The coincidence approach to stochastic point processes

By O. Macchi. 1975

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Citations in the corpus

Determinantal Point Processes for Machine Learning (2012, methodology): “In fact, years before Macchi gave them a general treatment, specific DPPs appeared in major results in random matrix theory [Mehta and Gaudin, 1960, Dyson, 1962a,b,c, Ginibre, 1965], where they continue to play an important role [Diaconis, 2003, Johansson, 2005b].”
Diversity Networks (2015, neutral): “Let T denote the training data, ` a layer of n` neurons, aij the activation of the i-th neuron on input tj , and vi = (ai1, . . . , ain`) > the activation vector of the i-th neuron obtained by feeding the training data through the network.”
Zeros of Random Analytic Functions (2006, background): “These point processes were introduced by Macchi (26) and are known as Determinantal (Fermionic) point processes.”
The Ubiquitous Ewens Sampling Formula (2016, background): “Heuristically, (23) interpolates between (21) and (22), Cauchy’s permanent (22) is the α-permanent with α = 1, and the determinant (21) equals (−1)n per−1(M), but its role is most prominent in modeling bosons and fermions in statistical physics [49, 66].”
On adding a list of numbers (and other one-dependent determinantal processes) (2009, background): “We first describe some results for the stationary case.”
Diverse Sequential Subset Selection for Supervised Video Summarization (2014, methodology): “The DPP was first used to characterize the Pauli exclusion principle, which states that two identical particles cannot occupy the same quantum state simultaneously [16].”
Determinantal random point fields (2000, methodology): “122) or exclusion probability densities (see [Ma]).”
Distributions on Partitions, Point Processes,¶ and the Hypergeometric Kernel (1999, methodology): “As a separate class, these processes were identified by Macchi [ Mac1 ,Mac2], who used the term fermion point processes, see also [DVJ].”
The Surprising Mathematics of Longest Increasing Subsequences (2015, background): “5 Determinantal point processes were first defined in 1975 by Macchi [83], who referred to them as fermion processes because they arise naturally as descriptions of many-particle systems in statistical quantum mechanics.”
The Random Matrix Theory of the Classical Compact Groups (2019, background): “It is a result of Macchi [75] and Soshnikov [96] that if a kernel K defines an operator K by K f (x) = ∫”
DLow: Diversifying Latent Flows for Diverse Human Motion Prediction (2020, unknown): “n has also been applied to select a diverse subset of garments from fashion images [31]. Another type of methods [40, 20, 19, 32, 5, 73, 70] seeks diversity using determinantal point processes (DPPs; [50, 41]) which are elegant and ecient probabilistic models that can measure the global diversity an”
Near-Optimal MAP Inference for Determinantal Point Processes (2012, background): “DPPs offer computationally attractive properties, including exact and efficient computation of marginals [8], sampling [12, 5], and (partial) parameter estimation [13].”
Determinantal Processes and Independence (2005, background): “Macchi [22] and Soshnikov [27] showed that there exists a determinantal point process with kernel K if and only if all eigenvalues of K are in the interval [0, 1].”
Determinantal probability measures (2002, background): “At about that same time, in studying fermions in physics, general point processes with a determinantal form were introduced by Macchi (1975) (see also the references therein) and are known as fermionic processes in mathematical physics.”
Lectures on the Poisson Process (2017, methodology): “14 Permanental Processes Permanental processes were introduced into the mathematics literature by Macchi [98, 99] as rigorous point process models for the description of bosons.”
Learning Determinantal Point Processes (2011, background): “Determinantal point processes, introduced to model fermions (Macchi, 1975), also arise in studies of non-intersecting random paths, random spanning trees, and eigenvalues of random matrices (Daley and Vere-Jones, 2003; Borodin and Soshnikov, 2003; Hough et al.”
Determinantal point processes (2018, methodology): “on locally ﬁnite subsets of X. Determinantal point processes (with X = R) have been used in random matrix theory since early 60’s. As a separate class determinantal processes were ﬁrst singled out in [Mac75] to model fermions in thermal equilibrium, cf. [Ben73], and the term ‘fermion’ point processe”