Information geometry is a branch of mathematics that applies the techniques of differential geometry to the field of probability theory. This is done by taking probability distributions for a statistical model as the points of a Riemannian manifold, forming a statistical manifold. The Fisher information metric provides the Riemannian metric.
Information geometry reached maturity through the work of Shun'ichi Amari and other Japanese mathematicians in the 1980s. Amari and Nagaoka's book, Methods of Information Geometry, is cited by most works of the relatively young field due to its broad coverage of significant developments attained using the methods of information geometry up to the year 2000. Many of these developments were previously only available in Japanese-language publications.
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Famous quotes containing the words information and/or geometry:
“Phenomenal nature shadows him wherever he goes. Clouds in the staring sky transmit to one another, by means of slow signs, incredibly detailed information regarding him. His inmost thoughts are discussed at nightfall, in manual alphabet, by darkly gesticulating trees. Pebbles or stains or sunflecks form patterns representing in some awful way messages which he must intercept. Everything is a cipher and of everything he is the theme.”
—Vladimir Nabokov (1899–1977)
“I am present at the sowing of the seed of the world. With a geometry of sunbeams, the soul lays the foundations of nature.”
—Ralph Waldo Emerson (1803–1882)