The exponential family
Chapter 8. The exponential family: Basics. 8.1 The exponential family
... This argument implies that a distribution in the exponential family can be parameterized not only by η—the canonical parameterization—but also by µ—the mean parameterization. Many distributions are ...
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Some Characterizations of The Exponential Family
... This paper introduces some characterizations concerning the exponential family. Recurrence relation between two consecutive conditional moments of ℎ(𝑍) given 𝑥 < 𝑍 < 𝑦 is presented. In addition, an ...
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Hierarchical statistical modeling of big spatial datasets using the exponential family of distributions
... In this article, we have developed a hierarchical spatial statistical model where the data model be- longs to the exponential family of distributions. The process model is spatially dependent and is based ...
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Optimal "anti-Bayesian" parametric pattern classification for the exponential family using order statistics criteria
... With these points at hand, we shall now demonstrate that, for doubly exponen- tial distributions, the classification based on the expected values of the moments of the 2-OS, CMOS, attains[r] ...
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Exponential Family Embeddings
... nential family representation ensures that the updates have to be derived only once, for the general model class, and properties of the exponential family distribution simplify the gradi- ...
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Finding the Maximizers of the Information Divergence from an Exponential Family: Finding the Maximizersof the Information Divergencefrom an Exponential Family
... the exponential family is convex, and this example is treated by Mat´ uˇs and Ay in ...convex exponential families, the partition exponential families, plays an important role in Chapters 4 ...
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4.1 INTRODUCTION TO THE FAMILY OF EXPONENTIAL FUNCTIONS
... Graphs of the Exponential Family: The Effect of the Parameter b The growth factor, b, is called the base of an exponential function. Provided a is positive, if b > 1, the graph climbs when read ...
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Exponential Family Harmoniums with an Application to Information Retrieval
... A type of two-layer model that has not enjoyed much attention is the undirected analogue of the above described family of models. It was first introduced in [10] where it was named “harmonium”. Later papers have ...
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Learning Node Embeddings with Exponential Family Distributions
... the exponential family distribution models enable to effectively capture the num- ber of occurrences of a node within the context of another one, while learning the embedding ...
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CiteSeerX — Exponential Family Techniques for the Lognormal Left Tail
... efficient implementations are readily available in the most commonly used software packages (eg. MATLAB, R). The paper is organized as follows. In Section 2, we study the exponential family (F θ ) θ≥0 . We ...
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Dimension reduction for exponential family data with applications to text data
... SPPCA SSPPCA GPCA SGPCA PCA 0.38 0.34 0.23 0.17 0.21 Table 5.5: Average silhouettes first the healthcare data. for inference on W and Y than SePCA. We have illustrated that by example in the spe- cific case where the ...
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Kernel Exponential Family Estimation via Doubly Dual Embedding
... the exponential family to an infinite- dimensional parameterization via reproducing kernel Hilbert spaces (RKHS) (Canu and Smola, ...dimensional exponential families, where desirable sta- tistical ...
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Learning Exponential Family Graphical Models with Latent Variables using Regularized Conditional Likelihood
... ρising(u) = log cosh(u) ρpoisson(u) = exp(u) ρexponential(u) = − log(−u). (2.12) If we do not account for the confounding effects of latent variables and set L = 0, then we recover a “coupled” analog of the neighborhood ...
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On Semiparametric Exponential Family Graphical Models
... We propose a new class of semiparametric exponential family graphical models for the anal- ysis of high dimensional mixed data. Different from the existing mixed graphical models, we allow the nodewise ...
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Parameter Uncertainty in Exponential Family Tail Estimation
... Abstract Actuaries are often faced with the task of estimating tails of loss distributions from just a few observations. Thus estimates of tail prob- abilities (reinsurance prices) and percentiles (solvency capital ...
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The odd generalized exponential family of distributions with applications
... new family of continuous distributions called the odd generalized exponential family, whose hazard rate could be increasing, decreasing, J, reversed-J, bathtub and upside-down ...the family ...
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epca: HIGH DIMENSIONAL EXPONENTIAL FAMILY PCA
... Error of covariance matrix estimation, measured as the spectral norm left and Frobenius norm right of the difference between each covariance estimate Sample, Debiased, Heterogenized, Sca[r] ...
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Exponential Family Techniques for the Lognormal Left Tail
... Let X be lognormal(µ, σ 2 ) with density f (x), let θ > 0 and define L(θ) = Ee −θX . We study properties of the exponentially tilted density (Esscher transform) f θ (x) = e −θx f (x)/L(θ), in particular its moments, ...
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Multiway Dependence in Exponential Family Conditional Distributions
... One approach to the formulation of conditionally specified models is to define a dependence structure among individual random variables such that the joint collection of variables forms a Markov Random Field (MRF). This ...
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The First- and Second-Order Large-Deviation Efficiency for an Exponential Family and Certain Curved Exponential Models
... an exponential family of ...curved exponential model, the first and second order lower bounds are obtained, and the MLE is shown not to be first order large-deviation ...
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