Graph structured data are abundant in the real world. Among different graph types, directed acyclic graphs (DAGs) are of particular interest to machine learning researchers, as many machine learning models are realized as computations on DAGs, including neural networks and Bayesian networks. In this paper, we study deep generative models for DAGs, and propose a novel DAG variational autoencoder (D-VAE). To encode DAGs into the latent space, we leverage graph neural networks. We propose an asynchronous message passing scheme that allows encoding the computations on DAGs, rather than using existing simultaneous message passing schemes to encode local graph structures. We demonstrate the effectiveness of our proposed DVAE through two tasks: neural architecture search and Bayesian network structure learning. Experiments show that our model not only generates novel and valid DAGs, but also produces a smooth latent space that facilitates searching for DAGs with better performance through Bayesian optimization.
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Bayesian Functional Principal Components Analysis via Variational Message Passing with Multilevel Extensions
Standard approaches for functional principal components analysis rely on an eigendecomposition of a smoothed covariance surface in order to extract the orthonormal eigenfunctions representing the major modes of variation in a set of functional data. This approach can be a computationally intensive procedure, especially in the presence of large datasets with irregular observations. In this article, we develop a variational Bayesian approach, which aims to determine the Karhunen-Loève decomposition directly without smoothing and estimating a covariance surface. More specifically, we incorporate the notion of variational message passing over a factor graph because it removes the need for rederiving approximate posterior density functions if there is a change in the model. Instead, model changes are handled by changing specific computational units, known as fragments, within the factor graph – we demonstrate this with an extension to multilevel functional data. Indeed, this is the first article to address a functional data model via variational message passing. Our approach introduces three new fragments that are necessary for Bayesian functional principal components analysis. We present the computational details, a set of simulations for assessing the accuracy and speed of the variational message passing algorithm and an application to United States temperature data.
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- Award ID(s):
- 1814840
- NSF-PAR ID:
- 10470131
- Publisher / Repository:
- Project Euclid
- Date Published:
- Journal Name:
- Bayesian Analysis
- Volume:
- -1
- Issue:
- -1
- ISSN:
- 1936-0975
- Subject(s) / Keyword(s):
- ["functional principal component scores","Kullback-Leibler divergence","Mean field","Nonparametric regression"]
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Estimation of an unstructured covariance matrix is difficult because of the challenges posed by parameter space dimensionality and the positive‐definiteness constraint that estimates should satisfy. We consider a general nonparametric covariance estimation framework for longitudinal data using the Cholesky decomposition of a positive‐definite matrix. The covariance matrix of time‐ordered measurements is diagonalized by a lower triangular matrix with unconstrained entries that are statistically interpretable as parameters for a varying coefficient autoregressive model. Using this dual interpretation of the Cholesky decomposition and allowing for irregular sampling time points, we treat covariance estimation as bivariate smoothing and cast it in a regularization framework for desired forms of simplicity in covariance models. Viewing stationarity as a form of simplicity or parsimony in covariance, we model the varying coefficient function with components depending on time lag and its orthogonal direction separately and penalize the components that capture the nonstationarity in the fitted function. We demonstrate construction of a covariance estimator using the smoothing spline framework. Simulation studies establish the advantage of our approach over alternative estimators proposed in the longitudinal data setting. We analyze a longitudinal dataset to illustrate application of the methodology and compare our estimates to those resulting from alternative models.
This article is categorized under:
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Algorithms and Computational Methods > Maximum Likelihood Methods
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Table of Contents: Foreword by the CI 2016 Workshop Chairs …………………………………vi Foreword by the CI 2016 Steering Committee ..…………………………..…..viii List of Organizing Committee ………………………….……....x List of Registered Participants .………………………….……..xi Acknowledgement of Sponsors ……………………………..…xiv Hackathon and Workshop Agenda .………………………………..xv Hackathon Summary .………………………….…..xviii Invited talks - abstracts and links to presentations ………………………………..xxi Proceedings: 34 short research papers ……………………………….. 1-135 Papers 1. BAYESIAN MODELS FOR CLIMATE RECONSTRUCTION FROM POLLEN RECORDS ..................................... 1 Lasse Holmström, Liisa Ilvonen, Heikki Seppä, Siim Veski 2. ON INFORMATION CRITERIA FOR DYNAMIC SPATIO-TEMPORAL CLUSTERING ..................................... 5 Ethan D. Schaeffer, Jeremy M. Testa, Yulia R. Gel, Vyacheslav Lyubchich 3. DETECTING MULTIVARIATE BIOSPHERE EXTREMES ..................................... 9 Yanira Guanche García, Erik Rodner, Milan Flach, Sebastian Sippel, Miguel Mahecha, Joachim Denzler 4. SPATIO-TEMPORAL GENERATIVE MODELS FOR RAINFALL OVER INDIA ..................................... 13 Adway Mitra 5. A NONPARAMETRIC COPULA BASED BIAS CORRECTION METHOD FOR STATISTICAL DOWNSCALING ..................................... 17 Yi Li, Adam Ding, Jennifer Dy 6. DETECTING AND PREDICTING BEAUTIFUL SUNSETS USING SOCIAL MEDIA DATA ..................................... 21 Emma Pierson 7. OCEANTEA: EXPLORING OCEAN-DERIVED CLIMATE DATA USING MICROSERVICES ..................................... 25 Arne N. Johanson, Sascha Flögel, Wolf-Christian Dullo, Wilhelm Hasselbring 8. IMPROVED ANALYSIS OF EARTH SYSTEM MODELS AND OBSERVATIONS USING SIMPLE CLIMATE MODELS ..................................... 29 Balu Nadiga, Nathan Urban 9. SYNERGY AND ANALOGY BETWEEN 15 YEARS OF MICROWAVE SST AND ALONG-TRACK SSH ..................................... 33 Pierre Tandeo, Aitor Atencia, Cristina Gonzalez-Haro 10. PREDICTING EXECUTION TIME OF CLIMATE-DRIVEN ECOLOGICAL FORECASTING MODELS ..................................... 37 Scott Farley and John W. Williams 11. SPATIOTEMPORAL ANALYSIS OF SEASONAL PRECIPITATION OVER US USING CO-CLUSTERING ..................................... 41 Mohammad Gorji–Sefidmazgi, Clayton T. Morrison 12. PREDICTION OF EXTREME RAINFALL USING HYBRID CONVOLUTIONAL-LONG SHORT TERM MEMORY NETWORKS ..................................... 45 Sulagna Gope, Sudeshna Sarkar, Pabitra Mitra 13. SPATIOTEMPORAL PATTERN EXTRACTION WITH DATA-DRIVEN KOOPMAN OPERATORS FOR CONVECTIVELY COUPLED EQUATORIAL WAVES ..................................... 49 Joanna Slawinska, Dimitrios Giannakis 14. COVARIANCE STRUCTURE ANALYSIS OF CLIMATE MODEL OUTPUT ..................................... 53 Chintan Dalal, Doug Nychka, Claudia Tebaldi 15. SIMPLE AND EFFICIENT TENSOR REGRESSION FOR SPATIOTEMPORAL FORECASTING ..................................... 57 Rose Yu, Yan Liu 16. TRACKING OF TROPICAL INTRASEASONAL CONVECTIVE ANOMALIES ..................................... 61 Bohar Singh, James L. Kinter 17. ANALYSIS OF AMAZON DROUGHTS USING SUPERVISED KERNEL PRINCIPAL COMPONENT ANALYSIS ..................................... 65 Carlos H. R. Lima, Amir AghaKouchak 18. A BAYESIAN PREDICTIVE ANALYSIS OF DAILY PRECIPITATION DATA ..................................... 69 Sai K. Popuri, Nagaraj K. Neerchal, Amita Mehta 19. INCORPORATING PRIOR KNOWLEDGE IN SPATIO-TEMPORAL NEURAL NETWORK FOR CLIMATIC DATA ..................................... 73 Arthur Pajot, Ali Ziat, Ludovic Denoyer, Patrick Gallinari 20. 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GLOBAL MONITORING OF SURFACE WATER EXTENT DYNAMICS USING SATELLITE DATA ..................................... 97 Anuj Karpatne, Ankush Khandelwal and Vipin Kumar 26. TOWARD QUANTIFYING TROPICAL CYCLONE RISK USING DIAGNOSTIC INDICES .................................... 101 Erica M. Staehling and Ryan E. Truchelut 27. OPTIMAL TROPICAL CYCLONE INTENSITY ESTIMATES WITH UNCERTAINTY FROM BEST TRACK DATA .................................... 105 Suz Tolwinski-Ward 28. EXTREME WEATHER PATTERN DETECTION USING DEEP CONVOLUTIONAL NEURAL NETWORK .................................... 109 Yunjie Liu, Evan Racah, Prabhat, Amir Khosrowshahi, David Lavers, Kenneth Kunkel, Michael Wehner, William Collins 29. INFORMATION TRANSFER ACROSS TEMPORAL SCALES IN ATMOSPHERIC DYNAMICS .................................... 113 Nikola Jajcay and Milan Paluš 30. 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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1214/23-BA1393
