Monotonicity of quadratic-approximation algorithms

Böhning, Dankmar; Lindsay, Bruce G.

doi:10.1007/bf00049423

Cited by 151 publications

(156 citation statements)

References 11 publications

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“…Similar to the bounding approach of the EM algorithm, the results in Bohning and Lindsay (1988) show that finding θ 1 that maximizes the right hand side of eq. (11) implies that l(θ 1 ) ≥ l(θ 0 ) with equality only at θ 1 = θ 0 .…”

Section: The Gem Algorithmmentioning

confidence: 91%

“…The method is based off of an important result in Bohning and Lindsay (1988) which says that for a twice differentiable, concave function l(θ), if there exists a symmetric, negative definite matrix B such that B ≤ 2 l(θ 0 ) for all values of θ 0 , then for any value θ, the following is true.…”

Section: The Gem Algorithmmentioning

confidence: 99%

“…(12) is difficult to maximize, the estimator will instead use the results of Bohning and Lindsay (1988) and bound the complicated function with a simpler function. Letting…”

Section: Repeating This Process the Parameters Converge Monotonicallmentioning

confidence: 99%

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A Tractable Estimator for General Mixed Multinomial Logit Models

James¹

2012

Working Paper (Federal Reserve Bank of Cleveland)

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The mixed logit is a framework for incorporating unobserved heterogeneity in discrete choice models in a general way. These models are diffi cult to estimate because they result in a complicated incomplete data likelihood. This paper proposes a new approach for estimating mixed logit models. The estimator is easily implemented as iteratively re-weighted least squares: the well known solution for complete data likelihood logits. The main benefi t of this approach is that it requires drastically fewer evaluations of the simulated likelihood function, making it signicantly faster than conventional methods that rely on numerically approximating the gradient. The method is rooted in a generalized expectation and maximization (GEM) algorithm, so it is asymptotically consistent, effi cient, and globally convergent.

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Section: The Gem Algorithmmentioning

confidence: 91%

Section: The Gem Algorithmmentioning

confidence: 99%

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A Tractable Estimator for General Mixed Multinomial Logit Models

James¹

2012

Working Paper (Federal Reserve Bank of Cleveland)

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“…Then, by majorizing the surrogate -finding its current maximum value -it can be shown that stepping to this value results in an increase in the value of the original objective function. A viable surrogate function for the log-likelihood function for dichotomous data was given in [28] and was extended to the multinomial situation in [6]. Iteration then results in convergence to the unique maximum.…”

Section: Methods and Theorymentioning

confidence: 99%

Automatic covariate selection in logistic models for chest pain diagnosis: A new approach

Harrison

Kennedy

2008

Computer Methods and Programs in Biomedicine

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A newly established method for optimizing logistic models via a minorizationmajorization procedure is applied to the problem of diagnosing acute coronary syndromes (ACS). The method provides a principled approach to the selection of covariates which would otherwise require the use of a suboptimal method owing to the size of the covariate set. A strategy for building models is proposed and two models optimized for performance and for simplicity are derived via ten-fold crossvalidation. These models confirm that a relatively small set of covariates including clinical and electrocardiographic features can be used successfully in this task.The performance of the models is comparable with previously published models using less principled selection methods. The models prove to be portable when tested on data gathered from three other sites. Whilst diagnostic accuracy and calibration diminishes slightly for these new settings, it remains satisfactory overall.The prospect of building predictive models that are as simple as possible for a required level of performance is valuable if data-driven decision aids are to gain wide acceptance in the clinical situation owing to the need to minimize the time taken to gather and enter data at the bedside.

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“…an additive or multiplicative way may be useful, at least for exact Hessian matrices and their regularization. Note also that numerical approximations of the Hessian matrix exist in the literature, and from [49] a justification of the approach can be derived.…”

Section: Derivatives Of the Objective Functionmentioning

confidence: 99%

Generalized topographic block model

Priam

Nadif²,

Govaert

2016

Neurocomputing

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Co-clustering leads to parsimony in data visualisation with a number of parameters dramatically reduced in comparison to the dimensions of the data sample. Herein, we propose a new generalized approach for nonlinear mapping by a re-parameterization of the latent block mixture model. The densities modeling the blocks are in an exponential family such that the Gaussian, Bernoulli and Poisson laws are particular cases. The inference of the parameters is derived from the block expectation-maximization algorithm with a Newton-Raphson procedure at the maximization step. Empirical experiments with textual data validate the interest of our generalized model.The authors have very carefully revised the document by following every comments from the editors and the two anonymous reviewers. It has been tried every possible effort to solve each remark that has been addressed. Below a detailed summary of the updates is provided. We would like to thank the editors and the reviewers for their constructive comments on this manuscript and positive support.To Editors:Once more, we would very much like to invite you to revise your paper, seriously taking into account the comments of the reviewers, and to resubmit your revised version by 02/25/2015 (mm/dd/yy). Any revision received after that may be treated as a new submission. Authors' response:The paper has been revised according to the comments and suggestions of reviewer 2.2) To Reviewer #1:The revised manuscript is sufficient to Neurocomputing publication standards, and I suggest accepting this manuscript. Authors' response:Thanks for the positive comments and the opportunity of publishing the document in Neurocomputing.3) To Reviewer #2: Q1. I thank the authors for the revised version of their manuscript. Authors' response:Thanks for the positive comments.Q2. They open the abstract with the statement: "Parametric methods for data visualisation are most of the time founded on an usual mixture model framework." Even a light-hearted revision of existing parametric methods for multivariate data visualization (See, for instance, Lee & Verleysen, 2007) would reveal that this is not the case. Therefore, I think this statement should be either removed or revised. Authors' response:Thanks for this suggestion. Indeed, the term « parametric methods » was meaning « probabilistic methods » or « parametric model » in a statistical framework and could have been read as any methods with parameters on the contrary to svd for instance. This sentence has been removed, and the summary updated for complying with other comments in the review.Q3. Co(Bi)-clustering in general and co(bi)-clustering with visualization-oriented self-organizing models are more adequately introduced in the new version. Authors' response:Thanks for this remark.Q4. I am a bit puzzled by the new introduction "storyline", though. It roughly goes like this:Revision Notes a) -Co-clustering was first proposed in the seventies and some more works [6][7][8][9][10][11] Authors' response:Thanks for this concern. Indeed, af...

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Monotonicity of quadratic-approximation algorithms

Abstract: Maximum likelihood estimation, curvature, monotonicity, algorithms, Newton-Raphson algorithm,

Cited by 151 publications

References 11 publications

A Tractable Estimator for General Mixed Multinomial Logit Models

A Tractable Estimator for General Mixed Multinomial Logit Models

Automatic covariate selection in logistic models for chest pain diagnosis: A new approach

Generalized topographic block model

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