Thang D. Bui

Thang D. Bui

In the rapidly evolving landscape of artificial intelligence, probabilistic machine learning has emerged as a crucial field for developing robust and interpretable AI models. One of the leading researchers in this area is Thang D. Bui, whose work focuses on Bayesian inference, Gaussian processes, and scalable probabilistic learning. His contributions have significantly impacted uncertainty quantification, reinforcement learning, and deep learning, making AI systems more reliable and efficient.

This essay explores Thang D. Bui’s academic journey, his groundbreaking research, and the broader implications of his work in AI. The first part delves into his background, key research areas, and contributions to Bayesian methods and Gaussian processes. The second part will explore his work in deep learning, real-world applications, and future directions for probabilistic AI.

Background and Academic Journey

Education and Research Affiliations

Thang D. Bui earned his PhD in Machine Learning from the University of Cambridge, where he worked under the supervision of Richard E. Turner. His research was centered on developing scalable inference methods for Gaussian processes, a fundamental approach in probabilistic modeling. After completing his doctoral studies, he continued postdoctoral research at the University of Sydney and later at Google DeepMind, where he collaborated with leading experts in Bayesian learning and reinforcement learning.

Mentors, Collaborators, and Influences

Throughout his career, Thang D. Bui has worked with several prominent researchers in machine learning. Some of his key mentors and collaborators include:

  • Richard E. Turner – His PhD advisor, known for work in probabilistic models and approximate inference.
  • Carl Edward Rasmussen – A pioneer in Gaussian processes, whose research influenced Bui’s approach to scalable probabilistic learning.
  • Edward Meeds – A collaborator in developing Bayesian optimization techniques.
  • Marc Deisenroth – A leading researcher in probabilistic reinforcement learning.
  • James Hensman – An expert in variational inference for Gaussian processes.

These collaborations have shaped Bui’s work in making Bayesian methods more scalable and applicable to large-scale machine learning problems.

Core Research Areas in AI

Probabilistic Machine Learning and Bayesian Inference

Probabilistic machine learning is a powerful paradigm that allows AI systems to quantify uncertainty and make decisions based on probabilistic reasoning. Bayesian inference plays a central role in this framework by updating beliefs about a model’s parameters as new data becomes available.

Thang D. Bui’s research has focused on developing scalable Bayesian inference methods, enabling probabilistic models to be applied to large datasets. Traditional Bayesian inference methods, such as Markov Chain Monte Carlo (MCMC), often struggle with scalability. To address this issue, Bui has worked on variational inference, which approximates posterior distributions in a computationally efficient manner.

Mathematically, Bayesian inference is formulated as follows:

\( p(\theta | D) = \frac{p(D | \theta) p(\theta)}{p(D)} \)

where:

  • \( p(\theta | D) \) is the posterior distribution of model parameters \( \theta \) given data \( D \).
  • \( p(D | \theta) \) is the likelihood function.
  • \( p(\theta) \) is the prior distribution over parameters.
  • \( p(D) \) is the evidence (normalizing constant).

Bui’s work has led to faster approximations of \( p(\theta | D) \), making Bayesian models more practical for large-scale applications.

Gaussian Processes and Their Role in AI

Gaussian processes (GPs) are a fundamental tool in Bayesian machine learning, providing a non-parametric approach to regression and classification. They model functions as distributions over possible outputs, allowing for uncertainty quantification.

A Gaussian process is defined as:

\( f(x) \sim GP(m(x), k(x, x’)) \)

where:

  • \( m(x) \) is the mean function.
  • \( k(x, x’) \) is the covariance function (kernel).

GPs are computationally expensive because they require inverting an \( O(N^3) \) covariance matrix for \( N \) training points. Thang D. Bui has developed sparse Gaussian process approximations, which reduce computational complexity by using a subset of inducing points. This approximation allows GPs to scale to larger datasets while retaining their probabilistic properties.

One of his notable contributions is the use of stochastic variational inference for GPs, which approximates the posterior distribution efficiently:

\( q(f) = \mathcal{N}(\mu, \Sigma) \)

where \( \mu \) and \( \Sigma \) are learned variational parameters.

This technique has been applied to various fields, including:

  • Robotics – For real-time motion prediction.
  • Reinforcement learning – For policy optimization with uncertainty estimation.
  • Medical diagnostics – For predicting disease progression with confidence intervals.

Scalable and Approximate Inference Methods

One of the key challenges in Bayesian machine learning is the computational cost of inference. Traditional inference methods become infeasible as dataset size grows. Thang D. Bui has contributed significantly to making inference methods more efficient using:

  • Stochastic Variational Inference (SVI) – Approximating posteriors with tractable variational distributions.
  • Low-Rank Approximations – Reducing the complexity of covariance matrices in Gaussian processes.
  • Expectation Propagation (EP) – An alternative inference method for Bayesian learning.

His work on scalable inference has enabled Bayesian deep learning models to operate at industrial scale.

Thang D. Bui’s research

Thang D. Bui’s research has fundamentally shaped the field of probabilistic machine learning. His work on Bayesian inference, Gaussian processes, and scalable probabilistic methods has made AI systems more interpretable and reliable. By addressing computational challenges, he has facilitated the application of Bayesian models to real-world AI problems.

In the second part of this essay, we will explore how his research integrates with deep learning, discuss real-world applications, and analyze the broader impact of his work in artificial intelligence.

Deep Learning Meets Bayesian Inference

One of the most significant trends in modern artificial intelligence is the integration of Bayesian inference with deep learning. While deep learning has revolutionized AI by enabling powerful neural network models, it often lacks a principled way to quantify uncertainty. This is where Bayesian methods, as developed by Thang D. Bui, play a crucial role.

Uncertainty Quantification in Neural Networks

Traditional deep learning models, such as deep neural networks (DNNs), rely on deterministic optimization techniques, typically minimizing a loss function using stochastic gradient descent (SGD). However, these models struggle with uncertainty estimation, which is essential for applications like medical diagnostics, autonomous driving, and decision-making under uncertainty.

Bayesian deep learning introduces a probability distribution over neural network parameters, allowing for uncertainty estimation. This is formally represented as:

\( p(y | x, D) = \int p(y | x, w) p(w | D) dw \)

where:

  • \( p(y | x, w) \) represents the predictive distribution given the network parameters \( w \).
  • \( p(w | D) \) is the posterior over weights given the dataset \( D \).

Computing this integral exactly is intractable, leading to the development of approximate Bayesian inference methods. Thang D. Bui has significantly contributed to this field by developing variational inference techniques that efficiently approximate the posterior distribution over weights.

Bayesian Neural Networks and Stochastic Variational Inference

One of the most promising approaches in Bayesian deep learning is Bayesian neural networks (BNNs), where weights are treated as probability distributions instead of fixed values. A key technique in BNNs is stochastic variational inference (SVI), which approximates the posterior using a parameterized distribution \( q(w) \):

\( q(w) = \mathcal{N}(\mu, \Sigma) \)

where:

  • \( \mu \) and \( \Sigma \) are learned variational parameters.

Thang D. Bui’s research has focused on making SVI scalable for deep learning applications. His work enables deep learning models to:

  • Quantify uncertainty in predictions.
  • Improve robustness to adversarial attacks.
  • Reduce overfitting in small-data scenarios.

These advances have found applications in medical AI, where reliable uncertainty estimates are critical for high-stakes decision-making.

Applications of Bayesian Deep Learning

Uncertainty-Aware AI in Healthcare

Medical diagnosis requires AI models that provide calibrated confidence scores along with predictions. Bayesian deep learning enables:

  • Uncertainty-aware medical imaging – Detecting anomalies in X-rays and MRIs with confidence scores.
  • Personalized treatment recommendations – Using probabilistic models to tailor interventions to individual patients.

Bui’s contributions to scalable Bayesian inference have made it feasible to apply these models in real-world clinical settings.

Probabilistic AI for Autonomous Systems

Autonomous systems, such as self-driving cars, must operate in uncertain and dynamic environments. Bayesian models help these systems:

  • Assess confidence levels in sensor readings.
  • Adapt decision-making under uncertain conditions.
  • Reduce catastrophic failures in critical scenarios.

Gaussian processes and Bayesian neural networks, as developed by Bui, have been used in robotics to model uncertainty in motion planning and reinforcement learning.

Probabilistic Models in Reinforcement Learning

Reinforcement learning (RL) is another domain where Bayesian methods have had a profound impact. Traditional RL algorithms, such as Q-learning and policy gradient methods, often rely on deterministic optimization. However, real-world RL applications require handling uncertainty in environments and rewards.

Bayesian Reinforcement Learning

In Bayesian reinforcement learning, the agent maintains a probability distribution over possible environments. This improves sample efficiency and decision-making under uncertainty. The Bayesian RL framework can be expressed as:

\( p(R | s, a, D) = \int p(R | s, a, \theta) p(\theta | D) d\theta \)

where:

  • \( p(R | s, a, D) \) is the expected reward given state-action pair \( (s, a) \) and observed data \( D \).
  • \( p(\theta | D) \) is the posterior over the environment model.

Thang D. Bui’s research has helped develop Bayesian policy optimization techniques, which improve sample efficiency by incorporating prior knowledge into RL algorithms.

Gaussian Processes in RL

Gaussian processes (GPs) are widely used in model-based RL, where an agent learns a predictive model of the environment. Bui’s work in sparse Gaussian processes has allowed RL agents to:

  • Learn environment dynamics with fewer samples.
  • Efficiently propagate uncertainty over multiple time steps.
  • Reduce exploration time in complex environments.

These techniques are particularly useful in robotics, where collecting real-world data is expensive and time-consuming.

Challenges and Future Directions

Despite the advances in probabilistic machine learning, several challenges remain.

Scalability Issues

While Bui’s research has made Bayesian methods more scalable, challenges persist in applying them to extremely large-scale deep learning models, such as transformers used in natural language processing. Efficient Bayesian inference for large models remains an open research problem.

Bridging Bayesian Learning and Deep Neural Networks

Although Bayesian methods improve uncertainty estimation, integrating them seamlessly with deep neural networks is non-trivial. Future research aims to develop more efficient hybrid models that combine the strengths of deep learning with principled Bayesian inference.

Applications in Explainable AI

Explainability is a major concern in AI deployment. Bayesian models naturally provide uncertainty estimates, which can improve model interpretability. Future work may focus on developing:

  • Probabilistic frameworks for interpretable AI.
  • Explainability metrics based on Bayesian inference.
  • Trustworthy AI systems for high-stakes applications.

Conclusion

Thang D. Bui’s work has fundamentally advanced probabilistic machine learning, particularly in Bayesian inference, Gaussian processes, and deep learning. His contributions have made Bayesian methods more scalable and applicable to real-world problems in healthcare, robotics, and autonomous systems.

By bridging the gap between deep learning and Bayesian reasoning, his research has paved the way for more uncertainty-aware AI models, improving reliability and interpretability in machine learning applications. As AI continues to evolve, probabilistic methods will play a central role in developing more robust, efficient, and trustworthy AI systems.

Kind regards
J.O. Schneppat


References

Academic Journals and Articles

  • Bui, T. D., Yan, J., & Turner, R. E. (2017). “A Unifying Framework for Gaussian Process Pseudo-Point Approximations Using Power Expectation Propagation.” Journal of Machine Learning Research (JMLR).
  • Bui, T. D., Hernández-Lobato, J. M., & Turner, R. E. (2016). “Streaming sparse Gaussian process approximations.” Advances in Neural Information Processing Systems (NeurIPS).
  • Bui, T. D., Deisenroth, M. P., & Turner, R. E. (2016). “A Gaussian process model of cross-modal visual-tactile learning.” International Conference on Machine Learning (ICML).

Books and Monographs

  • Rasmussen, C. E., & Williams, C. K. I. (2006). Gaussian Processes for Machine Learning. MIT Press.
  • Bishop, C. M. (2006). Pattern Recognition and Machine Learning. Springer.
  • Murphy, K. P. (2022). Probabilistic Machine Learning: An Introduction. MIT Press.

Online Resources and Databases

  • Google Scholar profile of Thang D. Bui: https://scholar.google.com
  • NeurIPS, ICML, and JMLR archives for Bayesian machine learning research
  • GitHub repositories on Gaussian processes and Bayesian deep learning