
The asymptotic distribution of sample quantiles in the classical definition is well-known to be normal for absolutely continuous distributions. However, this is no longer true for discrete
»Smooth test» for goodness of fit
Abstract Dedicated to the memory of Karl Pearson (27 March 1857—27 April 1936) who originated the problem of a test for goodness of fit and was first to advance its solution.
Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays.
  • U. Alon, N. Barkai, A. Levine
  • Biology
    Proceedings of the National Academy of Sciences of the United States of America
  • 1999
TLDR
A two-way clustering method is reported for analyzing a data set consisting of the expression patterns of different cell types, revealing broad coherent patterns that suggest a high degree of organization underlying gene expression in these tissues.