Masanari Kimura

Masanari Kimura, Hideitsu Hino

Many machine learning methods assume that the training and test data follow the same distribution. However, in the real world, this assumption is very often violated. In particular, the phenomenon that the marginal distribution of the data changes is called covariate shift, one of the most important research topics in machine learning. We show that the well-known family of covariate shift adaptation methods is unified in the framework of information geometry. Furthermore, we show that parameter search for geometrically generalized covariate shift adaptation method can be achieved efficiently. Numerical experiments show that our generalization can achieve better performance than the existing methods it encompasses.

Masanari Kimura, Hideitsu Hino

Dropout is one of the most popular regularization techniques in neural network training. Because of its power and simplicity of idea, dropout has been analyzed extensively and many variants have been proposed. In this paper, several properties of dropout are discussed in a unified manner from the viewpoint of information geometry. We showed that dropout flattens the model manifold and that their regularization performance depends on the amount of the curvature. Then, we showed that dropout essentially corresponds to a regularization that depends on the Fisher information, and support this result from numerical experiments. Such a theoretical analysis of the technique from a different perspective is expected to greatly assist in the understanding of neural networks, which are still in their infancy.

Ryotaro Shimizu, Yu Wang, Masanari Kimura et al.

In this work, we propose a fashion item recommendation model that incorporates hyperbolic geometry into user and item representations. Using hyperbolic space, our model aims to capture implicit hierarchies among items based on their visual data and users' purchase history. During training, we apply a multi-task learning framework that considers both hyperbolic and Euclidean distances in the loss function. Our experiments on three data sets show that our model performs better than previous models trained in Euclidean space only, confirming the effectiveness of our model. Our ablation studies show that multi-task learning plays a key role, and removing the Euclidean loss substantially deteriorates the model performance.

Ryotaro Shimizu, Masanari Kimura, Masayuki Goto

Several techniques to map various types of components, such as words, attributes, and images, into the embedded space have been studied. Most of them estimate the embedded representation of target entity as a point in the projective space. Some models, such as Word2Gauss, assume a probability distribution behind the embedded representation, which enables the spread or variance of the meaning of embedded target components to be captured and considered in more detail. We examine the method of estimating embedded representations as probability distributions for the interpretation of fashion-specific abstract and difficult-to-understand terms. Terms, such as "casual," "adult-casual,'' "beauty-casual," and "formal," are extremely subjective and abstract and are difficult for both experts and non-experts to understand, which discourages users from trying new fashion. We propose an end-to-end model called dual Gaussian visual-semantic embedding, which maps images and attributes in the same projective space and enables the interpretation of the meaning of these terms by its broad applications. We demonstrate the effectiveness of the proposed method through multifaceted experiments involving image and attribute mapping, image retrieval and re-ordering techniques, and a detailed theoretical/analytical discussion of the distance measure included in the loss function.

Waku Hatakeyama, Shirou Kawakita, Ryohei Izawa et al.

Detecting changes on the Earth, such as urban development, deforestation, or natural disaster, is one of the research fields that is attracting a great deal of attention. One promising tool to solve these problems is satellite imagery. However, satellite images require huge amount of storage, therefore users are required to set Area of Interests first, which was not suitable for detecting potential areas for disaster or development. To tackle with this problem, we develop the novel tool, namely GRASP EARTH, which is the simple change detection application based on Google Earth Engine. GRASP EARTH allows us to handle satellite imagery easily and it has used for disaster monitoring and urban development monitoring.

Masanari Kimura

The problem of matching two sets of multiple elements, namely set-to-set matching, has received a great deal of attention in recent years. In particular, it has been reported that good experimental results can be obtained by preparing a neural network as a matching function, especially in complex cases where, for example, each element of the set is an image. However, theoretical analysis of set-to-set matching with such black-box functions is lacking. This paper aims to perform a generalization error analysis in set-to-set matching to reveal the behavior of the model in that task.

Masanari Kimura, Howard Bondell

Data augmentation is known to contribute significantly to the robustness of machine learning models. In most instances, data augmentation is utilized during the training phase. Test-Time Augmentation (TTA) is a technique that instead leverages these data augmentations during the testing phase to achieve robust predictions. More precisely, TTA averages the predictions of multiple data augmentations of an instance to produce a final prediction. Although the effectiveness of TTA has been empirically reported, it can be expected that the predictive performance achieved will depend on the set of data augmentation methods used during testing. In particular, the data augmentation methods applied should make different contributions to performance. That is, it is anticipated that there may be differing degrees of contribution in the set of data augmentation methods used for TTA, and these could have a negative impact on prediction performance. In this study, we consider a weighted version of the TTA based on the contribution of each data augmentation. Some variants of TTA can be regarded as considering the problem of determining the appropriate weighting. We demonstrate that the determination of the coefficients of this weighted TTA can be formalized in a variational Bayesian framework. We also show that optimizing the weights to maximize the marginal log-likelihood suppresses candidates of unwanted data augmentations at the test phase.

Masanari Kimura

Test-Time Augmentation (TTA) is a very powerful heuristic that takes advantage of data augmentation during testing to produce averaged output. Despite the experimental effectiveness of TTA, there is insufficient discussion of its theoretical aspects. In this paper, we aim to give theoretical guarantees for TTA and clarify its behavior.

Masanari Kimura, Ryotaro Shimizu, Yuki Hirakawa et al.

Conventional machine learning algorithms have traditionally been designed under the assumption that input data follows a vector-based format, with an emphasis on vector-centric paradigms. However, as the demand for tasks involving set-based inputs has grown, there has been a paradigm shift in the research community towards addressing these challenges. In recent years, the emergence of neural network architectures such as Deep Sets and Transformers has presented a significant advancement in the treatment of set-based data. These architectures are specifically engineered to naturally accommodate sets as input, enabling more effective representation and processing of set structures. Consequently, there has been a surge of research endeavors dedicated to exploring and harnessing the capabilities of these architectures for various tasks involving the approximation of set functions. This comprehensive survey aims to provide an overview of the diverse problem settings and ongoing research efforts pertaining to neural networks that approximate set functions. By delving into the intricacies of these approaches and elucidating the associated challenges, the survey aims to equip readers with a comprehensive understanding of the field. Through this comprehensive perspective, we hope that researchers can gain valuable insights into the potential applications, inherent limitations, and future directions of set-based neural networks. Indeed, from this survey we gain two insights: i) Deep Sets and its variants can be generalized by differences in the aggregation function, and ii) the behavior of Deep Sets is sensitive to the choice of the aggregation function. From these observations, we show that Deep Sets, one of the well-known permutation-invariant neural networks, can be generalized in the sense of a quasi-arithmetic mean.

Masanari Kimura, Hideitsu Hino

Importance weighting is a fundamental procedure in statistics and machine learning that weights the objective function or probability distribution based on the importance of the instance in some sense. The simplicity and usefulness of the idea has led to many applications of importance weighting. For example, it is known that supervised learning under an assumption about the difference between the training and test distributions, called distribution shift, can guarantee statistically desirable properties through importance weighting by their density ratio. This survey summarizes the broad applications of importance weighting in machine learning and related research.

Masanari Kimura, Hiroki Naganuma

The key factor in implementing machine learning algorithms in decision-making situations is not only the accuracy of the model but also its confidence level. The confidence level of a model in a classification problem is often given by the output vector of a softmax function for convenience. However, these values are known to deviate significantly from the actual expected model confidence. This problem is called model calibration and has been studied extensively. One of the simplest techniques to tackle this task is focal loss, a generalization of cross-entropy by introducing one positive parameter. Although many related studies exist because of the simplicity of the idea and its formalization, the theoretical analysis of its behavior is still insufficient. In this study, our objective is to understand the behavior of focal loss by reinterpreting this function geometrically. Our analysis suggests that focal loss reduces the curvature of the loss surface in training the model. This indicates that curvature may be one of the essential factors in achieving model calibration. We design numerical experiments to support this conjecture to reveal the behavior of focal loss and the relationship between calibration performance and curvature.

Masanari Kimura

Discriminative Random Walks (DRWs) are a simple yet powerful tool for semi-supervised node classification, but their theoretical foundations remain fragmentary. We revisit DRWs through the lens of information geometry, treating the family of class-specific hitting-time laws on an absorbing Markov chain as a statistical manifold. Starting from a log-linear edge-weight model, we derive closed-form expressions for the hitting-time probability mass function, its full moment hierarchy, and the observed Fisher information. The Fisher matrix of each seed node turns out to be rank-one, taking the quotient by its null space yields a low-dimensional, globally flat manifold that captures all identifiable directions of the model. Leveraging the geometry, we introduce a sensitivity score for unlabeled nodes that bounds, and in one-dimensional cases attains, the maximal first-order change in DRW betweenness under unit Fisher perturbations. The score can lead to principled strategies for active label acquisition, edge re-weighting, and explanation.

Masanari Kimura, Howard Bondell

The power prior is a class of informative priors designed to incorporate historical data alongside current data in a Bayesian framework. It includes a power parameter that controls the influence of historical data, providing flexibility and adaptability. A key property of the power prior is that the resulting posterior minimizes a linear combination of KL divergences between two pseudo-posterior distributions: one ignoring historical data and the other fully incorporating it. We extend this framework by identifying the posterior distribution as the minimizer of a linear combination of Amari's $α$-divergence, a generalization of KL divergence. We show that this generalization can lead to improved performance by allowing for the data to adapt to appropriate choices of the $α$ parameter. Theoretical properties of this generalized power posterior are established, including behavior as a generalized geodesic on the Riemannian manifold of probability distributions, offering novel insights into its geometric interpretation.

Masanari Kimura

This study develops a higher-order asymptotic framework for test-time adaptation (TTA) of Batch Normalization (BN) statistics under distribution shift by integrating classical Edgeworth expansion and saddlepoint approximation techniques with a novel one-step M-estimation perspective. By analyzing the statistical discrepancy between training and test distributions, we derive an Edgeworth expansion for the normalized difference in BN means and obtain an optimal weighting parameter that minimizes the mean-squared error of the adapted statistic. Reinterpreting BN TTA as a one-step M-estimator allows us to derive higher-order local asymptotic normality results, which incorporate skewness and other higher moments into the estimator's behavior. Moreover, we quantify the trade-offs among bias, variance, and skewness in the adaptation process and establish a corresponding generalization bound on the model risk. The refined saddlepoint approximations further deliver uniformly accurate density and tail probability estimates for the BN TTA statistic. These theoretical insights provide a comprehensive understanding of how higher-order corrections and robust one-step updating can enhance the reliability and performance of BN layers in adapting to changing data distributions.

Masanari Kimura

Label shift adaptation aims to recover target class priors when the labelled source distribution $P$ and the unlabelled target distribution $Q$ share $P(X \mid Y) = Q(X \mid Y)$ but $P(Y) \neq Q(Y)$. Classical black-box shift estimators invert an empirical confusion matrix of a frozen classifier, producing a brittle point estimate that ignores sampling noise and similarity among classes. We present Graph-Smoothed Bayesian BBSE (GS-B$^3$SE), a fully probabilistic alternative that places Laplacian-Gaussian priors on both target log-priors and confusion-matrix columns, tying them together on a label-similarity graph. The resulting posterior is tractable with HMC or a fast block Newton-CG scheme. We prove identifiability, $N^{-1/2}$ contraction, variance bounds that shrink with the graph's algebraic connectivity, and robustness to Laplacian misspecification. We also reinterpret GS-B$^3$SE through information geometry, showing that it generalizes existing shift estimators.

Masanari Kimura

We develop a higher-order asymptotic analysis for the semi-hard triplet loss using the Edgeworth expansion. It is known that this loss function enforces that embeddings of similar samples are close while those of dissimilar samples are separated by a specified margin. By refining the classical central limit theorem, our approach quantifies the impact of the margin parameter and the skewness of the underlying data distribution on the loss behavior. In particular, we derive explicit Edgeworth expansions that reveal first-order corrections in terms of the third cumulant, thereby characterizing non-Gaussian effects present in the distribution of distance differences between anchor-positive and anchor-negative pairs. Our findings provide detailed insight into the sensitivity of the semi-hard triplet loss to its parameters and offer guidance for choosing the margin to ensure training stability.

Masanari Kimura

In many practical applications, regression models are employed to uncover relationships between predictors and a response variable, yet the common assumption of constant error variance is frequently violated. This issue is further compounded in high-dimensional settings where the number of predictors exceeds the sample size, necessitating regularization for effective estimation and variable selection. To address this problem, we propose the Heteroscedastic Double Bayesian Elastic Net (HDBEN), a novel framework that jointly models the mean and log-variance using hierarchical Bayesian priors incorporating both $\ell_1$ and $\ell_2$ penalties. Our approach simultaneously induces sparsity and grouping in the regression coefficients and variance parameters, capturing complex variance structures in the data. Theoretical results demonstrate that proposed HDBEN achieves posterior concentration, variable selection consistency, and asymptotic normality under mild conditions which justifying its behavior. Simulation studies further illustrate that HDBEN outperforms existing methods, particularly in scenarios characterized by heteroscedasticity and high dimensionality.

Masanari Kimura, Howard Bondell

Fréchet regression extends classical regression methods to non-Euclidean metric spaces, enabling the analysis of data relationships on complex structures such as manifolds and graphs. This work establishes a rigorous theoretical analysis for Fréchet regression through the lens of comparison geometry which leads to important considerations for its use in practice. The analysis provides key results on the existence, uniqueness, and stability of the Fréchet mean, along with statistical guarantees for nonparametric regression, including exponential concentration bounds and convergence rates. Additionally, insights into angle stability reveal the interplay between curvature of the manifold and the behavior of the regression estimator in these non-Euclidean contexts. Empirical experiments validate the theoretical findings, demonstrating the effectiveness of proposed hyperbolic mappings, particularly for data with heteroscedasticity, and highlighting the practical usefulness of these results.

Masanari Kimura, Howard Bondell

The density ratio of two probability distributions is one of the fundamental tools in mathematical and computational statistics and machine learning, and it has a variety of known applications. Therefore, density ratio estimation from finite samples is a very important task, but it is known to be unstable when the distributions are distant from each other. One approach to address this problem is density ratio estimation using incremental mixtures of the two distributions. We geometrically reinterpret existing methods for density ratio estimation based on incremental mixtures. We show that these methods can be regarded as iterating on the Riemannian manifold along a particular curve between the two probability distributions. Making use of the geometry of the manifold, we propose to consider incremental density ratio estimation along generalized geodesics on this manifold. To achieve such a method requires Monte Carlo sampling along geodesics via transformations of the two distributions. We show how to implement an iterative algorithm to sample along these geodesics and show how changing the distances along the geodesic affect the variance and accuracy of the estimation of the density ratio. Our experiments demonstrate that the proposed approach outperforms the existing approaches using incremental mixtures that do not take the geometry of the

Yuya Yoshikawa, Masanari Kimura, Ryotaro Shimizu et al.

Techniques that explain the predictions of black-box machine learning models are crucial to make the models transparent, thereby increasing trust in AI systems. The input features to the models often have a nested structure that consists of high- and low-level features, and each high-level feature is decomposed into multiple low-level features. For such inputs, both high-level feature attributions (HiFAs) and low-level feature attributions (LoFAs) are important for better understanding the model's decision. In this paper, we propose a model-agnostic local explanation method that effectively exploits the nested structure of the input to estimate the two-level feature attributions simultaneously. A key idea of the proposed method is to introduce the consistency property that should exist between the HiFAs and LoFAs, thereby bridging the separate optimization problems for estimating them. Thanks to this consistency property, the proposed method can produce HiFAs and LoFAs that are both faithful to the black-box models and consistent with each other, using a smaller number of queries to the models. In experiments on image classification in multiple instance learning and text classification using language models, we demonstrate that the HiFAs and LoFAs estimated by the proposed method are accurate, faithful to the behaviors of the black-box models, and provide consistent explanations.

Masanari Kimura, Takuma Nakamura, Yuki Saito

This paper addresses the problem of set-to-set matching, which involves matching two different sets of items based on some criteria, especially in the case of high-dimensional items like images. Although neural networks have been applied to solve this problem, most machine learning-based approaches assume that the training and test data follow the same distribution, which is not always true in real-world scenarios. To address this limitation, we introduce SHIFT15M, a dataset that can be used to evaluate set-to-set matching models when the distribution of data changes between training and testing. We conduct benchmark experiments that demonstrate the performance drop of naive methods due to distribution shift. Additionally, we provide software to handle the SHIFT15M dataset in a simple manner, with the URL for the software to be made available after publication of this manuscript. We believe proposed SHIFT15M dataset provide a valuable resource for evaluating set-to-set matching models under the distribution shift.

Masanari Kimura, Hideitsu Hino

The asymmetric skew divergence smooths one of the distributions by mixing it, to a degree determined by the parameter $λ$, with the other distribution. Such divergence is an approximation of the KL divergence that does not require the target distribution to be absolutely continuous with respect to the source distribution. In this paper, an information geometric generalization of the skew divergence called the $α$-geodesical skew divergence is proposed, and its properties are studied.

Masanari Kimura, Ryohei Izawa

Machine learning models suffer from overfitting, which is caused by a lack of labeled data. To tackle this problem, we proposed a framework of regularization methods, called density-fixing, that can be used commonly for supervised and semi-supervised learning. Our proposed regularization method improves the generalization performance by forcing the model to approximate the class's prior distribution or the frequency of occurrence. This regularization term is naturally derived from the formula of maximum likelihood estimation and is theoretically justified. We further provide the several theoretical analyses of the proposed method including asymptotic behavior. Our experimental results on multiple benchmark datasets are sufficient to support our argument, and we suggest that this simple and effective regularization method is useful in real-world machine learning problems.

Masanari Kimura

Machine learning techniques are used in a wide range of domains. However, machine learning models often suffer from the problem of over-fitting. Many data augmentation methods have been proposed to tackle such a problem, and one of them is called mixup. Mixup is a recently proposed regularization procedure, which linearly interpolates a random pair of training examples. This regularization method works very well experimentally, but its theoretical guarantee is not adequately discussed. In this study, we aim to discover why mixup works well from the aspect of the statistical learning theory.

Masanari Kimura

Earthquakes and tropical cyclones cause the suffering of millions of people around the world every year. The resulting landslides exacerbate the effects of these disasters. Landslide detection is, therefore, a critical task for the protection of human life and livelihood in mountainous areas. To tackle this problem, we propose a combination of satellite technology and Deep Neural Networks (DNNs). We evaluate the performance of multiple DNN-based methods for landslide detection on actual satellite images of landslide damage. Our analysis demonstrates the potential for a meaningful social impact in terms of disasters and rescue.

Masanari Kimura, Masayuki Tanaka

Deep neural networks (DNNs) are known as black-box models. In other words, it is difficult to interpret the internal state of the model. Improving the interpretability of DNNs is one of the hot research topics. However, at present, the definition of interpretability for DNNs is vague, and the question of what is a highly explanatory model is still controversial. To address this issue, we provide the definition of the human predictability of the model, as a part of the interpretability of the DNNs. The human predictability proposed in this paper is defined by easiness to predict the change of the inference when perturbating the model of the DNNs. In addition, we introduce one example of high human-predictable DNNs. We discuss that our definition will help to the research of the interpretability of the DNNs considering various types of applications.

Masanari Kimura

We propose the novel framework for anomaly detection in images. Our new framework, PNUNet, is based on many normal data and few anomalous data. We assume that some noises are added to the input images and learn to remove the noise. In addition, the proposed method achieves significant performance improvement by updating the noise assumed in the inputs using a self-training framework. The experimental results for the benchmark datasets show the usefulness of our new anomaly detection framework.

Masanari Kimura, Masayuki Tanaka

Convolutional Neural Networks have achieved impressive results in various tasks, but interpreting the internal mechanism is a challenging problem. To tackle this problem, we exploit a multi-channel attention mechanism in feature space. Our network architecture allows us to obtain an attention mask for each feature while existing CNN visualization methods provide only a common attention mask for all features. We apply the proposed multi-channel attention mechanism to multi-attribute recognition task. We can obtain different attention mask for each feature and for each attribute. Those analyses give us deeper insight into the feature space of CNNs. Furthermore, our proposed attention mechanism naturally derives a method for improving the robustness of CNNs. From the observation of feature space based on the proposed attention mask, we demonstrate that we can obtain robust CNNs by intentionally emphasizing features that are important for attributes. The experimental results for the benchmark dataset show that the proposed method gives high human interpretability while accurately grasping the attributes of the data, and improves network robustness.

Masanari Kimura, Masayuki Tanaka

Convolutional Neural Networks have achieved impressive results in various tasks, but interpreting the internal mechanism is a challenging problem. To tackle this problem, we exploit a multi-channel attention mechanism in feature space. Our network architecture allows us to obtain an attention mask for each feature while existing CNN visualization methods provide only a common attention mask for all features. We apply the proposed multi-channel attention mechanism to multi-attribute recognition task. We can obtain different attention mask for each feature and for each attribute. Those analyses give us deeper insight into the feature space of CNNs. The experimental results for the benchmark dataset show that the proposed method gives high interpretability to humans while accurately grasping the attributes of the data.

Masanari Kimura, Takashi Yanagihara

The detection and the quantification of anomalies in image data are critical tasks in industrial scenes such as detecting micro scratches on product. In recent years, due to the difficulty of defining anomalies and the limit of correcting their labels, research on unsupervised anomaly detection using generative models has attracted attention. Generally, in those studies, only normal images are used for training to model the distribution of normal images. The model measures the anomalies in the target images by reproducing the most similar images and scoring image patches indicating their fit to the learned distribution. This approach is based on a strong presumption; the trained model should not be able to generate abnormal images. However, in reality, the model can generate abnormal images mainly due to noisy normal data which include small abnormal pixels, and such noise severely affects the accuracy of the model. Therefore, we propose a novel anomaly detection method to distort the distribution of the model with existing abnormal images. The proposed method detects pixel-level micro anomalies with a high accuracy from 1024x1024 high resolution images which are actually used in an industrial scene. In this paper, we share experimental results on open datasets, due to the confidentiality of the data.

Kento Nozawa, Masanari Kimura, Atsunori Kanemura

Embedding graph nodes into a vector space can allow the use of machine learning to e.g. predict node classes, but the study of node embedding algorithms is immature compared to the natural language processing field because of a diverse nature of graphs. We examine the performance of node embedding algorithms with respect to graph centrality measures that characterize diverse graphs, through systematic experiments with four node embedding algorithms, four or five graph centralities, and six datasets. Experimental results give insights into the properties of node embedding algorithms, which can be a basis for further research on this topic.