Probabilistic Symmetries and Invariance Principles

By Olav Kallenberg. 2005

522 citations recorded by the source corpus.

Subfields: Geometry and Topology, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/6ba24c3c241429edb57f53cc38bf6a8b7c8b8f7c

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In Geometry and Topology

In Theoretical Computer Science

Citations in the corpus

Model recommendation: Generating object detectors from few samples (2015, methodology): “Although the rating distribution of model recommendation might be different from that of the typical consumer recommender system, the ratings store still has exchangeability properties—arrays of random variables whose distributions are invariant to permutations of rows and of columns, which makes it”
An introduction to large deviations for random graphs (2016, background): “nifying theory of graph limits has been developed by Laszlo Lov´asz and coauthors in recent years [8, 9, 10, 40, 41]. For connections with the theory of exchangeable arrays in probability theory, see [1, 24, 27, 31]. This section contains a brief review of some of the basic deﬁnitions and results fr”
Coherent permutations with descent statistic and the boundary problem for the graph of zigzag diagrams (2005, background): “See [1] for a survey of earlier results on spreadability and its relation to exchangeability, and see [ 23 ] for an updated exposition (in [23] ‘spreadability’ is also called ‘contractability’).”
Classification results for easy quantum groups (2009, unknown): “These are available for Sn, On from the book [24], for S + n from [25] then [19], and for O n from [20].”
Estimating and understanding exponential random graph models (2011, background): “(See also the related work of Austin [3] and Diaconis and Janson [18] which traces this back to work of Aldous [1], Hoover [33] and Kallenberg [35].)”
Bayesian Nonparametrics: Models beyond the Dirichlet process (2009, unknown): “In this paper we provide a review of Bayesian nonparametric models that go beyond the Dirichlet process.”
On exchangeable random variables and the statistics of large graphs and hypergraphs (2008, background): “Let us also note in passing that several other names for spreadability have also appeared in the literature, such as ‘spreading-invariant’ (as in Kingman [48]) and ‘contractible’ in Kallenberg’s recent book [46].”
Graphons, cut norm and distance, couplings and rearrangements (2010, background): “(This representation is essentially equivalent to the representation by Aldous and Hoover of exchangeable arrays of random variables, see [43] for details of this representation and [4, 24] for the connection, which is summarized in Appendix D.”
A nonparametric view of network models and Newman–Girvan and other modularities (2009, methodology): “We begin, using results of Aldous and Hoover (9), by introducing what we view as the analogues of arbitrary inﬁnite population models on inﬁnite unlabeled graphs which are “ergodic” and from which a subgraph with n vertices can be viewed as a piece.”
Bernstein's inequalities for general Markov chains (2018, unknown): “Exchangeability, particularly useful in the analysis of large networks, relies on de Finetti’s theorem de Finetti (1937) and the Aldous-Hoover-Kallenberg approach (Aldous, 1981; Hoover, 1979; Kallenberg, 2005).”
A hierarchical version of the de Finetti and Aldous-Hoover representations (2013, background): “8 in [11] for a rather stronger result guaranteeing that this can be do n .”
Like like alike — Joint Friendship and Interest Propagation in Social Networks Shuang (2011, methodology): “This model implicitly encodes the Aldous-Hoover theorem [6] for exchangeable matrices — yij are independent from each other given φi and φj .”
q-exchangeability via quasi-invariance (2009, background): “See [Al], [K] for survey of ideas around exchangeability and multiple generalizations of this fundamental kind of stochastic symmetry.”
De Finetti theorems for easy quantum groups (2009, background): “lts fail for ﬁnite sequences, approximation results may still be obtained (see [17, 18]). For a thorough treatment of probabilistic symmetries, the reader is referred to the recent text of Kallenberg [23]. The free analogues S+ n and On + of the permutation and orthogonal groups were constructed by ”