Gaussian process regression (GPR) or kernel ridge regression is a widely used and powerful tool for nonlinear prediction. Therefore, active learning (AL) for GPR, which actively collects data labels to achieve an accurate prediction with fewer data labels, is an important problem. However, existing AL methods do not theoretically guarantee prediction accuracy for target distribution. Furthermore, as discussed in the distributionally robust learning literature, specifying the target distribution is often difficult. Thus, this paper proposes two AL methods that effectively reduce the worst-case expected error for GPR, which is the worst-case expectation in target distribution candidates. We show an upper bound of the worst-case expected squared error, which suggests that the error will be arbitrarily small by a finite number of data labels under mild conditions. Finally, we demonstrate the effectiveness of the proposed methods through synthetic and real-world datasets.

Coreset selection, which involves selecting a small subset from an existing training dataset, is an approach to reducing training data, and various approaches have been proposed for this method. In practical situations where these methods are employed, it is often the case that the data distributions differ between the development phase and the deployment phase, with the latter being unknown. Thus, it is challenging to select an effective subset of training data that performs well across all deployment scenarios. We therefore propose Distributionally Robust Coreset Selection (DRCS). DRCS theoretically derives an estimate of the upper bound for the worst-case test error, assuming that the future covariate distribution may deviate within a defined range from the training distribution. Furthermore, by selecting instances in a way that suppresses the estimate of the upper bound for the worst-case test error, DRCS achieves distributionally robust training instance selection. This study is primarily applicable to convex training computation, but we demonstrate that it can also be applied to deep learning under appropriate approximations. In this paper, we focus on covariate shift, a type of data distribution shift, and demonstrate the effectiveness of DRCS through experiments.

Reducing the amount of training data while preserving model performance remains a fundamental challenge in machine learning. Dataset distillation seeks to generate synthetic instances that encapsulate the essential information of the original data [31]. This synthetic approach often proves more flexible and can potentially achieve greater data reduction than simply retaining subsets of actual instances. Such distilled datasets can also serve broader applications, for example by enabling efficient continual learning with reduced storage demands [14, 23, 3], and offering privacy safeguards through data corruption [2, 12]. Existing dataset distillation methods are essentially formulated as a bi-level optimization problem. This is because generating synthetic instances requires retraining the model with those instances as training data. Specifically, synthetic instances are created in the outer loop, and the model is trained in the inner loop, leading to high computational costs. A promising approach to avoid bi-level optimization is a method called Kernel Inducing Point (KIP) [18]. The KIP method avoids bi-level optimization by obtaining an analytical solution in its inner loop, effectively leveraging the fact that its loss function is a variant of squared loss.

The rapid discovery of new chemical compounds is essential for advancing global health and developing treatments. While generative models show promise in creating novel molecules, challenges remain in ensuring the real-world applicability of these molecules and finding such molecules efficiently. To address this, we introduce Conditional Latent Space Molecular Scaffold Optimization (CLaSMO), which combines a Conditional Variational Autoencoder (CVAE) with Latent Space Bayesian Optimization (LSBO) to modify molecules strategically while maintaining similarity to the original input. Our LSBO setting improves the sample-efficiency of our optimization, and our modification approach helps us to obtain molecules with higher chances of real-world applicability. CLaSMO explores substructures of molecules in a sample-efficient manner by performing BO in the latent space of a CVAE conditioned on the atomic environment of the molecule to be optimized. Our experiments demonstrate that CLaSMO efficiently enhances target properties with minimal substructure modifications, achieving state-of-the-art results with a smaller model and dataset compared to existing methods. We also provide an open-source web application that enables chemical experts to apply CLaSMO in a Human-in-the-Loop setting.

In this study, we propose a machine learning method called Distributionally Robust Safe Sample Screening (DRSSS). DRSSS aims to identify unnecessary training samples, even when the distribution of the training samples changes in the future. To achieve this, we effectively combine the distributionally robust (DR) paradigm, which aims to enhance model robustness against variations in data distribution, with the safe sample screening (SSS), which identifies unnecessary training samples prior to model training. Since we need to consider an infinite number of scenarios regarding changes in the distribution, we applied SSS because it does not require model training after the change of the distribution. In this paper, we employed the covariate shift framework to represent the distribution of training samples and reformulated the DR covariate-shift problem as a weighted empirical risk minimization problem, where the weights are subject to uncertainty within a predetermined range. By extending the existing SSS technique to accommodate this weight uncertainty, the DRSSS method is capable of reliably identifying unnecessary samples under any future distribution within a specified range. We provide a theoretical guarantee for the DRSSS method and validate its performance through numerical experiments on both synthetic and real-world datasets.

In this study, we propose a method Distributionally Robust Safe Screening (DRSS), for identifying unnecessary samples and features within a DR covariate shift setting. This method effectively combines DR learning, a paradigm aimed at enhancing model robustness against variations in data distribution, with safe screening (SS), a sparse optimization technique designed to identify irrelevant samples and features prior to model training. The core concept of the DRSS method involves reformulating the DR covariate-shift problem as a weighted empirical risk minimization problem, where the weights are subject to uncertainty within a predetermined range. By extending the SS technique to accommodate this weight uncertainty, the DRSS method is capable of reliably identifying unnecessary samples and features under any future distribution within a specified range. We provide a theoretical guarantee of the DRSS method and validate its performance through numerical experiments on both synthetic and real-world datasets.

In this study, we propose a novel multi-objective Bayesian optimization (MOBO) method to efficiently identify the Pareto front (PF) defined by risk measures for black-box functions under the presence of input uncertainty (IU). Existing BO methods for Pareto optimization in the presence of IU are risk-specific or without theoretical guarantees, whereas our proposed method addresses general risk measures and has theoretical guarantees. The basic idea of the proposed method is to assume a Gaussian process (GP) model for the black-box function and to construct high-probability bounding boxes for the risk measures using the GP model. Furthermore, in order to reduce the uncertainty of non-dominated bounding boxes, we propose a method of selecting the next evaluation point using a maximin distance defined by the maximum value of a quasi distance based on bounding boxes. As theoretical analysis, we prove that the algorithm can return an arbitrary-accurate solution in a finite number of iterations with high probability, for various risk measures such as Bayes risk, worst-case risk, and value-at-risk. We also give a theoretical analysis that takes into account approximation errors because there exist non-negligible approximation errors (e.g., finite approximation of PFs and sampling-based approximation of bounding boxes) in practice. We confirm that the proposed method outperforms compared with existing methods not only in the setting with IU but also in the setting of ordinary MOBO through numerical experiments.

Predictive pattern mining is an approach used to construct prediction models when the input is represented by structured data, such as sets, graphs, and sequences. The main idea behind predictive pattern mining is to build a prediction model by considering substructures, such as subsets, subgraphs, and subsequences (referred to as patterns), present in the structured data as features of the model. The primary challenge in predictive pattern mining lies in the exponential growth of the number of patterns with the complexity of the structured data. In this study, we propose the Safe Pattern Pruning (SPP) method to address the explosion of pattern numbers in predictive pattern mining. We also discuss how it can be effectively employed throughout the entire model building process in practical data analysis. To demonstrate the effectiveness of the proposed method, we conduct numerical experiments on regression and classification problems involving sets, graphs, and sequences.

In this study, we have developed an incremental machine learning (ML) method that efficiently obtains the optimal model when a small number of instances or features are added or removed. This problem holds practical importance in model selection, such as cross-validation (CV) and feature selection. Among the class of ML methods known as linear estimators, there exists an efficient model update framework called the low-rank update that can effectively handle changes in a small number of rows and columns within the data matrix. However, for ML methods beyond linear estimators, there is currently no comprehensive framework available to obtain knowledge about the updated solution within a specific computational complexity. In light of this, our study introduces a method called the Generalized Low-Rank Update (GLRU) which extends the low-rank update framework of linear estimators to ML methods formulated as a certain class of regularized empirical risk minimization, including commonly used methods such as SVM and logistic regression. The proposed GLRU method not only expands the range of its applicability but also provides information about the updated solutions with a computational complexity proportional to the amount of dataset changes. To demonstrate the effectiveness of the GLRU method, we conduct experiments showcasing its efficiency in performing cross-validation and feature selection compared to other baseline methods.

Automated high-stake decision-making such as medical diagnosis requires models with high interpretability and reliability. As one of the interpretable and reliable models with good prediction ability, we consider Sparse High-order Interaction Model (SHIM) in this study. However, finding statistically significant high-order interactions is challenging due to the intrinsic high dimensionality of the combinatorial effects. Another problem in data-driven modeling is the effect of "cherry-picking" a.k.a. selection bias. Our main contribution is to extend the recently developed parametric programming approach for selective inference to high-order interaction models. Exhaustive search over the cherry tree (all possible interactions) can be daunting and impractical even for a small-sized problem. We introduced an efficient pruning strategy and demonstrated the computational efficiency and statistical power of the proposed method using both synthetic and real data.