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97
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
Exponential Stochastic Cellular Automata for Massively Parallel Inference
"... Abstract We propose an embarrassingly parallel, memory efficient inference algorithm for latent variable models in which the complete data likelihood is in the exponential family. The algorithm is a stochastic cellular automaton and converges to a valid maximum a posteriori fixed point. Applied to ..."
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Abstract We propose an embarrassingly parallel, memory efficient inference algorithm for latent variable models in which the complete data likelihood is in the exponential family. The algorithm is a stochastic cellular automaton and converges to a valid maximum a posteriori fixed point. Applied
Variational inference in a truncated Dirichlet process
, 2003
"... The Ncomponent truncated Dirichlet process (DPN) is defined in Ishwaran and James [2001] and converges almost surely to a true Dirichlet process (DP∞). Like a full Dirichlet process, this distribution can be used as a nonparametric Bayesian prior in a mixture model. Ishwaran and James show that thi ..."
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prior. An exponential family mixture model with DPN prior on the natural parameter of the mixture component is illustrated in Figure 2. The random variables are distributed as follows: p(Vn  α) = Γ(1+α) Γ(α) (1 − Vi) α−1 for n ∈ [1, N − 1] p(VN = 1) = 1 p(ηn  λ) = h(ηn) exp{λ1ηn + λ2(−a(ηn)) − a
Bethe Projections for NonLocal Inference
"... Many inference problems in structured prediction are naturally solved by augmenting a tractable dependency structure with complex, nonlocal auxiliary objectives. This includes the mean field family of variational inference algorithms, soft or hardconstrained inference using Lagrangian relaxation ..."
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relaxation or linear programming, collective graphical models, and forms of semisupervised learning such as posterior regularization. We present a method to discriminatively learn broad families of inference objectives, capturing powerful nonlocal statistics of the latent variables, while maintaining
The Variational Bayesian EM Algorithm for Incomplete Data: with Application to . . .
, 2003
"... this paper we describe the use of variational methods to approximate the marginal likelihood and posterior distributions of complex models. Variational methods, which have been used extensively in Bayesian machine learning for several years, provide a lower bound on the marginal likelihood which can ..."
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Cited by 6 (0 self)
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(MAP) estimation. In section 3, we focus on models in the conjugateexponential family and derive the basic results. Section 4 introduces the speci c problem of learning the conditional independence structure of directed acyclic graphical models with latent variables. We compare variational methods
DOI: 10.1007/s0052600302104
, 2003
"... Abstract. We give a new proof of regularity of biharmonic maps from fourdimensional domains into spheres, showing first that the biharmonic map system is equivalent to a set of bilinear identities in divergence form. The method of reverse Hölder inequalities is used next to prove continuity of sol ..."
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Abstract. We give a new proof of regularity of biharmonic maps from fourdimensional domains into spheres, showing first that the biharmonic map system is equivalent to a set of bilinear identities in divergence form. The method of reverse Hölder inequalities is used next to prove continuity of solutions and higher integrability of their second order derivatives. As a byproduct, we also prove that a weak limit of biharmonic maps into a sphere is again biharmonic. The proof of regularity can be adapted to biharmonic maps on the Heisenberg group, and to other functionals leading to fourth order elliptic equations with critical nonlinearities in lower order derivatives. Mathematics Subject Classification (2000): 35J60, 35H20 1.
COSMOLOGICAL MODELS OF MODIFIED GRAVITY
, 2013
"... The recent discovery of dark energy has prompted an investigation of ways in which the accelerated expansion of the universe can be realized. In this dissertation, we present two separate projects related to dark energy. The first project analyzes a class of braneworld models in which multiple brane ..."
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The recent discovery of dark energy has prompted an investigation of ways in which the accelerated expansion of the universe can be realized. In this dissertation, we present two separate projects related to dark energy. The first project analyzes a class of braneworld models in which multiple
Disthbution IJnli~nited CONTRACT TITLE: THEORETICAL STUDIES OF HIGHPOWER ULTRAVIOLET AND INFRARED MATERIALS
, 1978
"... ~f d1400 Wilson Boulevard nc assi ie ..."
1Robust MEstimation for Heavy Tailed Nonlinear ARGARCH (with Supplemental Appendix C)
, 2011
"... We develop new tailtrimmed Mestimation methods for heavy tailed Nonlinear ARGARCH models. Tailtrimming allows both identi…cation of the true parameter and asymptotic normality for nonlinear models with asymmetric errors. In heavy tailed cases the rate of convergence is in…nitesimally close to th ..."
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of the covariance matrix that permits classic inference without knowledge of the rate of convergence, and explore asymptotic covariance and bootstrap meansquarederror methods for selecting trimming parameters. A simulation study shows the estimator trumps existing ones for AR and GARCH models based on sharpness
Results 1  10
of
97