Robust mixture modelling using the t distribution

By David Peel, Geoffrey J. McLachlan. Statistics and computing, 2000

999 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/99ad63b1c7a70e2022ed0f82671ed1e3e8ef2772

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Citations in the corpus

Estimation Methods for the Multivariate t Distribution (2008, methodology): “McLachlan and Peel [39], McLachlan et al. [40], and Peel and McLachlan [44] used a mixture model of t distributions for a robust method of mixture estimation of clustering .”
The student-t mixture as a natural image patch prior with application to image compression (2014, methodology): “…800k 900k 1M Number of training samples 150 151 152 153 154 155 Log-likelihood gmm stm (b) Figure 3: We also train the STM with the EM algorithm (Peel and McLachlan, 2000; Dempster et al., 1977): E-step: γ nk = π k T (x n |ν k , µ k , Σ k ) K j=1 π j T (x n |ν j , µ j , Σ j ) , w nk = ν k +p ν…”
Model-Based Clustering (2016, background): “McLachlan and Peel (1998) and Peel and McLachlan (2000) motivate the t-distribution as a heavy-tailed alternative to the Gaussian distribution.”
Multiple Edit/Multiple Imputation for Multivariate Continuous Data (2003, background): “Under these assumptions, the marginal distribution of yi is a high-dimensional mixture of normals with 2p components (Titterington, Smith, and Makov 1985; Peel and McLachlan 2000).”
Adaptive importance sampling in general mixture classes (2007, methodology): “In the sequel, we refer to the criterion in (2) as the entropy criterion since it is obviously related to the performance measure used in the cross-entropy method of Rubinstein and Kroese (2004). In Douc et al.”
Nearest-Neighbor Variance Estimation (NNVE) (2002, background): “McLachlan and Peel (1998) and Peel and McLachlan (2000) suggested using mixtures of t components as an alternative, because the t components are less sensitive to outliers, having longer tails than the normal.”
Adaptive sequential Monte Carlo by means of mixture of experts (2011, background): “A similar choice has been made by, among others, Peel and McLachlan (2000, Sect.”
A General Method for Robust Bayesian Modeling (2015, methodology): “For example, this is the motivation for replacing a Gaussian with a student’s t in robust linear regression (Lange et al., 1989; Fernández and Steel, 1999; Gelman et al., 2003) and robust mixture modeling (Peel and McLachlan, 2000; Svensén and Bishop, 2005).”
Adaptive Multiple Importance Sampling (2009, methodology): “Note that the extension to a mixture of t densities is equally feasible since there exists a corresponding EM algorithm (Peel & McLachlan, 2000).”
Robust estimation in the normal mixture model based on robust clustering (2008, background): “For the analysis involving the mixture of t-distributions method we carry out the computations with the EMMIX algorithm of McLachlan, Peel, Basford and Adams, using the k-means as an initial solution, but also starting from 100 initial randomly chosen solutions, choosing from the results the one tha”
On strong identifiability and convergence rates of parameter estimation in finite mixtures (2016, background): “Then, for a fixed compact subset G of Ek0(Θ × Ω), there is a positive constant C0 = C0(G0) such that V (pG, pG0) ≥ C0W1(G,G0) for all G ∈ G.”