Jian Xu

Jian Xu

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Publications

You can also find my articles on my Google Scholar profile.

Journal Articles

Sparse Variational Student-t Processes for Heavy-Tailed Modeling

Published in IEEE Transactions on Neural Networks and Learning Systems (TNNLS), 2026

Journal extension of the AAAI 2024 SVTP paper. Closed-form Fisher information matrix for the multivariate Student-t variational distribution via the “beta link”, enabling tractable natural-gradient optimisation at scale.

Recommended citation: Xu, J., Zeng, D. and Paisley, J. (2026). Sparse Variational Student-t Processes for Heavy-Tailed Modeling. IEEE Transactions on Neural Networks and Learning Systems, pp.1-14, doi:10.1109/TNNLS.2026.3673350.
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Fully Bayesian Differential Gaussian Processes through Stochastic Differential Equations

Published in Knowledge-Based Systems, 2025

Latent-state SDE driven by a sparse GP, where the GP kernel length scales themselves evolve via a second SDE — a fully Bayesian treatment of kernel hyperparameters instead of point estimation.

Recommended citation: Xu, J., Lin, Z., Chen, M., Yang, J., Zeng, D. and Paisley, J. (2025). Fully Bayesian differential Gaussian processes through stochastic differential equations. Knowledge-Based Systems, 314, p.113187.
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Neural Operator Variational Inference Based on Regularized Stein Discrepancy for Deep Gaussian Processes

Published in IEEE Transactions on Neural Networks and Learning Systems (TNNLS), 36(4), 2024

Replaces the mean-field Gaussian posterior over inducing variables in a Deep GP with a neural-network generator trained via a regularized Stein discrepancy — a neural operator that maps noise to inducing-variable samples.

Recommended citation: Xu, J., Du, S., Yang, J., Ma, Q. and Zeng, D. (2025). Neural Operator Variational Inference Based on Regularized Stein Discrepancy for Deep Gaussian Processes. IEEE Transactions on Neural Networks and Learning Systems, 36(4), pp.6723-6737.
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Conference Papers

Diffusion Bridge Variational Inference for Deep Gaussian Processes

Published in The Fourteenth International Conference on Learning Representations (ICLR 2026), 2026

Doob-bridged variational inference for Deep GPs — score network is trained against the closed-form bridge marginal so the variational posterior interpolates between a data-anchored initial distribution and a fixed terminal noise.

Recommended citation: Xu, J., Zeng, D., Zhao, Q. and Paisley, J. (2026). Diffusion Bridge Variational Inference for Deep Gaussian Processes. ICLR 2026.
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Bayesian Gaussian Process ODEs via Double Normalizing Flows

Published in Proceedings of the 28th International Conference on Artificial Intelligence and Statistics (AISTATS 2025), 2025

Two normalizing flows for Bayesian GP-ODEs: one reparameterises the ODE vector field into a data-driven prior, the other relaxes the mean-field assumption on the inducing-variable posterior. Improves accuracy and uncertainty on dynamical systems and CMU MoCap.

Recommended citation: Xu, J., Du, S., Yang, J., Ding, X., Zeng, D. and Paisley, J. (2025). Bayesian Gaussian Process ODEs via Double Normalizing Flows. AISTATS 2025, PMLR 258, pp.235-243.
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Sparse Inducing Points in Deep Gaussian Processes: Enhancing Modeling with Denoising Diffusion Variational Inference

Published in Proceedings of the 41st International Conference on Machine Learning (ICML 2024), 2024

ICML 2024 (Oral). DDVI replaces the mean-field Gaussian posterior over inducing variables with the terminal of a reverse-time VP-SDE driven by a learned score network, jointly trained with denoising score matching.

Recommended citation: Xu, J., Zeng, D. and Paisley, J. (2024). Sparse Inducing Points in Deep Gaussian Processes: Enhancing Modeling with Denoising Diffusion Variational Inference. ICML 2024, PMLR 235, pp.55490-55500. (Oral)
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Sparse Variational Student-t Processes

Published in Proceedings of the AAAI Conference on Artificial Intelligence, 38(14), 2024

Extends sparse inducing-point inference from GPs to Student-t Processes, giving robustness to outliers and heavy-tailed observations while preserving SVGP-level computational complexity.

Recommended citation: Xu, J. and Zeng, D. (2024). Sparse variational student-t processes. Proceedings of the AAAI Conference on Artificial Intelligence, 38(14), pp.16156-16163.
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