Information Theory, Inference, and Learning Algorithms

By Yuhong Yang. 2005

2,089 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/277b6accc82872010ebebfc79214ca2913c483b7

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Citations in the corpus

Optimal Existence and Uniqueness Theory for the Fractional Heat Equation (2016, background): “These operators are generators of Lévy processes that include jumps and long-distance interactions, resulting in anomalous diffusion [4, 8].”
Certain properties related to well posedness of switching diffusions (2017, background): “Suppose that the switching process α(t) has generator Q = ( −f(x) f(x) 0 0 ) , where f(x) is a smooth positive function with compact support and f(x) = x for x ∈ [1, 2].”
BIFURCATION AND MULTIPLICITY RESULTS FOR CRITICAL NONLOCAL FRACTIONAL LAPLACIAN PROBLEMS (2016, neutral): “, the papers [2, 7, 10, 16, 21, 34, 35, 36] and references therein).”
Delay differential equations driven by Lévy processes: Stationarity and Feller properties (2005, background): “On the other hand, there exists for every σ ∈ [1, 2] a stationary Ornstein–Uhlenbeck process X which solves the equation (we suppose that W is a two-sided Wiener process) dX (t) = −X (t) dt + σ dW (t) for t ∈ R.”
A General Fractional Porous Medium Equation (2011, positive): “The linear model has been well studied by probabilists, since the fractional Laplacians of order σ are infinitesimal generators of stable Lévy processes [1], [7].”
Detecting the overlapping and hierarchical community structure in complex networks (2008, neutral): “Here, we briefly discuss the issue within the framework of information theory [48].”
Mathematics of Two-Dimensional Turbulence (2012, neutral): “10 in [App04].”
Lévy Processes—From Probability to Finance and Quantum Groups (2004, background): “Readers who want to learn more about “Lévy finance” should consult [12], [4] , chapter 5 of [1], and references therein.”
Brownian subordinators and fractional Cauchy problems (2007, methodology): “In the case where X 0 ( t ) is a L´evy process started at zero and [3, 31, 58] that can be explicitly computed by inverting the L´evy representation.”
Ergodicity and exponential β-mixing bounds for multidimensional diffusions with jumps (2007, background): “Among other publications, we refer the reader to the recent monograph Applebaum [1] for fundamental facts of the process.”
Foundations and Advances in Deep Learning (2014, positive): “The Hopfield network aims to finding a set of weights that makes the energy of the presented patterns low via the training set D = { x(1), . . . ,x(N) } (see, e.g., Mackay, 2002).”
Stochastic flows for Lévy processes with Hölder drifts (2015, background): “1) when Z is a non-degenerate symmetric (but possibly non-isotropic) α-stable process in R with α ∈ [1, 2) and time-independent b(t, x) = b(x) ∈ C b (R) with β ∈ (1−α/2, 1).”
SELF‐DECOMPOSABILITY AND OPTION PRICING (2007, methodology): “The use of these processes for option pricing is now covered in a number of books and we cite by way of example, Schoutens (2003), Cont and Tankov (2004), and Applebaum (2004).”
Super Polyharmonic Property of Solutions for PDE Systems and Its Applications (2011, background): “While fractional powers of Laplacian in (4) have many applications in mathematical physics and related fields, such as anomalous diffusion and quasi-geostrophic flows, turbulence models and water waves, molecular dynamics and relativistic quantum mechanics of stars [5] [6] [22] [49] [61], as well as”
Properties and numerical evaluation of the Rosenblatt distribution (2013, methodology): “chi-squared distributions, we can use the Lévy Khintchine representation of a chi-square ([4], Example 1.”
Approximation properties for solutions to non‐Lipschitz stochastic differential equations with Lévy noise (2015, methodology): “Now, using the Lévy–Itô decomposition (1) and the technique of interlacing [29], it yields the more general integral form of Equation (18) as follows: y.”