Computer simulations are amply utilized in scientific, industrial, and business environments for analyzing complex real-world phenomena. For a simulation to match realistic scenarios, it is often necessary to conduct time-consuming parameter calibration, i.e., finding the optimal simulation parameters given a set of observations. In this work, we employ a machine learning-based approach to perform calibration faster and more accurately, with two components: a surrogate model of the simulation that is easy to obtain but not physically interpretable and a bridge model that maps the surrogate to the calibrated parameters. This bridge is learned using a dataset of simulations with known parameters. We propose a geometry-based surrogate, tangent slope-intercept (TSI) descriptors, that can effectively represent the simulation with low dimensionality. This property allows the bridge model to avoid the curse of dimensionality, learning without needing large datasets and avoiding overfitting. We showcase the effectiveness of TSI descriptors through experiments with synthetic signals and physical simulations of turbulent flow dynamics.

Because human movement spreads infection, and mobility is a good proxy for other social distancing measures, human mobility has been an important factor in the COVID19 epidemic. Therefore, the control of human mobility is one of the countermeasures used to suppress an epidemic.As a notable feature, COVID19 has had multiple waves (subepidemics). Understanding the causes of the start and end of each wave has important implications for a policy evaluation and the timely implementation of countermeasures. Some of the waves have been correlated with the changes in mobility, and some can be attributed to the emergence of new variants. However, the start and end of some of the waves are difficult to explain through known factors.To evaluate the effect of human mobility, we built a stochastic model incorporating individual movements of 500,000 people obtained from anonymized, user-approved location data of smartphones throughout Japan. Instead of using aggregate values of human mobility, our model tracks the movements of individuals and predicts the infection of all persons within the entire country. Although the model only has a single static parameter, it successfully reproduced the occurrence of three waves of the number of confirmed cases within the study period of March 01 to December 31, 2020 in Japan. It was previously difficult to explain the end of the second wave and the start of the third wave in the study period by human mobility alone. Our results suggest the importance of tracking individual movements instead of relaying the aggregate values of human mobility.

Robots are being developed to perform tasks in homes and factories autonomously. Several studies have examined motion generation based on haptic information, and some studies consider the environment as physical property information. However, there is a trade-off between the accuracy and the time required for the physical property estimation. Therefore, in this study, we propose a method for estimating physical properties based on training the relationship between the two estimation models. The first is a fast sequential estimation model, and the second is a highly accurate posterior estimation model. Training the relationship between the two models makes highly accurate sequential property estimation possible. Validation results showed improved accuracy of property estimation for learning samples and some untrained samples.

We propose a novel calibration method for computer simulators, dealing with the problem of covariate shift.Covariate shift is the situation where input distributions for training and test are different, and ubiquitous in applications of simulations. Our approach is based on Bayesian inference with kernel mean embedding of distributions, and on the use of an importance-weighted reproducing kernel for covariate shift adaptation.We provide a theoretical analysis for the proposed method, including a novel theoretical result for conditional mean embedding, as well as empirical investigations suggesting its effectiveness in practice.The experiments include calibration of a widely used simulator for industrial manufacturing processes, where we also demonstrate how the proposed method may be useful for sensitivity analysis of model parameters.

We propose a novel approach to parameter estimation for simulator-based statistical models with intractable likelihood. Our proposed method involves recursive application of kernel ABC and kernel herding to the same observed data. We provide a theoretical explanation regarding why the approach works, showing (for the population setting) that, under a certain assumption, point estimates obtained with this method converge to the true parameter, as recursion proceeds. We have conducted a variety of numerical experiments, including parameter estimation for a real-world pedestrian flow simulator, and show that in most cases our method outperforms existing approaches.

Analysis of traffic flow is one of the prominent concerns in traffic engineering, and it seeks to both elucidate the generation process of traffic jams and to ease them. A zero-range process (ZRP) is a representative traffic-flow model described as a probabilistic cellular automaton. There is a parameter that controls the behavior of the vehicles in the model, and parameter estimation enables us to determine the unobservable behavior from the observable flow data. There are few studies on estimating the parameter, but the properties of models with a known parameter have been well investigated mathematically. In the present paper, we determine the accuracy of parameter estimation and propose an optimization method to collect the data, which corresponds to active learning.

In supervised learning, we commonly assume that training and test data are sampled from the same distribution. However, this assumption can be violated in practice and then standard machine learning techniques perform poorly. This paper focuses on revealing and improving the performance of Bayesian estimation when the training and test distributions are different. We formally analyze the asymptotic Bayesian generalization error and establish its upper bound under a very general setting. Our important finding is that lower order terms---which can be ignored in the absence of the distribution change---play an important role under the distribution change. We also propose a novel variant of stochastic complexity which can be used for choosing an appropriate model and hyper-parameters under a particular distribution change.

It is well known that Boltzmann machines are nonregular statistical models. The set of their parameters for a small size model is an analytic set with singularities in the space of a large size one. The mathematical foundation of their learning is not yet constructed because of these singularities, though they are applied to information engineering. Recently we established a method to calculate the Bayes generalization errors using an algebraic geometric method even if the models are nonregular. This paper clarifies that the upper bounds of generalization errors in Boltzmann machines are smaller than those in regular statistical models.