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Explaining variational approximations
 The American Statistician
, 2010
"... Variational approximations facilitate approximate inference for the parameters in complex statistical models and provide fast, deterministic alternatives to Monte Carlo methods. However, much of the contemporary literature on variational approximations is in Computer Science rather than Statistics, ..."
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Cited by 30 (9 self)
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Variational approximations facilitate approximate inference for the parameters in complex statistical models and provide fast, deterministic alternatives to Monte Carlo methods. However, much of the contemporary literature on variational approximations is in Computer Science rather than Statistics
Primer on Variational Approximation 5 ‘Undergraduate ’ Variational Approximation‘Undergraduate ’ Variational Approximation
"... Consider the Bayesian Poisson regression model [yiβ] ind. ∼ Poisson(exp(β0 + β1x1i +... + βkxki)) Prior on regression coefficients: (β0,..., βk) ∼ N(0, F).‘Undergraduate ’ Variational Approximation Consider the Bayesian Poisson regression model [yiβ] ind. ∼ Poisson(exp(β0 + β1x1i +... + βkxki)) P ..."
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Consider the Bayesian Poisson regression model [yiβ] ind. ∼ Poisson(exp(β0 + β1x1i +... + βkxki)) Prior on regression coefficients: (β0,..., βk) ∼ N(0, F).‘Undergraduate ’ Variational Approximation Consider the Bayesian Poisson regression model [yiβ] ind. ∼ Poisson(exp(β0 + β1x1i +... + βkxki
Tutorial on Variational Approximation Methods
 IN ADVANCED MEAN FIELD METHODS: THEORY AND PRACTICE
, 2000
"... We provide an introduction to the theory and use of variational methods for inference and estimation in the context of graphical models. Variational methods become useful as ecient approximate methods when the structure of the graph model no longer admits feasible exact probabilistic calculations. T ..."
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Cited by 88 (1 self)
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We provide an introduction to the theory and use of variational methods for inference and estimation in the context of graphical models. Variational methods become useful as ecient approximate methods when the structure of the graph model no longer admits feasible exact probabilistic calculations
On Structured Variational Approximations
, 2002
"... The problem of approximating a probability distribution occurs frequently in many areas of applied mathematics, including statistics, communication theory, machine learning, and the theoretical analysis of complex systems such as neural networks. Saul and Jordan (1996) have recently proposed a pow ..."
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Cited by 14 (3 self)
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powerful method for eciently approximating probability distributions known as structured variational approximations.
Grid Based Variational Approximations
"... Variational methods for approximate Bayesian inference provide fast, flexible, deterministic alternatives to Monte Carlo methods. Unfortunately, unlike Monte Carlo methods, variational approximations cannot, in general, be made to be arbitrarily accurate. This paper develops gridbased variational ..."
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Variational methods for approximate Bayesian inference provide fast, flexible, deterministic alternatives to Monte Carlo methods. Unfortunately, unlike Monte Carlo methods, variational approximations cannot, in general, be made to be arbitrarily accurate. This paper develops grid
Optimal approximation by piecewise smooth functions and associated variational problems
 Commun. Pure Applied Mathematics
, 1989
"... (Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation Mumford, David Bryant, and Jayant Shah. 1989. Optimal approximations by piecewise smooth functions and associated variational problems. ..."
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Cited by 1294 (14 self)
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(Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation Mumford, David Bryant, and Jayant Shah. 1989. Optimal approximations by piecewise smooth functions and associated variational problems
Variational algorithms for approximate Bayesian inference
, 2003
"... The Bayesian framework for machine learning allows for the incorporation of prior knowledge in a coherent way, avoids overfitting problems, and provides a principled basis for selecting between alternative models. Unfortunately the computations required are usually intractable. This thesis presents ..."
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Cited by 440 (9 self)
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a unified variational Bayesian (VB) framework which approximates these computations in models with latent variables using a lower bound on the marginal likelihood. Chapter 1 presents background material on Bayesian inference, graphical models, and propagation algorithms. Chapter 2 forms
On variational approximations in quantum molecular dynamics
 Math. Comp
, 2005
"... Abstract. The DiracFrenkelMcLachlan variational principle is the basic tool for obtaining computationally accessible approximations in quantum molecular dynamics. It determines equations of motion for an approximate timedependent wave function on an approximation manifold of reduced dimension. Thi ..."
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Cited by 27 (8 self)
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Abstract. The DiracFrenkelMcLachlan variational principle is the basic tool for obtaining computationally accessible approximations in quantum molecular dynamics. It determines equations of motion for an approximate timedependent wave function on an approximation manifold of reduced dimension
Determining the Number of Factors in Approximate Factor Models
, 2000
"... In this paper we develop some statistical theory for factor models of large dimensions. The focus is the determination of the number of factors, which is an unresolved issue in the rapidly growing literature on multifactor models. We propose a panel Cp criterion and show that the number of factors c ..."
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Cited by 561 (30 self)
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of the number of factors for configurations of the panel data encountered in practice. The idea that variations in a large number of economic variables can be modelled bya small number of reference variables is appealing and is used in manyeconomic analysis. In the finance literature, the arbitrage pricing
Improved Variational Approximation for Bayesian PCA
, 2003
"... As with most nontrivial models, an exact Bayesian treatment of the probabilistic PCA model (under a meaningful prior) is analytically intractable. Various approximations have therefore been proposed in the literature; these include approximations based on typeII maximum likelihood as well as varia ..."
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as variational approximations. In this document, we describe an improved variational approximation for Bayesian PCA. This is achieved by defining a more general prior over the model parameters that has stronger conjugacy properties, thereby allowing for a more accurate variational approximation to the true
Results 1  10
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