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Register a new userUsing Fisher Information In Big Data
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Added by
Nasir Ahmad
Publication date
2015
fields
Informatics Engineering
and research's language is
English
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In this era of Big Data, proficient use of data mining is the key to capture useful information from any dataset. As numerous data mining techniques make use of information theory concepts, in this paper, we discuss how Fisher information (FI) can be applied to analyze patterns in Big Data. The main advantage of FI is its ability to combine multiple variables together to inform us on the overall trends and stability of a system. It can therefore detect whether a system is losing dynamic order and stability, which may serve as a signal of an impending regime shift. In this work, we first provide a brief overview of Fisher information theory, followed by a simple step-by-step numerical example on how to compute FI. Finally, as a numerical demonstration, we calculate the evolution of FI for GDP per capita (current US Dollar) and total population of the USA from 1960 to 2013.
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Two new proofs of the Fisher information inequality (FII) using data processing inequalities for mutual information and conditional variance are presented.
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In this article we study lossless compression of strings of pure quantum states of indeterminate-length quantum codes which were introduced by Schumacher and Westmoreland. Past work has assumed that the strings of quantum data are prepared to be encoded in an independent and identically distributed way. We introduce the notion of quantum stochastic ensembles, allowing us to consider strings of quantum states prepared in a more general way. For any identically distributed quantum stochastic ensemble we define an associated quantum Markov chain and prove that the optimal average codeword length via lossless coding is equal to the quantum dynamical entropy of the associated quantum Markov chain.
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