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Approximations in Probabilistic Programs
[article]
2019
arXiv
pre-print
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If these terms are such that R t 1 γ , ( stat(t 0 , λx .t 1 ) γ ), C, ρ holds, then for all Iterate N (m 1 , λx .t 1 ) γ − Iterate N (m 2 , λx .t 1 ) γ tv ≤ Cρ N m 1 γ − m 2 γ . Proof. ...
Thus the semantics is given as: sample(t) γ , A = t γ , A , where t γ ∈ M( A ). ...
arXiv:1912.06791v1
fatcat:c4wyee3lsjhbjag3cvubzntdry
Integrating Biological Control into Conservation Practice Roy G. van Driesche, Daniel Simberloff, Bernd Blossey, Charlotte Causton, Mark S. Hoddle, David L. Wagner, Christian O. Marks, Kevin M. Heinz and Keith D. Warner (eds.)
2017
American Entomologist
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The lead editor, Roy van Driesche, has worked for years to bring together two important groups of applied ecologists: conservation biologists concerned with protecting and restoring threatened, minimally ...
doi:10.1093/ae/tmx029
fatcat:urqfdgn3zfbvrnueueg3id2hgq
The Mondrian Kernel
[article]
2016
arXiv
pre-print
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The features are constructed by sampling trees via a Mondrian process [Roy and Teh, 2009], and we highlight the connection to Mondrian forests [Lakshminarayanan et al., 2014], where trees are also sampled ...
MONDRIAN PROCESS For completeness, we review the Mondrian process [Roy and Teh, 2009, Roy, 2011, Chapter 5] . ...
This confirms equivalence of our generative process to the one proposed by Roy and Teh [2009] . ...
arXiv:1606.05241v1
fatcat:ongsiwdkhrgitjpyjo76wlc72e
Sampling and Estimation for (Sparse) Exchangeable Graphs
[article]
2016
arXiv
pre-print
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Then there is a coupling such that P(H r = M r | G) ≤ r s a.s. (4.34) Proof. ...
On this basis, Veitch and Roy argue that sparse exchangeable graphs can serve as a general statistical model for network data. ...
Conditional on G k and s k , let X k r be an r/s k -sampling of G k and let M k r be a random subgraph of G k given by sampling Poi(v(G k )r/s k ) vertices with replacement and returning the edge set of ...
arXiv:1611.00843v1
fatcat:6qnwaioetnaznlytscbctaph6a
On the computability of graphons
[article]
2018
arXiv
pre-print
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Suppose h : N → M is a computable map. We say that a computable map g : M → N is a computable equivalence witnessed by h if d x, h(g(x)) = 0 for all x ∈ M and f y, g(h(y)) = 0 for all y ∈ N . ...
Also, for each n ∈ N, let n := 1 − 2 −(2n+1) , let r n := 1 − 2 −(2n+2) , and let m n := n+rn 2 , so that 0 < 0 < m 0 < r 0 < 1 < m 1 < r 1 < . . . < 1. Define the constant graphon H * ≡ 1 2 . ...
arXiv:1801.10387v1
fatcat:5vg7wxb52rc7jjq476jqa2zt3a
Neural Network Matrix Factorization
[article]
2015
arXiv
pre-print
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., 2009 ), we may have N users and M movies, and for some collection J ⊆ [N ] × [M ] of user-movie pairs (n, m), we have recorded the rating X n,m that user n gave movie m. ...
Similarly, to each column, m ∈ M , we associate a latent feature vector V m ∈ R D and latent feature matrix V m ∈ R D ×K . ...
arXiv:1511.06443v2
fatcat:jboltjd7yvdypno3zz2ptl46c4
Existence of matching priors on compact spaces
[article]
2020
arXiv
pre-print
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The function ψ αβγδη (·, x ; π) is β-Lipschitz for all x ∈ X and π ∈ M(Θ).
H. DUANMU, D. M. ROY, AND A. ...
These tools have been used recently to establish general complete class theorems connecting Bayesian and frequentist statistics (Duanmu & Roy, 2020) . ...
If π ∈ M(S) ∩ A b,a | S , then Inequality (2) implies Q S (π) ∈ A 1 2 b,a | S . If π ∈ M(S) \ A b,a | S , then Inequality (9) and the fact that a, b < 0.001 imply Q S (π) ∈ A b,a | S . ...
arXiv:2011.03655v1
fatcat:5ujwlown7zgo5pjxfy4kwox7ye
Particle Gibbs for Bayesian Additive Regression Trees
[article]
2015
arXiv
pre-print
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M. Roy, and Y. W. ...
j=1 , σ 2 |Y, X) ∝ (Y |{T j , µ j } m j=1 , σ 2 , X) p({T j , µ j } m j=1 , σ 2 |X). (7) {T j , µ j } m j=1 . ...
arXiv:1502.04622v1
fatcat:w2ab2c5n3ndpbbbajcgvstduna
Gibbs-type Indian Buffet Processes
2019
Bayesian Analysis
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) T (Y − M ) , (7.5) where M = (W • Z)A. ...
This representation results from an application of Roy (2014, Theorem 1.4). ...
doi:10.1214/19-ba1166
fatcat:xg4zww5pc5dztndxupp7ckmdma
Gibbs-type Indian buffet processes
[article]
2015
arXiv
pre-print
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Roy [44, Lem. 4.4] shows that M is the index of the first customer in the IBP to sample the k-th dish. ...
−1 µ 1 (dp) [0,1] (1 − p) M −1 µ 1 (dp) (5.2) for some random element M in N. ...
Constructions by Roy [44, Def. 6 .1] provide alternative simulation procedures, however, posterior inference algorithms have yet to be developed. ...
arXiv:1512.02543v1
fatcat:pgiatld7xngwtbs3a2u757pro4
Black-box constructions for exchangeable sequences of random multisets
[article]
2019
arXiv
pre-print
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, 2014; Heaukulani and Roy, 2019) and hierarchies thereof (Thibaux and Jordan, 2007; Roy, 2014) , in which case it is convenient to have a black-box method. ...
In particular, we call a random base measure H in M 0 (Ω, A) a hierarchy of beta processes if there exists a beta process B ∼ BP(c, B 0 ) such that H | B ∼ BP(c, B). (3.11) Roy (2014) provides the following ...
arXiv:1908.06349v1
fatcat:szjf5km6ofdkbltwcazjm2eajm
Instabilities in two-photon lasers
1993
Chaos in Optics
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The two-photon laser represents an entirely new class of quantum optical oscillator that promises to display a wealth of new and exciting nonlinear behavior. For example, the prediction that the turnon behavior of the laser is indicative of a first-order phase transition was verified in recent studies of the first continuous-wave two-photon laser. In addition, it was found experimentally that the field generated by the laser displayed dynamical instabilities under some conditions. We briefly
doi:10.1117/12.164764
fatcat:br7ajwpmi5h3pmunt7fpp6jvoe
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... iew the properties of two-photon lasers that are pertinent to its dynamical characteristics and show that many of the interesting properties can be understood from a simple rate-equation model. Also, we describe our efforts at Duke to address the origin of instabilities in two-photon lasers.
The Class of Random Graphs Arising from Exchangeable Random Measures
[article]
2015
arXiv
pre-print
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× n arrays to their leading m × m subarrays. ...
. | M iid ∼ M. (2.4) We can express the distribution µ in terms of P: For a distribution m on R, let m ∞ be the distribution of an infinite i.i.d.-m sequence. ...
arXiv:1512.03099v1
fatcat:detwdgbhzbemrgr2anlhdln2wq
Not Only English: Affirming America's Multilingual Heritage
1991
College composition and communication
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Daniels). (KEH) ...
Victor Villanueva, Jr.); ( 9 ) "Anglo-Conformity: Folk Remedy for Lost Hegemony" (James Sledd); (10) "Disillusionment with Official English and the Search for Alternatives" (Mary Carol Combs and Lynn M. ...
Daniels enunciated pluralistic position of their profession and their own worries. ...
doi:10.2307/358016
fatcat:2naqikns4zdtzpuqswekt3crvi
Probabilistically Accurate Program Transformations
[chapter]
2011
Lecture Notes in Computer Science
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Define Y n 1 = A Y = n i=1 Y i and Y m 1 = P Y = m i=1 Y i and define X n 1 and X m 1 analogously. ...
Therefore, the sum Y m 1 also has a gamma distribution with parameters α = mα, θ = θ, 1 Y m 1 has an inverse gamma distribution with mean (θ(mα − 1)) −1 , and so var(D) = σ 2 Z θ 1 mα − 1 − 1 nα − 1 . ...
doi:10.1007/978-3-642-23702-7_24
fatcat:dy7orqhh6zfcnise6o44jqzhwi
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