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Generic Inference in Latent Gaussian Process Models [article]

Edwin V. Bonilla and Karl Krauth and Amir Dezfouli
2018 arXiv   pre-print
We develop an automated variational method for inference in models with Gaussian process (GP) priors and general likelihoods.  ...  Using a mixture of Gaussians as the variational distribution, we show that the evidence lower bound and its gradients can be estimated efficiently using samples from univariate Gaussian distributions.  ...  South Wales (unsw sydney) and was partially supported by unsw's Faculty of Engineering Research Grant Program project # PS37866; unsw's Academic Start-Up Funding Scheme project # PS41327; and an aws in  ... 
arXiv:1609.00577v2 fatcat:ngpjezdvv5egheozyzc2pr3qya

Warped Mixtures for Nonparametric Cluster Shapes [article]

Tomoharu Iwata, David Duvenaud, Zoubin Ghahramani
2014 arXiv   pre-print
To produce more appropriate clusterings, we introduce a model which warps a latent mixture of Gaussians to produce nonparametric cluster shapes.  ...  We derive a simple inference scheme for this model which analytically integrates out both the mixture parameters and the warping function.  ...  In addition, the iWMM assumes that the latent coordinates are generated from a Dirichlet process mixture model.  ... 
arXiv:1408.2061v1 fatcat:b5svigdi3jhxjdq7zcgpc6ehs4

The Variational Gaussian Process [article]

Dustin Tran, Rajesh Ranganath, David M. Blei
2016 arXiv   pre-print
The VGP achieves new state-of-the-art results for unsupervised learning, inferring models such as the deep latent Gaussian model and the recently proposed DRAW.  ...  Variational inference is a powerful tool for approximate inference, and it has been recently applied for representation learning with deep generative models.  ...  A SPECIAL CASES OF THE VARIATIONAL GAUSSIAN PROCESS We now analyze two special cases of the VGP: by limiting its generative process in various ways, we recover well-known models.  ... 
arXiv:1511.06499v4 fatcat:rxtue3ahoveytj5im3ubye5vyu

Warped Mixtures for Nonparametric Cluster Shapes [article]

Tomoharu Iwata, David Duvenaud, Zoubin Ghahramani
2013 arXiv   pre-print
To produce more appropriate clusterings, we introduce a model which warps a latent mixture of Gaussians to produce nonparametric cluster shapes.  ...  We derive a simple inference scheme for this model which analytically integrates out both the mixture parameters and the warping function.  ...  In addition, the iWMM assumes that the latent coordinates are generated from a Dirichlet process mixture model.  ... 
arXiv:1206.1846v2 fatcat:vgq276gmuzhnjmc55ofbnrko2i

Variational Latent Gaussian Process for Recovering Single-Trial Dynamics from Population Spike Trains

Yuan Zhao, Il Memming Park
2017 Neural Computation  
Here, we propose a practical and efficient inference method, called the variational latent Gaussian process (vLGP).  ...  The vLGP combines a generative model with a history-dependent point process observation together with a smoothness prior on the latent trajectories.  ...  Therefore, we propose to relax this modeling assumption and impose a general Gaussian process prior to nonparametrically infer the latent dynamics, similar to the Gaussian process factor analysis (GPFA  ... 
doi:10.1162/neco_a_00953 pmid:28333587 fatcat:ac4cktpxxzdnni4p57wapmjewq

Point process latent variable models of larval zebrafish behavior

Anuj Sharma, Robert Johnson, Florian Engert, Scott W. Linderman
2018 Neural Information Processing Systems  
We incorporate these variables as latent marks of a point process and explore various models for their dynamics.  ...  To infer the latent variables and fit the parameters of this model, we develop an amortized variational inference algorithm that targets the collapsed posterior distribution, analytically marginalizing  ...  The class of Gaussian process-modulated point processes are well-studied in statistics and machine learning more generally.  ... 
dblp:conf/nips/SharmaJEL18 fatcat:wjkyzukogze6fg5h6l36ztdyoa

Joint Distribution across Representation Space for Out-of-Distribution Detection [article]

JingWei Xu, Siyuan Zhu, Zenan Li, Chang Xu
2021 arXiv   pre-print
Specifically, We construct a generative model, called Latent Sequential Gaussian Mixture (LSGM), to depict how the in-distribution latent features are generated in terms of the trace of DNN inference across  ...  We first construct the Gaussian Mixture Model (GMM) based on in-distribution latent features for each hidden layer, and then connect GMMs via the transition probabilities of the inference traces.  ...  Conclusions In this paper, we propose a generative probabilistic graphical model across representation spaces, Latent Sequential Gaussian Mixture, to depict the process of DNN inference.  ... 
arXiv:2103.12344v2 fatcat:hii5ttcw65e3nmjdurhazmaswq

Automated Variational Inference for Gaussian Process Models

Trung V. Nguyen, Edwin V. Bonilla
2014 Neural Information Processing Systems  
We develop an automated variational method for approximate inference in Gaussian process (GP) models whose posteriors are often intractable.  ...  Our method can be a valuable tool for practitioners and researchers to investigate new models with minimal effort in deriving model-specific inference algorithms.  ...  Discussion We have developed automated variational inference for Gaussian process models (AGP).  ... 
dblp:conf/nips/NguyenB14 fatcat:apfqukc2l5gjta4jfeptvrpzsu

The Gaussian Process Density Sampler

Ryan Prescott Adams, Iain Murray, David J. C. MacKay
2008 Neural Information Processing Systems  
We present the Gaussian Process Density Sampler (GPDS), an exchangeable generative model for use in nonparametric Bayesian density estimation.  ...  We can also infer the hyperparameters of the Gaussian process. We compare this density modeling technique to several existing techniques on a toy problem and a skullreconstruction task.  ...  Introduction We present the Gaussian Process Density Sampler (GPDS), a generative model for probability density functions, based on a Gaussian process.  ... 
dblp:conf/nips/AdamsMM08 fatcat:kdfjeallbbdlnahefcuyxyhd5e

Temporal alignment and latent Gaussian process factor inference in population spike trains [article]

Lea Duncker, Maneesh Sahani
2018 bioRxiv   pre-print
Our approach is based on shared latent Gaussian processes (GPs) which are combined linearly, as in the Gaussian Process Factor Analysis (GPFA) algorithm.  ...  We extend GPFA to handle unbinned spike-train data by incorporating a continuous time point-process likelihood model, achieving scalability with a sparse variational approximation.  ...  Temporal alignment and latent factor inference using Gaussian processes The svGPFA model we have developed in section 3 aims to extract different latent trajectories on each trial.  ... 
doi:10.1101/331751 fatcat:nxaijfww7fbpfakfijytgkaxo4

Structured Bayesian Gaussian process latent variable model [article]

Steven Atkinson, Nicholas Zabaras
2018 arXiv   pre-print
We introduce a Bayesian Gaussian process latent variable model that explicitly captures spatial correlations in data using a parameterized spatial kernel and leveraging structure-exploiting algebra on  ...  Modeling high-dimensional time series systems is enabled through use of a dynamical GP latent variable prior.  ...  Bayesian generative models such as the Gaussian process latent variable model [2, 3, 1] and the related unsupervised deep Gaussian processes [4, 5] leverage the expressive, yet regularized flexibility  ... 
arXiv:1805.08665v1 fatcat:fftbpnsavrdsdfzblpnplclkcu

Kernel Topic Models [article]

Philipp Hennig, David Stern, Ralf Herbrich, Thore Graepel
2011 arXiv   pre-print
The KTM can also be interpreted as a type of Gaussian process latent variable model, or as a topic model conditional on document features, uncovering links between earlier work in these areas.  ...  The main challenge is efficient approximate inference on the latent Gaussian. We present an approximate algorithm cast around a Laplace approximation in a transformed basis.  ...  GPLVMs learn mappings from data-space to a lower-dimensional space, assuming the generative model for the data in the latent space is a Gaussian process.  ... 
arXiv:1110.4713v1 fatcat:klwrebjkqvakxo6n24d7iccudi

Semi-supervised Gaussian process latent variable model with pairwise constraints

Xiumei Wang, Xinbo Gao, Yuan Yuan, Dacheng Tao, Jie Li
2010 Neurocomputing  
+ Informative Vector Machine [Lawrence 2004] • Introduction to Gaussian Processes Interlude • Gaussian Process Latent Variable ModelsGaussian Process Dynamical Models Observation model: GPLVM for the  ...  Variable ModelsGaussian Process Dynamical Models -Application to motion capture data [Lawrence, 2004; 2005] 16 Gaussian Process Latent Variable Models Observations (output): Latent variables  ... 
doi:10.1016/j.neucom.2010.01.021 fatcat:p7aelt5rtjeqfdfddy7sygcase

Scalable Inference for Gaussian Process Models with Black-Box Likelihoods

Amir Dezfouli, Edwin V. Bonilla
2015 Neural Information Processing Systems  
We propose a sparse method for scalable automated variational inference (AVI) in a large class of models with Gaussian process (GP) priors, multiple latent functions, multiple outputs and non-linear likelihoods  ...  Gaussians.  ...  Acknowledgments This work has been partially supported by UNSW's Faculty of Engineering Research Grant Program project # PS37866 and an AWS in Education Research Grant award.  ... 
dblp:conf/nips/DezfouliB15 fatcat:fhx5627irzdm7imeppau36lcry

Latent Gaussian Processes for Distribution Estimation of Multivariate Categorical Data [article]

Yarin Gal, Yutian Chen, Zoubin Ghahramani
2015 arXiv   pre-print
Our model ties together many existing models, linking the linear categorical latent Gaussian model, the Gaussian process latent variable model, and Gaussian process classification.  ...  We derive inference for our model based on recent developments in sampling based variational inference.  ...  Gaussian process latent variable model (top to bottom, Lawrence (2005) ).  ... 
arXiv:1503.02182v1 fatcat:yu4k5o5tujbu5lacf6wb5kx6cq
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