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Line search is a fundamental part of iterative optimization methods for unconstrained and bound-constrained optimization problems to determine suitable step lengths that provide sufficient improvement in each iteration. Traditional line…

Using a Bayesian network to analyze the causal relationship between nodes is a hot spot. The existing network learning algorithms are mainly constraint-based and score-based network generation methods. The constraint-based method is mainly…

A simple strategy for improving LLM accuracy, especially in math and reasoning problems, is to sample multiple responses and submit the answer most consistently reached. In this paper we leverage Bayesian prior information to save on…

Empirical Bayes (EB) improves the accuracy of simultaneous inference "by learning from the experience of others" (Efron, 2012). Classical EB theory focuses on latent variables that are iid draws from a fitted prior (Efron, 2019). Modern…

We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We show that this model can be easily lifted into a novel latent…

Autonomous methods to align beamlines can decrease the amount of time spent on diagnostics, and also uncover better global optima leading to better beam quality. The alignment of these beamlines is a high-dimensional, expensive-to-sample…

This chapter introduces the Bayesian reflex -- an analogy with the autonomic nervous system -- as a unifying framework for online learning in AI. Bayesian online algorithms automatically maintain equilibrium in dynamic environments via…

In the Bayesian community, an ongoing imperative is to develop efficient algorithms. An appealing approach is to form a hybrid algorithm by combining ideas from competing existing techniques. This paper addresses issues in designing hybrid…

The increasing availability of structured but high dimensional data has opened new opportunities for optimization. One emerging and promising avenue is the exploration of unsupervised methods for projecting structured high dimensional data…

Bayesian optimal experiments that maximize the information gained from collected data are critical to efficiently identify behavioral models. We extend a seminal method for designing Bayesian optimal experiments by introducing two…

Multiple kernel learning algorithms are proposed to combine kernels in order to obtain a better similarity measure or to integrate feature representations coming from different data sources. Most of the previous research on such methods is…

Bayesian methods are useful for statistical inference. However, real-world problems can be challenging using Bayesian methods when the data analyst has only limited prior knowledge. In this paper we consider a class of problems, called…

Bayesian optimization (BO) provides a powerful framework for optimizing black-box, expensive-to-evaluate functions. It is therefore an attractive tool for engineering design problems, typically involving multiple objectives. Thanks to the…

In this paper we consider the problem of multiple testing when the hypotheses are dependent. In most of the existing literature, either Bayesian or non-Bayesian, the decision rules mainly focus on the validity of the test procedure rather…

Unifying probabilistic and logical learning is a key challenge in AI. We introduce a Bayesian inductive logic programming approach that learns minimum message length hypotheses from noisy data. Our approach balances hypothesis complexity…

We address the problem of Bayesian reinforcement learning using efficient model-based online planning. We propose an optimism-free Bayes-adaptive algorithm to induce deeper and sparser exploration with a theoretical bound on its performance…

Bayesian optimization provides an effective method to optimize expensive-to-evaluate black box functions. It has been widely applied to problems in many fields, including notably in computer science, e.g. in machine learning to optimize…

Bayesian methods in machine learning, such as Gaussian processes, have great advantages com-pared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to…

At present, high-dimensional global optimization problems with time-series models have received much attention from engineering fields. Since it was proposed, Bayesian optimization has quickly become a popular and promising approach for…

Bayesian inference has many advantages in robotic motion planning over four perspectives: The uncertainty quantification of the policy, safety (risk-aware) and optimum guarantees of robot motions, data-efficiency in training of…