Fundamentals of statistical exponential families: with applications in statistical decision theory

By Lawrence D. Brown. 1986

Subfields: Probabilistic & Bayesian Methods

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Citations in the corpus

Energy-Inspired Models: Learning with Sampler-Induced Distributions (2019, background): “Energy-based models (EBMs) are powerful probabilistic models [8, 43], but suffer from intractable sampling and density evaluation due to the partition function.”
Density Estimation in Infinite Dimensional Exponential Families (2013, methodology): “On the theoretical front, the consistency in [14, Theorem 6] is established by assuming a decay rate on the eigenvalues of the covariance operator (see (A-2) and the discussion in Section 1.4 of [14] for details), which is usually diﬃcult to check in practice.”
Machine Teaching for Bayesian Learners in the Exponential Family (2013, methodology): “This research is supported in part by National Science Foundation grants IIS-0953219 and IIS-0916038.”
Exponential Family Embeddings (2016, methodology): “We use the tools of exponential families (Brown, 1986) and generalized linear models ( glms ) (McCullagh and Nelder, 1989) to adapt this idea beyond language.”
Social network analysis: A methodological introduction (2008, methodology): “This relationship hints at another important insight regarding the ERG parameterization: models in this form can be understood as providing distributions of maximum entropy over their support, conditional on fixing the expected sufficient statistics (as determined by q) (Brown, 1986; Strauss, 1986).”
Information Geometry of the Gaussian Distribution in View of Stochastic Optimization (2015, methodology): “G.1.6 [Mathematics of Computing]: Optimization — Stochastic programming ; G.3 [Mathematics of Computing]: Probabilistic algorithms (including Monte Carlo)”
One-sided confidence intervals in discrete distributions (2005, background): “See Morris (1982) and Brown (1986).”
Optimal Inference After Model Selection (2014, background): “See Lehmann and Romano (2005) or Brown (1986) for thorough reviews of the rich literature on testing in exponential family models.”
The Group-Lasso for generalized linear models: uniqueness of solutions and efficient algorithms (2008, background): “In particular, we demonstrate that the proposed completeness test successfully detects ambiguous solutions and thus avoids the misinterpretation of “identiﬁed” explanatory factors.”
A hierarchical eigenmodel for pooled covariance estimation (2008, methodology): “As a full, regular exponential family, maximum likelihood estimation with the Bingham model provides consistent estimates of the population expectations of the sufficient statistics, even if the true distribution is not Bingham (see, for example, chapter 5 of Brown (1986)).”
Restricted Strong Convexity Implies Weak Submodularity (2016, methodology): “We refer the reader to the standard literature for more details on GLMs and exponential families [9, 14].”
Belief Propagation, Dykstra's Algorithm, and Iterated Information Projections (2010, background): “in which each factor is an exponential density [53], [54] of the form”
Sequences of regressions and their independences (2011, methodology): “With distributions generated over parent graphs, one excludes incomplete families of distributions; see Lehmann and Scheffé (1955), Brown (1986), Mandelbaum and”
On the toric algebra of graphical models (2006, methodology): “The factorization of distributions according to exponential models is well studied (e.g., [2, 4 , 5, 24]).”
Parameter Estimation of Statistical Models Using Convex Optimization (2010, methodology): “Furthermore, K 1l 2 is called cumulant generating function, which is a convex function of the natural parameters l and independent of X.”
INTERVAL ESTIMATION IN EXPONENTIAL FAMILIES (2003, background): “NEF-QVF families consist of six important distributions, three continuous: normal, gamma, and NEF-GHS distributions; three discrete: binomial, negative binomial, and Poisson (see, e.g., Morris (1982) and Brown (1986)).”