“mixture models” papers · AI for Research

Finite mixture models: McLachlan/finite mixture models

McLachlan, Geoffrey, Peel, David · Queensland's institutional digital repository (The University of Queensland) · 2000

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Mixture Models

Steve Pressé, Ioannis Sgouralis · Cambridge University Press eBooks · 2023

In this chapter we introduce the clustering problem and use it to motivate mixture models. We start by describing clustering in a frequentist paradigm and introduce the relevant likelihoods and latent variables. We then discuss properties of the likelihoods including invariance with respect to label swapping. Finally, we expand this discussion to describe clustering and mixture models more generally within a Bayesian paradigm. This allows us to introduce Dirichlet priors used in inferring the weight we ascribe to each cluster component from which the data are drawn. Finally, we describe the infinite mixture model and Dirichlet process priors within the Bayesian nonparametric paradigm, appropriate for the analysis of uncharacterized data that may contain an unspecified number of clusters.

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Mixture models

Biernacki, Christophe · HAL (Le Centre pour la Communication Scientifique Directe) · 2017

International audience

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Mixture models.

Nedialko I. Krouchev (535037), Frank Rattay (127304), Mohamad Sawan (535039) et al. · Figshare · 2015

A: Red trace: Existence/creation P parameter-range for the 2 additional fixed points (saddle-node in the middle branch, and unstable center/focus in the top branch of the B.D.’s) With ΔV1/2 = 13 mV, P ≥ 0.648, which is very close to the minimum relative Na/K conductivity ratio (0.663) needed for 3 FP’s in the single-Nav-subtype model with ΔV1/2 = 0 mV. In the voltage range of peak M3 current, the contribution from the Nav1.2 channels is low and does not change much the total current profile. Hence, the upper branch of FP’s is due the contribution of the Nav1.6 channels. B: Resting threshold of the mixed models as a function of the P parameter. The figure shows κ(P) = ITHR(P, ΔV1/2)/ITHR(1,ΔV1/2) of the mixed model for TSTIM = 100 μs. Notice that there is an approximately twofold difference between the thresholds of the M3 and M1 single-Nav-subtype models More than 60% of this difference vanishes for P as low as 0.1. The difference becomes minimal for ΔV1/2 < 4 mV (see also Panel C) or P ≥ 0.1. C: As the ΔV1/2 parameter is decreased (from 13 mV down to 0), the M1 contribution becomes larger, thereby reducing the proportion of M3 current needed for 3FP-dynamics. Notice that the proportion of Nav1.6 channels may decrease significantly when ΔV1/2 < 4 mV. Importantly, this is also about where the transition from M1 to M3 occurs (ΔV1/2 = LP1 ≈ -2.94 mV.

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Mixture models

Kevin P. Murphy · 2006

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Mixture models

Biernacki, C. (Christophe) · LillOA (Université de Lille (University Of Lille)) · 2017

Finite mixture models are one of the probabilistic frameworks which reach an especially diverse community of people, including statisticians and practitioners (scientific or not). Initial reasons for being confronted with mixtures may be different for impacted communities but lead finally to close interconnections between them. Indeed, applied statisticians and practitioners usually discover finite mixture models from the numerous application fields where they meet numerous successes. It typically gathers {none,un,semi-} supervised classification and density estimation. The keys of these successes are both their high meaningfulness and flexibility. However, flexibility is in return a matter of algorithmic and mathematical questionings for methodological and theoretical statisticians. In particular, it addresses estimation and model selection issues, on both computational and mathematical aspects. But, solutions to be provided to these issues highly beneficiate to depend on initial related application fields.

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Mixture Models

C. R. Rosario E, Z. García E, S. D. Smith B et al. · 1998

www.elsevier.com/locate/vetpar Spatial distribution of acaricide profiles (Boophilus microplus strains susceptible or resistant to acaricides) in southeastern Mexico R.I. Rodríguez-Vivas a, A.L. Rivas a,b, *, G. Chowell c, S.H. Fragoso d,

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Mixture Models

Gabriela Zdilar · Repository of Faculty of Science · 2024

Modeli miješanih distribucija dobro su poznat pojam u statistici u kojoj su se kroz povijest koristili za modeliranje heterogenosti populacije i generalizaciju pretpostavki distribucije. U novije vrijeme, ovi modeli također pružaju pogodan i formalan okvir za grupiranje i klasifikaciju, što su pojmovi usko vezani uz strojno učenje. Glavni cilj ovog rada je pregled modela miješanih distribucija, s posebnim naglaskom na Gaussov i Bernoullijev model miješanih distribucija. Čitatelj će biti detaljno upoznat s EM-algoritmom koji je ključan za procjenu parametara modela miješanih distribucija, a primijenit ćemo ga na spomenute Gaussove i Bernoullijeve modele te dati njegov općeniti oblik. Naposlijetku, EM-algoritam ćemo implementirati u RStudiju na raznim primjerima te analizirati dobivene rezultate.

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Mixture models

Gary Koop, Dale J. Poirier, Justin L. Tobias · Cambridge University Press eBooks · 2007

The reader has undoubtedly noted that the majority of exercises in previous chapters have included normality assumptions. These assumptions should not be taken as necessarily “correct,” and indeed, such assumptions will not be appropriate in all situations (see, e.g., Exercise 11.13 for a question related to error-term diagnostic checking). In this chapter, we review a variety of computational strategies for extending analyses beyond the textbook normality assumption. The strategies we describe, perhaps ironically, begin with the normal model and proceed to augment it in some way. In the first section, we describe scale mixtures of normals models, which enable the researcher to generalize error distributions to the Student t and double exponential classes (among others). Exercises 15.5 and 15.6 then describe finite normal mixture models, which can accommodate, among other features, skewness and multimodality in error distributions. Importantly, these models are conditionally normal (given values of certain mixing or component indicator variables), and thus standard computational techniques for the normal linear regression model can be directly applied (see, e.g., Exercises 10.1 and 11.8). The techniques described here are thus computationally tractable, flexible, and generalizable. That is, the basic methods provided in this chapter can often be adapted in a straightforward manner to add flexibility to many of the models introduced in previous and future exercises. Some exercises related to mixture models beyond those involving conditional normal sampling distributions are also provided within this chapter.

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Mixture models

David Barber · Cambridge University Press eBooks · 2012

Machine learning methods extract value from vast data sets quickly and with modest resources. They are established tools in a wide range of industrial applications, including search engines, DNA sequencing, stock market analysis, and robot locomotion, and their use is spreading rapidly. People who know the methods have their choice of rewarding jobs. This hands-on text opens these opportunities to computer science students with modest mathematical backgrounds. It is designed for final-year undergraduates and master's students with limited background in linear algebra and calculus. Comprehensive and coherent, it develops everything from basic reasoning to advanced techniques within the framework of graphical models. Students learn more than a menu of techniques, they develop analytical and problem-solving skills that equip them for the real world. Numerous examples and exercises, both computer based and theoretical, are included in every chapter. Resources for students and instructors, including a MATLAB toolbox, are available online.

Cited by 1

Mixture Models

Foreman-Mackey, Daniel · Zenodo (CERN European Organization for Nuclear Research) · 2014

A post from my blog: http://dan.iel.fm/posts/mixture-models/ Source: https://github.com/dfm/dfm.io/blob/b6c2f375c1c320b1dfd72e2f487a687fd0e15356/content/downloads/notebooks/mixture-models.ipynb

Cited by 0Open access

Mixture Models

Mehdi Razzaghi, Geoffrey J. McLachan, Kaye E. Basford · Technometrics · 1991

Cited by 2

Mixture Models

SpringerReference · 2012

Cited by 0

Mixture Models

Encyclopedia of Measurement and Statistics · 2007

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Mixture Models

Steffen Fieuws, Bart Spiessens, Karen Draney · 2004

Cited by 9

Mixture models

Biernacki, C. (Christophe) · LillOA (Université de Lille (University Of Lille)) · 2017

Finite mixture models are one of the probabilistic frameworks which reach an especially diverse community of people, including statisticians and practitioners (scientific or not). Initial reasons for being confronted with mixtures may be different for impacted communities but lead finally to close interconnections between them. Indeed, applied statisticians and practitioners usually discover finite mixture models from the numerous application fields where they meet numerous successes. It typically gathers {none,un,semi-} supervised classification and density estimation. The keys of these successes are both their high meaningfulness and flexibility. However, flexibility is in return a matter of algorithmic and mathematical questionings for methodological and theoretical statisticians. In particular, it addresses estimation and model selection issues, on both computational and mathematical aspects. But, solutions to be provided to these issues highly beneficiate to depend on initial related application fields.

Cited by 0Open access

Mixture models

Vermunt, J.K., Paas, L.J., Leeflang, P.S.H. et al. · Data Archiving and Networked Services (DANS) · 2017

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Mixture Models

Bruce G. Lindsay · NSF-CBMS regional conference series in probability and statistics · 1995

Cited by 1,085

Mixture Models

Bruce G. Lindsay, Michael Stewart · The New Palgrave Dictionary of Economics · 2008

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Mixture Models

Bruce G. Lindsay, Michael Stewart · The New Palgrave Dictionary of Economics · 2018

This article discusses statistical models involving mixture distributions. As well as being useful in identifying and describing sub-populations within a mixed population, mixture models are useful data-analytic tools, providing flexible families of distributions to fit to unusually shaped data. Theoretical advances since the mid-1970s, as well as advances in computing technology, have led to the widespread use of mixture models in ecology, machine learning, genetics, medical research, psychology, reliability and survival analysis. In particular, recent advances in non-linear time series involving mixtures have helped explain various features of financial and econometric data that more traditional models cannot capture.

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