Bayesian Optimization (BO) is a widely-used method for optimizing expensive-to-evaluate black-box functions. Traditional BO assumes that the learner has full control over all query variables without additional constraints. However, in many real-world scenarios, controlling certain query variables may incur costs. Therefore, the learner needs to balance the selection of informative subsets for targeted learning against leaving some variables to be randomly sampled to minimize costs. This problem is known as Bayesian Optimization with cost-varying variable subsets (BOCVS). While the goal of BOCVS is to identify the optimal solution with minimal cost, previous works have only guaranteed finding the optimal solution without considering the total costs incurred. Moreover, these works assume precise knowledge of the cost for each subset, which is often unrealistic. In this paper, we propose a novel algorithm for the extension of the BOCVS problem with random and unknown costs that separates the process into exploration and exploitation phases. The exploration phase will filter out low-quality variable subsets, while the exploitation phase will leverage high-quality ones. Furthermore, we theoretically demonstrate that our algorithm achieves a sub-linear rate in both quality regret and cost regret, addressing the objective of the BOCVS problem more effectively than previous analyses. Finally, we show that our proposed algorithm outperforms comparable baselines across a wide range of benchmarks.

This article explores the extension of well-known F1 score used for assessing the performance of binary classifiers. We propose the new metric using probabilistic interpretation of precision, recall, specificity, and negative predictive value. We describe its properties and compare it to common metrics. Then we demonstrate its behavior in edge cases of the confusion matrix. Finally, the properties of the metric are tested on binary classifier trained on the real dataset.

Recently, training support vector machines with indefinite kernels has attracted great attention in the machine learning community. In this paper, we tackle this problem by formulating a joint optimization model over SVM classifications and kernel principal component analysis. We first reformulate the kernel principal component analysis as a general kernel transformation framework, and then incorporate it into the SVM classification to formulate a joint optimization model. The proposed model has the advantage of making consistent kernel transformations over training and test samples. It can be used for both binary classification and multi-class classification problems. Our experimental results on both synthetic data sets and real world data sets show the proposed model can significantly outperform related approaches.