Article
Mathematics, Interdisciplinary Applications
David J. Nott, Max Seah, Luai Al-Labadi, Michael Evans, Hui Khoon Ng, Berthold-Georg Englert
Summary: In Bayesian analysis, combining information from different model components and detecting conflicts between sources of information are crucial. By expanding the prior used for analysis into a larger family of priors and considering a marginal likelihood score statistic, it is possible to gain insights into the nature of conflicts and choose appropriate expansions for sensitive conflict checks. Extensions to hierarchically specified priors and connections with other approaches are considered, with illustrations of implementation in complex situations using two applications.
Article
Biology
Antonio R. Linero
Summary: This paper discusses the application of Bayesian nonparametric methods in causal inference and points out that priors in high-dimensional or nonparametric spaces may contradict substantive knowledge in causal inference. The authors provide tools to verify that the prior distribution avoids inductive bias away from confounded models and verify that the posterior distribution contains sufficient information to overcome this issue.
Article
Automation & Control Systems
Shailesh Garg, Souvik Chakraborty
Summary: VB-DeepONet is a Bayesian operator learning framework that addresses the challenges faced by the deterministic DeepONet architecture. It provides better resistance against overfitting, improved generalization, and allows for the quantification of predictive uncertainty. The results from various mechanics problems demonstrate the effectiveness of VB-DeepONet in uncertainty quantification.
ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE
(2023)
Article
Physics, Multidisciplinary
Ali Unlu, Laurence Aitchison
Summary: The study introduces a Variational Laplace method for estimating ELBO without the need for stochastic sampling of neural network weights, outperforming maximum a posteriori inference and standard sampling-based variational inference in test performance and expected calibration errors. Care is necessary when benchmarking standard VI to avoid stopping before variance parameters have converged.
Article
Automation & Control Systems
Xiaolong Chen, Yi Chai, Qie Liu, Pengfei Huang, Linchuan Fan
Summary: In this paper, a novel Bayesian sparse multiple kernel-based identification method (BSMKM) for multiple-input single-output (MISO) Hammerstein system is proposed. The method represents the nonlinear part and the linear part using basis-function model and finite impulse response model respectively and estimates all unknown model parameters through hierarchical prior distribution and full Bayesian method based on variational Bayesian inference.
Article
Engineering, Civil
Pinghe Ni, Qiang Han, Xiuli Du, Xiaowei Cheng, Hongyuan Zhou
Summary: This paper presents a data-driven approach for post-earthquake reliability assessments of civil structures. It updates the probability density functions of random variables using measured vibration data, and generates the posterior probability density functions of structural parameters using two approximate Bayesian computation techniques. The updated probability density functions are then used for reliability assessments, and numerical studies verify the accuracy and efficiency of the proposed techniques.
ENGINEERING STRUCTURES
(2022)
Article
Engineering, Multidisciplinary
Jan Povala, Ieva Kazlauskaite, Eky Febrianto, Fehmi Cirak, Mark Girolami
Summary: Inverse problems involving partial differential equations (PDEs) are commonly used in science and engineering. While Markov Chain Monte Carlo (MCMC) has been the go-to method for sampling from posterior probability measures, it is computationally infeasible for large-scale problems. Variational Bayes (VB) has emerged as a more computationally tractable alternative, approximating posterior distributions with simpler trial distributions. This work presents a flexible and efficient approach to solving inverse problems using VB methods.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Computer Science, Artificial Intelligence
Younghwan Jeon, Ganguk Hwang
Summary: This paper addresses the data association problem and proposes a Bayesian approach based on a mixture of Gaussian Processes (GPs) to adapt to changing observations. Experimental results and theoretical analysis demonstrate the effectiveness of the proposed method.
PATTERN RECOGNITION
(2022)
Article
Engineering, Mechanical
Felipe Igea, Alice Cicirello
Summary: Multi-modal distributions of physics-based model parameters are common in engineering, but traditional sampling techniques struggle to accurately capture them with limited simulations. This can lead to numerical errors in assessing structures under uncertainty. To overcome this, a cyclical annealing schedule is proposed for the Variational Bayes Monte Carlo (VBMC) method, improving exploration and finding high probability areas in multi-modal distributions. Comparisons with other algorithms show that the proposed cyclical VBMC outperforms in terms of accuracy and required model runs.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2023)
Article
Automation & Control Systems
Augusto Fasano, Daniele Durante
Summary: This article discusses the challenges of Bayesian inference in multinomial probit models and proposes a method using unified skew-normal distributions as conjugate priors. By leveraging this method, improvements in posterior inference and classification results can be achieved, especially in high-dimensional studies.
JOURNAL OF MACHINE LEARNING RESEARCH
(2022)
Article
Computer Science, Artificial Intelligence
Chihao Zhang, Shihua Zhang
Summary: Matrix decomposition is a popular method in machine learning and data mining, and a joint matrix decomposition framework has been proposed for multi-view data and heterogeneous noise, with two algorithms developed to solve the model, showing superiority over existing methods in experiments.
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
(2021)
Article
Mathematics, Applied
Prateek Jaiswal, Harsha Honnappa, Vinayak A. Rao
Summary: This paper investigates data-driven chance-constrained stochastic optimization problems using a Bayesian framework. The study focuses on the statistical consistency and probabilistic rate of convergence of the optimal value obtained using an approximate posterior distribution. The research also establishes the convex feasibility of the approximate Bayesian stochastic optimization problem and demonstrates its utility through a staffing problem for an M/M/c queueing model.
SIAM JOURNAL ON OPTIMIZATION
(2023)
Article
Computer Science, Artificial Intelligence
Simon Rodriguez-Santana, Daniel Hernandez-Lobato
Summary: Neural networks are state-of-the-art models for machine learning, but conventional methods have limitations in predicting uncertainty. This paper proposes a method for approximate Bayesian inference based on minimizing alpha-divergences, which allows for more flexible estimation of posterior distributions. Experiments show that this method may lead to better results in regression problems and remains competitive in classification problems.
Article
Engineering, Electrical & Electronic
Lei Cheng, Zhongtao Chen, Qingjiang Shi, Yik-Chung Wu, Sergios Theodoridis
Summary: The study investigates the learning of tensor rank and introduces Bayesian inference under the Gaussian-gamma prior as an effective strategy. However, it is found that this strategy does not perform well for high-rank tensors and/or low signal-to-noise ratios. To overcome this issue, a more advanced generalized hyperbolic prior is introduced and an algorithm based on variational inference is developed, resulting in significantly improved performance.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2022)
Article
Computer Science, Artificial Intelligence
Qing-Qing Zhang, Shao-Wu Zhang, Yue-Hua Feng, Jian-Yu Shi
Summary: A novel method called HyperSynergy is proposed to address the drug synergy prediction problem in data-poor cell lines. It utilizes a prior-guided Hypernetwork architecture to generate cell line-dependent parameters for drug synergy prediction. Experimental results demonstrate that HyperSynergy outperforms other methods not only on data-poor cell lines but also on data-rich cell lines.
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
(2023)
Article
Statistics & Probability
Nadja Klein, David J. Nott, Michael Stanley Smith
Summary: This article presents an approach to construct predictive distributions that are marginally calibrated, improving uncertainty quantification. By combining DNN regression models with implicit copula processes, the method enhances accuracy in applications like ecological time series analysis.
JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
(2021)
Article
Statistics & Probability
Xuejun Yu, David J. Nott, Minh-Ngoc Tran, Nadja Klein
Summary: The article introduces a moment-based alternative method for assessing and adjusting approximate inference methods by relating prior and posterior expectations and covariances. The method adjusts approximate inferences to maintain correct prior to posterior relationships. Examples include using an auxiliary model in likelihood-free inference, corrections for variational Bayes approximations in a deep neural network GLMM, and using a deep neural network surrogate for approximating Gaussian process regression predictive inference.
JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
(2021)
Article
Statistics & Probability
Berthold-Georg Englert, Michael Evans, Gun Ho Jang, Hui Khoon Ng, David Nott, Yi-Lin Seah
Summary: Multinomial models can be challenging to use with probability constraints. An exact model checking procedure has been developed based on a uniform prior, and a consistency theorem has been proven for inference with a nonuniform prior. The study also introduces a new elicitation methodology for multinomial models with ordered probabilities.
Article
Economics
Ruben Loaiza-Maya, Michael Stanley Smith, David J. Nott, Peter J. Danaher
Summary: Models with a large number of latent variables can be difficult to estimate, but variational inference methods provide an attractive solution. This study proposes a tractable variational approximation that combines a parsimonious approximation for the parameter posterior with the exact conditional posterior of the latent variables. The method is more accurate and faster to calibrate, and allows for the implementation of data sub-sampling in variational inference.
JOURNAL OF ECONOMETRICS
(2022)
Article
Multidisciplinary Sciences
Mikolaj M. Paraniak, Berthold-Georg Englert
Summary: This study revisits the fundamental question of the reversibility of evolution in quantum mechanics, showing that the quantum dynamics of the transversal Stern-Gerlach interferometer is fundamentally irreversible even under ideal conditions with perfect control of the associated magnetic fields and beams.
Article
Economics
David Gunawan, Robert Kohn, David Nott
Summary: The study focuses on developing fast and accurate variational Bayes methods to approximate the posterior distribution of states and parameters in high dimensional multivariate factor stochastic volatility models, and extends it for prediction purposes; validated on simulated and real datasets, it shows to produce faster results compared to traditional approaches.
INTERNATIONAL JOURNAL OF FORECASTING
(2021)
Article
Statistics & Probability
David T. Frazier, David J. Nott, Christopher Drovandi, Robert Kohn
Summary: Implementing Bayesian inference in complex models with difficult likelihood calculations can be challenging. Synthetic likelihood, which constructs an approximate likelihood by simulating from the model, offers a computationally efficient alternative. This article demonstrates that the Bayesian implementation of synthetic likelihood is more efficient than approximate Bayesian computation and provides adjusted inference methods to further speed up computation. Supplementary materials are available online.
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
(2022)
Article
Computer Science, Theory & Methods
Lucas Kock, Nadja Klein, David J. Nott
Summary: This research introduces a new clustering method that combines mixtures of factor analyzers, sparse priors, and Bayesian inference to handle high-dimensional problems. The experimental results demonstrate the effectiveness of the proposed method in both simulated and real data.
STATISTICS AND COMPUTING
(2022)
Article
Chemistry, Physical
Jerzy Cioslowski, Berthold-Georg Englert, Martin-Isbjoern Trappe, Jun Hao Hue
Summary: At the limit of infinite confinement strength, the ground state of a system containing two interacting fermions or bosons in harmonic confinement remains strongly correlated. The natural orbitals of this system exhibit peculiar properties, such as nonzero collective occupancies for all angular momenta and a relationship with eigenfunctions and eigenvalues of a zero-energy Schrodinger equation with an attractive Gaussian potential. These properties have implications for the decay behavior and energy contributions of the system.
JOURNAL OF CHEMICAL PHYSICS
(2023)
Article
Quantum Science & Technology
Yanwu Gu, Rajesh Mishra, Berthold-Georg Englert, Hui Khoon Ng
Summary: Randomized linear gate-set tomography is an easy-to-implement procedure that combines the idea of state-preparation-and-measurement-error-free characterization with no-design randomized tomographic circuits, showing comparable performance to standard gate-set tomography in simulations and experiments while requiring less computational time.
Article
Mathematics, Interdisciplinary Applications
David J. Nott, Max Seah, Luai Al-Labadi, Michael Evans, Hui Khoon Ng, Berthold-Georg Englert
Summary: In Bayesian analysis, combining information from different model components and detecting conflicts between sources of information are crucial. By expanding the prior used for analysis into a larger family of priors and considering a marginal likelihood score statistic, it is possible to gain insights into the nature of conflicts and choose appropriate expansions for sensitive conflict checks. Extensions to hierarchically specified priors and connections with other approaches are considered, with illustrations of implementation in complex situations using two applications.
Article
Optics
Yiping Lu, Jun Yan Sim, Jun Suzuki, Berthold-Georg Englert, Hui Khoon Ng
Article
Optics
Jun Yan Sim, Jun Suzuki, Berthold-Georg Englert, Hui Khoon Ng