In real-world applications, anomaly detection (AD) often operates without access to anomalous data, necessitating semi-supervised methods that rely solely on normal data. Among these methods, deep $k$-nearest neighbor (deep $k$NN) AD stands out for its interpretability and flexibility, leveraging distance-based scoring in deep latent spaces. Despite its strong performance, deep $k$NN lacks a mechanism to quantify uncertainty—an essential feature for critical applications such as industrial inspection. To address this limitation, we propose a statistical framework that quantifies the significance of detected anomalies in the form of $p$-values, thereby enabling control over false positive rates at a user-specified significance level (e.g.,0.05). A central challenge lies in managing selection bias, which we tackle using Selective Inference—a principled method for conducting inference conditioned on data-driven selections. We evaluate our method on diverse datasets and demonstrate that it provides reliable AD well-suited for industrial use cases.

The Vision Transformer (ViT) demonstrates exceptional performance in various computer vision tasks. Attention is crucial for ViT to capture complex wide-ranging relationships among image patches, allowing the model to weigh the importance of image patches and aiding our understanding of the decision-making process. However, when utilizing the attention of ViT as evidence in high-stakes decision-making tasks such as medical diagnostics, a challenge arises due to the potential of attention mechanisms erroneously focusing on irrelevant regions. In this study, we propose a statistical test for ViT's attentions, enabling us to use the attentions as reliable quantitative evidence indicators for ViT's decision-making with a rigorously controlled error rate. Using the framework called selective inference, we quantify the statistical significance of attentions in the form of p-values, which enables the theoretically grounded quantification of the false positive detection probability of attentions. We demonstrate the validity and the effectiveness of the proposed method through numerical experiments and applications to brain image diagnoses.

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, 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 the generalized low-rank update (GLRU) method, 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 support vector machines 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 number of data set 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.

Parametric excitation walking is one of methods to realize dynamic walking on a level ground. This method has first applied to a biped robot with telescopic legs and later to a robot with actuated knee joints. In parametric excitation walking, mechanical energy is increased by periodic up-and-down motion of the center of mass. While parametric excitation walking with telescopic legs has verified by an experimental robot, that with actuated knees has not yet as far as we know. The purpose of this paper is to present demonstration experiment of parametric excitation walking with a kneed biped robot. To do this, we develop an experimental kneed biped robot having four parallel legs with semicircular feet. In the experiment, the robot achieves walking on a level ground more than 15 steps. We also measure the movements of the robot during walking by a 3D motion capture and compare with simulation results.

Parametric excitation walking is one of methods that realize a passive dynamic like walking on the level ground. In parametric excitation walking, up-and-down motion of the center of mass restores mechanical energy and sustainable gait is generated. Walking ability and walking performance strongly depend on the reference trajectory of the center of mass. In this paper, we propose an optimization method for the reference trajectory of parametric excitation walking. There are two problems for optimization. One is that search space of a reference trajectory is inherently infinite dimensional. Another is that it takes long simulation time to generate steady gait for a given reference trajectory. Therefore, the proposing optimization method adopts the following strategy. For the former, we confine the reference trajectory to the quartic spline curve and take the parameter of spline curve as decision variables. For the latter, we discretize the search space and adopt a local search method usually used in combinational optimization problems. We apply the proposed method to a kneed biped robot, and optimize the reference trajectory of its swing leg.

In the passive dynamic walking proposed by McGeer, mechanical energy lost by heel strike is restored by transporting potential energy to kinetic energy as walking down a slope. When energy input is large such as an angle of slope is steep, bifurcation of walking period occurs. In parametric excitation walking, which is one method to realize passive dynamic-like walking on level ground, bifurcation has also been observed when walking speed is fast. Asano et al. have shown that bifurcation exerts an adverse influence upon walking performance by using rimless wheel model. In this paper, we apply delayed feedback control (DFC) originally used in chaos control to parametric excitation walking to suppress bifurcation. We show in numerical simulation that the proposed method makes two-period walking to one-period walking, and energy efficiency is improved. The analyses using Poincare¿ map reveal that the one-period walking with DFC is unstable periodic orbit and that the robot dealt in this paper satisfies the sufficient condition of applicability of DFC.

The parametric excitation based gait generation method proposed by Asano et al. restores mechanical energy lost by heel-strike collisions. Harata et. al. applied this method to a kneed biped robot which is proper for the parametric excitation, and show that sustainable gait has been generated with only knee torque. A swing-leg of a kneed biped robot has similar mechanism to an acrobot, and many acrobots bends a joint in inverse direction like ornithoid walking. This suggests that inverse bending a knee restores more mechanical energy than forward bending like human walking, and hence, inverse bending may be more efficient. In this paper, we propose a parametric excitation based ornithoid gait generation method for a kneed biped robot, and show that it can walk sustainably by numerical simulation. We also show that parametric excitation based inverse bending walking is more efficient than parametric excitation based forward bending walking with respect to performance indices in our model.

Restoring mechanical energy lost by heel-strike collisions is necessary for stable gait generation. One principle to realize this is parametric excitation. Recently, Asano et al. applied this principle to a biped robot with telescopic-legs, and succeeded in generating a sustainable biped gait by computer simulation. In this paper, we deal with a model of a biped robot that has not only semicircular feet but also actuated knees. Though this robot has no actuator at the hip, knee actuators can sustain gait by parametric excitation. We first verify that an actuated knee can cause parametric excitation, and then show by computer simulation that the proposed biped robot can walk continuously with actuated knees only.

This paper aims at developing a methodology of decision analysis for mitigating natural disaster risks arising with low probability for which the expected utility theory of von Neumann and Morgenstern (1947) is inadequate. It is shown that the value function under risk is a useful model for evaluating public risks of extreme events that influence numerous people enormously or the environment badly with low probability.