Information geometry on hierarchy of probability distributions

By Shun-ichi Amari. 2001

454 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics, Signal Processing

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Citations in the corpus

Inferring deterministic causal relations (2010, methodology): “not completely obvious, so we will explain it in more detail. First, assume that E X contains the uniform distribution u 0. Because uis the projection of p X onto E X, !p Xu and !uu 0 are orthogonal [Amari, 2001]. Using Lemma 1, we obtain R p(x)logu(x)dx= S(u). In general, one can imagine that eleme”
Information-geometric approach to inferring causal directions (2012, background): “Because U X is the projection of P X onto EX , (P X , U X , U ) form a Pythagorean triple [18].”
Information Geometry of the Gaussian Distribution in View of Stochastic Optimization (2015, background): “As a consequence, the exponential manifold associated to the multivariate Gaussian distribution has a straightforward hierarchical structure, similar to what happens in the case of binary variables, cf [6].”
Distinguishing Cause and Effect via Second Order Exponential Models (2009, methodology): “In this sense, second order models generate the simplest non-trivial family of conditional densities within a hierarchy of exponential models [20] that are given by entropy maximization subject to higher order moments.”
A new class of upper bounds on the log partition function (2002, background): “5Since the constraints on (T ) are affine, each such E(T ) is an e-flat manifold in the sense of information geometry [1], [2].”
Semi-supervised interpolation in an anticausal learning scenario (2015, background): “It is known in information geometry (Amari, 2001) that many theorems have such a 'dual' counterpart. interpolation outperforms standard linear interpolation with respect to two substantially different loss functions: the first one is a squared distance, the second one the Bayesian surprise.”
MAP estimation via agreement on trees: message-passing and linear programming (2005, background): “When the collection of potential functions � do not satisfy any linear constraints, then the representation (1 ) is said to be minimal [ 3 ], [4].”
Justifying Additive Noise Model-Based Causal Discovery via Algorithmic Information Theory (2009, background): “To this end, we assume without loss of generality that Λ is contained in the cube [0, 1]d.”
A Maximum Entropy Model Applied to Spatial and Temporal Correlations from Cortical Networks In Vitro (2008, unknown): “Antecedentsofthesemethodscanbefoundin (Martignonetal.,2000;Amari,2001;Schneidmanetal.,2003),andan overviewisgivenin(NirenbergandVictor,2007).”