22 papers · ranked by Valyu relevance
Authors not listed
Solving optimization problems, especially for nonlinear and constrained systems, is a challenge. Decades of specialized algorithms have been developed for general and special cases of root finding, minimization (including constraints), for parameter estimation, and mapping connected spaces. These approaches typically…
Jie You, Zhaoxuan Li, Junli Du, Praveen Kumar Donta
For d-dimensional random variable X with n samples, the probability distribution of a finite Gaussian mixture model can be expressed by a weighted sum of K components : P ( X | Θ ) = ∑ m = 1 K α m p m ( X | θ m ) , (1) where α*m is m-th mixing proportion, which must satisfy α**m > 0, m = 1, …, K and ∑ m = 1 K α m = 1.…
Rachel C W Chan, Maxwell W Libbrecht, Eric G Roberts, Jeffrey A Bilmes + 3 more
Segway learns Gaussian distributions over signal values to represent different patterns. Previously, Segway used a single-component Gaussian to model the signal in each dataset given some label such that there is one learned mean parameter for each track-label pair, and one fixed variance for a given track. To enable…
Abdelghafour Talibi, Boujemâa Achchab, Rafik Lasri
The mixture models have become widely used in clustering, given its probabilistic framework in which its based, however, for modern databases that are characterized by their large size, these models behave disappointingly in setting out the model, making essential the selection of relevant variables for this type of…
Andrea Rau, Cathy Maugis-Rabusseau
Although a large number of clustering algorithms have been proposed to identify groups of co-expressed genes from microarray data, the question of if and how such methods may be applied to RNA-seq data remains unaddressed. In this work, we investigate the use of data transformations in conjunction with Gaussian mixture…
Zachary R. McCaw, Hanna Julienne, Hugues Aschard
Although missing data are prevalent in genetic and genomics data sets, existing implementations of Gaussian mixture models (GMMs) require complete data. Standard practice is to perform complete case analysis or imputation prior to model fitting. Both approaches have serious drawbacks, potentially resulting in biased…
Jinkai Tian, Peifeng Yan, Da Huang
Kernels play a crucial role in Gaussian process regression. Analyzing kernels from their spectral domain has attracted extensive attention in recent years. Gaussian mixture models (GMM) are used to model the spectrum of kernels. However, the number of components in a GMM is fixed. Thus, this model suffers from…
Johannes Blömer, Kathrin Bujna
We present new initialization methods for the expectationmaximization algorithm for multivariate Gaussian mixture models. Our methods are adaptions of the well-known K-means++ initialization and the Gonzalez algorithm. Thereby we aim to close the gap between simple random, e.g. uniform, and complex methods, that…
Haley Colgate Kottler, Julia Lindberg, Jose Israel Rodriguez
Gaussian mixture models are universal approximators in the sense that any smooth density can be approximated arbitrarily well with a Gaussian mixture model with enough components. Due to their broad expressive power, Gaussian mixture models appear in many applications. As a result, algebraic parameter recovery for…
Siva Rajesh Kasa, Vaibhav Rajan
We study two practically important cases of model based clustering using Gaussian Mixture Models: (1) when there is misspecification and (2) on high dimensional data, in the light of recent advances in Gradient Descent (GD) based optimization using Automatic Differentiation (AD). Our simulation studies show that EM has…
Virgilio Gómez‐Rubio
Mixture models are a convenient way of modeling data using a convex combination of different parametric distributions. In this paper, we present a novel approach to fitting mixture models based on estimating first the posterior distribution of the auxiliary variables that assign each observation to a group in the…
Weiguo Lu, Xuan Wu, Deng Ding, Gangnan Yuan
We propose an Gaussian Mixture Model(GMM) learning algorithm, based on our previous work of GMM expansion idea. The new algorithm brings more robustness and simplicity than classic Expectation Maximization (EM) algorithm. It also improves the accuracy and only take 1 iteration for learning. We theoretically proof that…
Authors not listed
Inverse problems, where we seek the values of inputs to a model that lead to a desired set of outputs, are a challenges subset of problems in science and engineering. In this work we demonstrate the use of two generative AI methods to solve inverse problems. We compare this approach to two more conventional approaches…
Matthieu Marbac, Christophe Biernacki, Vincent Vandewalle
Clustering task of mixed data is a challenging problem. In a probabilistic framework, the main difficulty is due to a shortage of conventional distributions for such data. In this paper, we propose to achieve the mixed data clustering with a Gaussian copula mixture model, since copulas, and in particular the Gaussian…
Marko Jamšek, Tadej Petrič, Jan Babič
There was an error in the original article [1]. The variable used for the superscript in the denominator of the equation, denoting the dimensionality of the model, was incorrectly written as K and thus conflicted with the variable denoting the number of Gaussian mixtures. A correction has therefore been made to Section…
Sami Bourouis, Yogesh Pawar, Nizar Bouguila, Gemine Vivone
Finite Gamma mixture models have proved to be flexible and can take prior information into account to improve generalization capability, which make them interesting for several machine learning and data mining applications. In this study, an efficient Gamma mixture model-based approach for proportional vector…
Kazem Nasserinejad, Joost van Rosmalen, Wim de Kort, Emmanuel Lesaffre + 1 more
'Emmanuel Lesaffre' 'Ulrich S Tran'] Identifying the number of classes in Bayesian finite mixture models is a challenging problem. Several criteria have been proposed, such as adaptations of the deviance information criterion, marginal likelihoods, Bayes factors, and reversible jump MCMC techniques. It was recently…
Faïcel Chamroukhi
Regression mixture models are widely studied in statistics, machine learning and data analysis. Fitting regression mixtures is challenging and is usually performed by maximum likelihood by using the expectation-maximization (EM) algorithm. However, it is well-known that the initialization is crucial for EM. If the…
Elio Nushi, François P. Douillard, Katja Selby, Miia Lindström + 1 more
In this study, we introduce a Bayesian model-based method for clustering transcriptomics time series data with multiple replicates. This technique is based on sampling Gaussian processes (GPs) within an infinite mixture model from a Dirichlet process (DP). Our method uses multiple GP models to accommodate for multiple…
Michael Minyi Zhang, Sinead A. Williamson
Training Gaussian process-based models typically involves an O(N3 ) computational bottleneck due to inverting the covariance matrix. Popular methods for overcoming this matrix inversion problem cannot adequately model all types of latent functions, and are often not parallelizable. However, judicious choice of model…
Zoubin Ghahramani
Modelling is fundamental to many fields of science and engineering. A model can be thought of as a representation of possible data one could predict from a system. The probabilistic approach to modelling uses probability theory to express all aspects of uncertainty in the model. The probabilistic approach is synonymous…
Aryan Deshwal, Cory Simon, Janardhan Rao Doppa
Given a gas storage or separation task, we wish to search a library of nanoporous materials (NPMs) for the one with the optimal adsorption property. The high cost of measuring the adsorption property of an NPM, whether in the lab or a simulation, precludes exhaustive search. We explain, demonstrate, and advocate…