Ichiro Takeuchi

Joshua Butke, Noriaki Hashimoto, Ichiro Takeuchi et al.

Whole-slide image analysis via the means of computational pathology often relies on processing tessellated gigapixel images with only slide-level labels available. Applying multiple instance learning-based methods or transformer models is computationally expensive as, for each image, all instances have to be processed simultaneously. The MLP-Mixer is an under-explored alternative model to common vision transformers, especially for large-scale datasets. Due to the lack of a self-attention mechanism, they have linear computational complexity to the number of input patches but achieve comparable performance on natural image datasets. We propose a combination of feature embedding and clustering to preprocess the full whole-slide image into a reduced prototype representation which can then serve as input to a suitable MLP-Mixer architecture. Our experiments on two public benchmarks and one inhouse malignant lymphoma dataset show comparable performance to current state-of-the-art methods, while achieving lower training costs in terms of computational time and memory load. Code is publicly available at https://github.com/butkej/ProtoMixer.

Shota Hozumi, Kentaro Kutsukake, Kota Matsui et al.

In material characterization, identifying defective areas on a material surface is fundamental. The conventional approach involves measuring the relevant physical properties point-by-point at the predetermined mesh grid points on the surface and determining the area at which the property does not reach the desired level. To identify defective areas more efficiently, we propose adaptive mapping methods in which measurement resources are used preferentially to detect the boundaries of defective areas. We interpret this problem as an active-learning (AL) of the level set estimation (LSE) problem. The goal of AL-based LSE is to determine the level set of the physical property function defined on the surface with as small number of measurements as possible. Furthermore, to handle the situations in which materials with similar specifications are repeatedly produced, we introduce a transfer learning approach so that the information of previously produced materials can be effectively utilized. As a proof-of-concept, we applied the proposed methods to the red-zone estimation problem of silicon wafers and demonstrated that we could identify the defective areas with significantly lower measurement costs than those of conventional methods.

Ryota Ozaki, Kazuki Ishikawa, Youhei Kanzaki et al.

There are a lot of real-world black-box optimization problems that need to optimize multiple criteria simultaneously. However, in a multi-objective optimization (MOO) problem, identifying the whole Pareto front requires the prohibitive search cost, while in many practical scenarios, the decision maker (DM) only needs a specific solution among the set of the Pareto optimal solutions. We propose a Bayesian optimization (BO) approach to identifying the most preferred solution in the MOO with expensive objective functions, in which a Bayesian preference model of the DM is adaptively estimated by an interactive manner based on the two types of supervisions called the pairwise preference and improvement request. To explore the most preferred solution, we define an acquisition function in which the uncertainty both in the objective functions and the DM preference is incorporated. Further, to minimize the interaction cost with the DM, we also propose an active learning strategy for the preference estimation. We empirically demonstrate the effectiveness of our proposed method through the benchmark function optimization and the hyper-parameter optimization problems for machine learning models.

Shion Takeno, Yu Inatsu, Masayuki Karasuyama et al.

Among various acquisition functions (AFs) in Bayesian optimization (BO), Gaussian process upper confidence bound (GP-UCB) and Thompson sampling (TS) are well-known options with established theoretical properties regarding Bayesian cumulative regret (BCR). Recently, it has been shown that a randomized variant of GP-UCB achieves a tighter BCR bound compared with GP-UCB, which we call the tighter BCR bound for brevity. Inspired by this study, this paper first shows that TS achieves the tighter BCR bound. On the other hand, GP-UCB and TS often practically suffer from manual hyperparameter tuning and over-exploration issues, respectively. Therefore, we analyze yet another AF called a probability of improvement from the maximum of a sample path (PIMS). We show that PIMS achieves the tighter BCR bound and avoids the hyperparameter tuning, unlike GP-UCB. Furthermore, we demonstrate a wide range of experiments, focusing on the effectiveness of PIMS that mitigates the practical issues of GP-UCB and TS.

Yu Inatsu, Shion Takeno, Kentaro Kutsukake et al.

Level set estimation (LSE), the problem of identifying the set of input points where a function takes value above (or below) a given threshold, is important in practical applications. When the function is expensive-to-evaluate and black-box, the \textit{straddle} algorithm, which is a representative heuristic for LSE based on Gaussian process models, and its extensions having theoretical guarantees have been developed. However, many of existing methods include a confidence parameter $β^{1/2}_t$ that must be specified by the user, and methods that choose $β^{1/2}_t$ heuristically do not provide theoretical guarantees. In contrast, theoretically guaranteed values of $β^{1/2}_t$ need to be increased depending on the number of iterations and candidate points, and are conservative and not good for practical performance. In this study, we propose a novel method, the \textit{randomized straddle} algorithm, in which $β_t$ in the straddle algorithm is replaced by a random sample from the chi-squared distribution with two degrees of freedom. The confidence parameter in the proposed method has the advantages of not needing adjustment, not depending on the number of iterations and candidate points, and not being conservative. Furthermore, we show that the proposed method has theoretical guarantees that depend on the sample complexity and the number of iterations. Finally, we confirm the usefulness of the proposed method through numerical experiments using synthetic and real data.

Tomonari Tanaka, Hiroyuki Hanada, Hanting Yang et al.

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.

Hiroyuki Hanada, Satoshi Akahane, Tatsuya Aoyama et al.

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.

Shuichi Nishino, Tomohiro Shiraishi, Teruyuki Katsuoka et al.

Graph Neural Networks (GNNs) have gained prominence for their ability to process graph-structured data across various domains. However, interpreting GNN decisions remains a significant challenge, leading to the adoption of saliency maps for identifying salient subgraphs composed of influential nodes and edges. Despite their utility, the reliability of GNN saliency maps has been questioned, particularly in terms of their robustness to input noise. In this study, we propose a statistical testing framework to rigorously evaluate the significance of saliency maps. Our main contribution lies in addressing the inflation of the Type I error rate caused by double-dipping of data, leveraging the framework of Selective Inference. Our method provides statistically valid $p$-values while controlling the Type I error rate, ensuring that identified salient subgraphs contain meaningful information rather than random artifacts. The method is applicable to a variety of saliency methods with piecewise linearity (e.g., Class Activation Mapping). We validate our method on synthetic and real-world datasets, demonstrating its capability in assessing the reliability of GNN interpretations.

Daiki Nishiyama, Hiroaki Miyoshi, Noriaki Hashimoto et al.

Malignant lymphoma subtype classification directly impacts treatment strategies and patient outcomes, necessitating classification models that achieve both high accuracy and sufficient explainability. This study proposes a novel explainable Multi-Instance Learning (MIL) framework that identifies subtype-specific Regions of Interest (ROIs) from Whole Slide Images (WSIs) while integrating cell distribution characteristics and image information. Our framework simultaneously addresses three objectives: (1) indicating appropriate ROIs for each subtype, (2) explaining the frequency and spatial distribution of characteristic cell types, and (3) achieving high-accuracy subtyping by leveraging both image and cell-distribution modalities. The proposed method fuses cell graph and image features extracted from each patch in the WSI using a Mixture-of-Experts (MoE) approach and classifies subtypes within an MIL framework. Experiments on a dataset of 1,233 WSIs demonstrate that our approach achieves state-of-the-art accuracy among ten comparative methods and provides region-level and cell-level explanations that align with a pathologist's perspectives.

Shion Takeno, Yoshito Okura, Yu Inatsu et al.

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.

Tatsuya Aoyama, Hanting Yang, Hiroyuki Hanada et al.

We propose Duality Gap KIP (DGKIP), an extension of the Kernel Inducing Points (KIP) method for dataset distillation. While existing dataset distillation methods often rely on bi-level optimization, DGKIP eliminates the need for such optimization by leveraging duality theory in convex programming. The KIP method has been introduced as a way to avoid bi-level optimization; however, it is limited to the squared loss and does not support other loss functions (e.g., cross-entropy or hinge loss) that are more suitable for classification tasks. DGKIP addresses this limitation by exploiting an upper bound on parameter changes after dataset distillation using the duality gap, enabling its application to a wider range of loss functions. We also characterize theoretical properties of DGKIP by providing upper bounds on the test error and prediction consistency after dataset distillation. Experimental results on standard benchmarks such as MNIST and CIFAR-10 demonstrate that DGKIP retains the efficiency of KIP while offering broader applicability and robust performance.

Kazuki Ishikawa, Ryota Ozaki, Yohei Kanzaki et al.

Selecting the optimal combination of a machine learning (ML) algorithm and its hyper-parameters is crucial for the development of high-performance ML systems. However, since the combination of ML algorithms and hyper-parameters is enormous, the exhaustive validation requires a significant amount of time. Many existing studies use Bayesian optimization (BO) for accelerating the search. On the other hand, a significant difficulty is that, in general, there exists a different hyper-parameter space for each one of candidate ML algorithms. BO-based approaches typically build a surrogate model independently for each hyper-parameter space, by which sufficient observations are required for all candidate ML algorithms. In this study, our proposed method embeds different hyper-parameter spaces into a shared latent space, in which a surrogate multi-task model for BO is estimated. This approach can share information of observations from different ML algorithms by which efficient optimization is expected with a smaller number of total observations. We further propose the pre-training of the latent space embedding with an adversarial regularization, and a ranking model for selecting an effective pre-trained embedding for a given target dataset. Our empirical study demonstrates effectiveness of the proposed method through datasets from OpenML.

Tomohiro Shiraishi, Tatsuya Matsukawa, Shuichi Nishino et al.

A data analysis pipeline is a structured sequence of steps that transforms raw data into meaningful insights by integrating various analysis algorithms. In this paper, we propose a novel statistical test to assess the significance of data analysis pipelines in feature selection problems. Our approach enables the systematic development of valid statistical tests applicable to any feature selection pipeline composed of predefined components. We develop this framework based on selective inference, a statistical technique that has recently gained attention for data-driven hypotheses. As a proof of concept, we consider feature selection pipelines for linear models, composed of three missing value imputation algorithms, three outlier detection algorithms, and three feature selection algorithms. We theoretically prove that our statistical test can control the probability of false positive feature selection at any desired level, and demonstrate its validity and effectiveness through experiments on synthetic and real data. Additionally, we present an implementation framework that facilitates testing across any configuration of these feature selection pipelines without extra implementation costs.

Hiroyuki Hanada, Tatsuya Aoyama, Satoshi Akahane et al.

We consider a machine learning setup where one training dataset is used to train multiple models across slightly different data distributions. This occurs when customized models are needed for various deployment environments. To reduce storage and training costs, we propose the DRSSS method, which combines distributionally robust (DR) optimization and safe sample screening (SSS). The key benefit of this method is that models trained on the reduced dataset will perform the same as those trained on the full dataset for all possible different environments. In this paper, we focus on covariate shift as a type of data distribution change and demonstrate the effectiveness of our method through experiments.

Ryota Sugiyama, Hiroki Toda, Vo Nguyen Le Duy et al.

In this paper, we study statistical inference of change-points (CPs) in multi-dimensional sequence. In CP detection from a multi-dimensional sequence, it is often desirable not only to detect the location, but also to identify the subset of the components in which the change occurs. Several algorithms have been proposed for such problems, but no valid exact inference method has been established to evaluate the statistical reliability of the detected locations and components. In this study, we propose a method that can guarantee the statistical reliability of both the location and the components of the detected changes. We demonstrate the effectiveness of the proposed method by applying it to the problems of genomic abnormality identification and human behavior analysis.

Vo Nguyen Le Duy, Ichiro Takeuchi

Conditional selective inference (SI) has been studied intensively as a new statistical inference framework for data-driven hypotheses. The basic concept of conditional SI is to make the inference conditional on the selection event, which enables an exact and valid statistical inference to be conducted even when the hypothesis is selected based on the data. Conditional SI has mainly been studied in the context of model selection, such as vanilla lasso or generalized lasso. The main limitation of existing approaches is the low statistical power owing to over-conditioning, which is required for computational tractability. In this study, we propose a more powerful and general conditional SI method for a class of problems that can be converted into quadratic parametric programming, which includes generalized lasso. The key concept is to compute the continuum path of the optimal solution in the direction of the selected test statistic and to identify the subset of the data space that corresponds to the model selection event by following the solution path. The proposed parametric programming-based method not only avoids the aforementioned major drawback of over-conditioning, but also improves the performance and practicality of SI in various respects. We conducted several experiments to demonstrate the effectiveness and efficiency of our proposed method.

Toshiaki Tsukurimichi, Yu Inatsu, Vo Nguyen Le Duy et al.

In practical data analysis under noisy environment, it is common to first use robust methods to identify outliers, and then to conduct further analysis after removing the outliers. In this paper, we consider statistical inference of the model estimated after outliers are removed, which can be interpreted as a selective inference (SI) problem. To use conditional SI framework, it is necessary to characterize the events of how the robust method identifies outliers. Unfortunately, the existing methods cannot be directly used here because they are applicable to the case where the selection events can be represented by linear/quadratic constraints. In this paper, we propose a conditional SI method for popular robust regressions by using homotopy method. We show that the proposed conditional SI method is applicable to a wide class of robust regression and outlier detection methods and has good empirical performance on both synthetic data and real data experiments.

Eugene Ndiaye, Ichiro Takeuchi

Conformal prediction constructs a confidence set for an unobserved response of a feature vector based on previous identically distributed and exchangeable observations of responses and features. It has a coverage guarantee at any nominal level without additional assumptions on their distribution. Its computation deplorably requires a refitting procedure for all replacement candidates of the target response. In regression settings, this corresponds to an infinite number of model fits. Apart from relatively simple estimators that can be written as pieces of linear function of the response, efficiently computing such sets is difficult, and is still considered as an open problem. We exploit the fact that, \emph{often}, conformal prediction sets are intervals whose boundaries can be efficiently approximated by classical root-finding algorithms. We investigate how this approach can overcome many limitations of formerly used strategies; we discuss its complexity and drawbacks.

Yu Inatsu, Shogo Iwazaki, Ichiro Takeuchi

Many cases exist in which a black-box function $f$ with high evaluation cost depends on two types of variables $\bm x$ and $\bm w$, where $\bm x$ is a controllable \emph{design} variable and $\bm w$ are uncontrollable \emph{environmental} variables that have random variation following a certain distribution $P$. In such cases, an important task is to find the range of design variables $\bm x$ such that the function $f(\bm x, \bm w)$ has the desired properties by incorporating the random variation of the environmental variables $\bm w$. A natural measure of robustness is the probability that $f(\bm x, \bm w)$ exceeds a given threshold $h$, which is known as the \emph{probability threshold robustness} (PTR) measure in the literature on robust optimization. However, this robustness measure cannot be correctly evaluated when the distribution $P$ is unknown. In this study, we addressed this problem by considering the \textit{distributionally robust PTR} (DRPTR) measure, which considers the worst-case PTR within given candidate distributions. Specifically, we studied the problem of efficiently identifying a reliable set $H$, which is defined as a region in which the DRPTR measure exceeds a certain desired probability $α$, which can be interpreted as a level set estimation (LSE) problem for DRPTR. We propose a theoretically grounded and computationally efficient active learning method for this problem. We show that the proposed method has theoretical guarantees on convergence and accuracy, and confirmed through numerical experiments that the proposed method outperforms existing methods.

Kazuya Sugiyama, Vo Nguyen Le Duy, Ichiro Takeuchi

Conditional selective inference (SI) has been actively studied as a new statistical inference framework for data-driven hypotheses. The basic idea of conditional SI is to make inferences conditional on the selection event characterized by a set of linear and/or quadratic inequalities. Conditional SI has been mainly studied in the context of feature selection such as stepwise feature selection (SFS). The main limitation of the existing conditional SI methods is the loss of power due to over-conditioning, which is required for computational tractability. In this study, we develop a more powerful and general conditional SI method for SFS using the homotopy method which enables us to overcome this limitation. The homotopy-based SI is especially effective for more complicated feature selection algorithms. As an example, we develop a conditional SI method for forward-backward SFS with AIC-based stopping criteria and show that it is not adversely affected by the increased complexity of the algorithm. We conduct several experiments to demonstrate the effectiveness and efficiency of the proposed method.

Rory Bunker, Keisuke Fujii, Hiroyuki Hanada et al.

Given a set of sequences comprised of time-ordered events, sequential pattern mining is useful to identify frequent subsequences from different sequences or within the same sequence. However, in sport, these techniques cannot determine the importance of particular patterns of play to good or bad outcomes, which is often of greater interest to coaches and performance analysts. In this study, we apply a recently proposed supervised sequential pattern mining algorithm called safe pattern pruning (SPP) to 490 labelled event sequences representing passages of play from one rugby team's matches from the 2018 Japan Top League. We compare the SPP-obtained patterns that are the most discriminative between scoring and non-scoring outcomes from both the team's and opposition teams' perspectives, with the most frequent patterns obtained with well-known unsupervised sequential pattern mining algorithms when applied to subsets of the original dataset, split on the label. Our obtained results found that linebreaks, successful lineouts, regained kicks in play, repeated phase-breakdown play, and failed exit plays by the opposition team were identified as as the patterns that discriminated most between the team scoring and not scoring. Opposition team linebreaks, errors made by the team, opposition team lineouts, and repeated phase-breakdown play by the opposition team were identified as the patterns that discriminated most between the opposition team scoring and not scoring. It was also found that, by virtue of its supervised nature as well as its pruning and safe-screening properties, SPP obtained a greater variety of generally more sophisticated patterns than the unsupervised models, which are likely to be of more utility to coaches and performance analysts.

Vo Nguyen Le Duy, Shogo Iwazaki, Ichiro Takeuchi

Although a vast body of literature relates to image segmentation methods that use deep neural networks (DNNs), less attention has been paid to assessing the statistical reliability of segmentation results. In this study, we interpret the segmentation results as hypotheses driven by DNN (called DNN-driven hypotheses) and propose a method by which to quantify the reliability of these hypotheses within a statistical hypothesis testing framework. Specifically, we consider a statistical hypothesis test for the difference between the object and background regions. This problem is challenging, as the difference would be falsely large because of the adaptation of the DNN to the data. To overcome this difficulty, we introduce a conditional selective inference (SI) framework -- a new statistical inference framework for data-driven hypotheses that has recently received considerable attention -- to compute exact (non-asymptotic) valid p-values for the segmentation results. To use the conditional SI framework for DNN-based segmentation, we develop a new SI algorithm based on the homotopy method, which enables us to derive the exact (non-asymptotic) sampling distribution of DNN-driven hypothesis. We conduct experiments on both synthetic and real-world datasets, through which we offer evidence that our proposed method can successfully control the false positive rate, has good performance in terms of computational efficiency, and provides good results when applied to medical image data.

Shogo Iwazaki, Yu Inatsu, Ichiro Takeuchi

We consider active learning (AL) in an uncertain environment in which trade-off between multiple risk measures need to be considered. As an AL problem in such an uncertain environment, we study Mean-Variance Analysis in Bayesian Optimization (MVA-BO) setting. Mean-variance analysis was developed in the field of financial engineering and has been used to make decisions that take into account the trade-off between the average and variance of investment uncertainty. In this paper, we specifically focus on BO setting with an uncertain component and consider multi-task, multi-objective, and constrained optimization scenarios for the mean-variance trade-off of the uncertain component. When the target blackbox function is modeled by Gaussian Process (GP), we derive the bounds of the two risk measures and propose AL algorithm for each of the above three problems based on the risk measure bounds. We show the effectiveness of the proposed AL algorithms through theoretical analysis and numerical experiments.

Shogo Iwazaki, Yu Inatsu, Ichiro Takeuchi

In many product development problems, the performance of the product is governed by two types of parameters called design parameter and environmental parameter. While the former is fully controllable, the latter varies depending on the environment in which the product is used. The challenge of such a problem is to find the design parameter that maximizes the probability that the performance of the product will meet the desired requisite level given the variation of the environmental parameter. In this paper, we formulate this practical problem as active learning (AL) problems and propose efficient algorithms with theoretically guaranteed performance. Our basic idea is to use Gaussian Process (GP) model as the surrogate model of the product development process, and then to formulate our AL problems as Bayesian Quadrature Optimization problems for probabilistic threshold robustness (PTR) measure. We derive credible intervals for the PTR measure and propose AL algorithms for the optimization and level set estimation of the PTR measure. We clarify the theoretical properties of the proposed algorithms and demonstrate their efficiency in both synthetic and real-world product development problems.

Vo Nguyen Le Duy, Ichiro Takeuchi

Selective Inference (SI) has been actively studied in the past few years for conducting inference on the features of linear models that are adaptively selected by feature selection methods such as Lasso. The basic idea of SI is to make inference conditional on the selection event. Unfortunately, the main limitation of the original SI approach for Lasso is that the inference is conducted not only conditional on the selected features but also on their signs -- this leads to loss of power because of over-conditioning. Although this limitation can be circumvented by considering the union of such selection events for all possible combinations of signs, this is only feasible when the number of selected features is sufficiently small. To address this computational bottleneck, we propose a parametric programming-based method that can conduct SI without conditioning on signs even when we have thousands of active features. The main idea is to compute the continuum path of Lasso solutions in the direction of a test statistic, and identify the subset of the data space corresponding to the feature selection event by following the solution path. The proposed parametric programming-based method not only avoids the aforementioned computational bottleneck but also improves the performance and practicality of SI for Lasso in various respects. We conduct several experiments to demonstrate the effectiveness and efficiency of our proposed method.

Vo Nguyen Le Duy, Hiroki Toda, Ryota Sugiyama et al.

There is a vast body of literature related to methods for detecting changepoints (CP). However, less attention has been paid to assessing the statistical reliability of the detected CPs. In this paper, we introduce a novel method to perform statistical inference on the significance of the CPs, estimated by a Dynamic Programming (DP)-based optimal CP detection algorithm. Based on the selective inference (SI) framework, we propose an exact (non-asymptotic) approach to compute valid p-values for testing the significance of the CPs. Although it is well-known that SI has low statistical power because of over-conditioning, we address this disadvantage by introducing parametric programming techniques. Then, we propose an efficient method to conduct SI with the minimum amount of conditioning, leading to high statistical power. We conduct experiments on both synthetic and real-world datasets, through which we offer evidence that our proposed method is more powerful than existing methods, has decent performance in terms of computational efficiency, and provides good results in many practical applications.

Tomoki Yoshida, Ichiro Takeuchi, Masayuki Karasuyama

Graphs are versatile tools for representing structured data. As a result, a variety of machine learning methods have been studied for graph data analysis. Although many such learning methods depend on the measurement of differences between input graphs, defining an appropriate distance metric for graphs remains a controversial issue. Hence, we propose a supervised distance metric learning method for the graph classification problem. Our method, named interpretable graph metric learning (IGML), learns discriminative metrics in a subgraph-based feature space, which has a strong graph representation capability. By introducing a sparsity-inducing penalty on the weight of each subgraph, IGML can identify a small number of important subgraphs that can provide insight into the given classification task. Because our formulation has a large number of optimization variables, an efficient algorithm that uses pruning techniques based on safe screening and working set selection methods is also proposed. An important property of IGML is that solution optimality is guaranteed because the problem is formulated as a convex problem and our pruning strategies only discard unnecessary subgraphs. Furthermore, we show that IGML is also applicable to other structured data such as itemset and sequence data, and that it can incorporate vertex-label similarity by using a transportation-based subgraph feature. We empirically evaluate the computational efficiency and classification performance of IGML on several benchmark datasets and provide some illustrative examples of how IGML identifies important subgraphs from a given graph dataset.

Noriaki Hashimoto, Daisuke Fukushima, Ryoichi Koga et al.

We propose a new method for cancer subtype classification from histopathological images, which can automatically detect tumor-specific features in a given whole slide image (WSI). The cancer subtype should be classified by referring to a WSI, i.e., a large-sized image (typically 40,000x40,000 pixels) of an entire pathological tissue slide, which consists of cancer and non-cancer portions. One difficulty arises from the high cost associated with annotating tumor regions in WSIs. Furthermore, both global and local image features must be extracted from the WSI by changing the magnifications of the image. In addition, the image features should be stably detected against the differences of staining conditions among the hospitals/specimens. In this paper, we develop a new CNN-based cancer subtype classification method by effectively combining multiple-instance, domain adversarial, and multi-scale learning frameworks in order to overcome these practical difficulties. When the proposed method was applied to malignant lymphoma subtype classifications of 196 cases collected from multiple hospitals, the classification performance was significantly better than the standard CNN or other conventional methods, and the accuracy compared favorably with that of standard pathologists.

Kota Matsui, Shunya Kusakawa, Keisuke Ando et al.

In this paper, we propose an active learning method for an inverse problem that aims to find an input that achieves a desired structured-output. The proposed method provides new acquisition functions for minimizing the error between the desired structured-output and the prediction of a Gaussian process model, by effectively incorporating the correlation between multiple outputs of the underlying multi-valued black box output functions. The effectiveness of the proposed method is verified by applying it to two synthetic shape search problem and real data. In the real data experiment, we tackle the input parameter search which achieves the desired crystal growth rate in silicon carbide (SiC) crystal growth modeling, that is a problem of materials informatics.

Shogo Iwazaki, Yu Inatsu, Ichiro Takeuchi

In the manufacturing industry, it is often necessary to repeat expensive operational testing of machine in order to identify the range of input conditions under which the machine operates properly. Since it is often difficult to accurately control the input conditions during the actual usage of the machine, there is a need to guarantee the performance of the machine after properly incorporating the possible variation in input conditions. In this paper, we formulate this practical manufacturing scenario as an Input Uncertain Reliable Level Set Estimation (IU-rLSE) problem, and provide an efficient algorithm for solving it. The goal of IU-rLSE is to identify the input range in which the outputs smaller/greater than a desired threshold can be obtained with high probability when the input uncertainty is properly taken into consideration. We propose an active learning method to solve the IU-rLSE problem efficiently, theoretically analyze its accuracy and convergence, and illustrate its empirical performance through numerical experiments on artificial and real data.

Eugene Ndiaye, Ichiro Takeuchi

If you are predicting the label $y$ of a new object with $\hat y$, how confident are you that $y = \hat y$? Conformal prediction methods provide an elegant framework for answering such question by building a $100 (1 - α)\%$ confidence region without assumptions on the distribution of the data. It is based on a refitting procedure that parses all the possibilities for $y$ to select the most likely ones. Although providing strong coverage guarantees, conformal set is impractical to compute exactly for many regression problems. We propose efficient algorithms to compute conformal prediction set using approximated solution of (convex) regularized empirical risk minimization. Our approaches rely on a new homotopy continuation technique for tracking the solution path with respect to sequential changes of the observations. We also provide a detailed analysis quantifying its complexity.

Kosuke Tanizaki, Noriaki Hashimoto, Yu Inatsu et al.

Image segmentation is one of the most fundamental tasks of computer vision. In many practical applications, it is essential to properly evaluate the reliability of individual segmentation results. In this study, we propose a novel framework to provide the statistical significance of segmentation results in the form of p-values. Specifically, we consider a statistical hypothesis test for determining the difference between the object and the background regions. This problem is challenging because the difference can be deceptively large (called segmentation bias) due to the adaptation of the segmentation algorithm to the data. To overcome this difficulty, we introduce a statistical approach called selective inference, and develop a framework to compute valid p-values in which the segmentation bias is properly accounted for. Although the proposed framework is potentially applicable to various segmentation algorithms, we focus in this paper on graph cut-based and threshold-based segmentation algorithms, and develop two specific methods to compute valid p-values for the segmentation results obtained by these algorithms. We prove the theoretical validity of these two methods and demonstrate their practicality by applying them to segmentation problems for medical images.

Vo Nguyen Le Duy, Takuto Sakuma, Taiju Ishiyama et al.

We study the problem of discriminative sub-trajectory mining. Given two groups of trajectories, the goal of this problem is to extract moving patterns in the form of sub-trajectories which are more similar to sub-trajectories of one group and less similar to those of the other. We propose a new method called Statistically Discriminative Sub-trajectory Mining (SDSM) for this problem. An advantage of the SDSM method is that the statistical significance of the extracted sub-trajectories are properly controlled in the sense that the probability of finding a false positive sub-trajectory is smaller than a specified significance threshold alpha (e.g., 0.05), which is indispensable when the method is used in scientific or social studies under noisy environment. Finding such statistically discriminative sub-trajectories from massive trajectory dataset is both computationally and statistically challenging. In the SDSM method, we resolve the difficulties by introducing a tree representation among sub-trajectories and running an efficient permutation-based statistical inference method on the tree. To the best of our knowledge, SDSM is the first method that can efficiently extract statistically discriminative sub-trajectories from massive trajectory dataset. We illustrate the effectiveness and scalability of the SDSM method by applying it to a real-world dataset with 1,000,000 trajectories which contains 16,723,602,505 sub-trajectories.

Yu Inatsu, Daisuke Sugita, Kazuaki Toyoura et al.

We study active learning (AL) based on Gaussian Processes (GPs) for efficiently enumerating all of the local minimum solutions of a black-box function. This problem is challenging due to the fact that local solutions are characterized by their zero gradient and positive-definite Hessian properties, but those derivatives cannot be directly observed. We propose a new AL method in which the input points are sequentially selected such that the confidence intervals of the GP derivatives are effectively updated for enumerating local minimum solutions. We theoretically analyze the proposed method and demonstrate its usefulness through numerical experiments.

Shion Takeno, Hitoshi Fukuoka, Yuhki Tsukada et al.

In a standard setting of Bayesian optimization (BO), the objective function evaluation is assumed to be highly expensive. Multi-fidelity Bayesian optimization (MFBO) accelerates BO by incorporating lower fidelity observations available with a lower sampling cost. In this paper, we focus on the information-based approach, which is a popular and empirically successful approach in BO. For MFBO, however, existing information-based methods are plagued by difficulty in estimating the information gain. We propose an approach based on max-value entropy search (MES), which greatly facilitates computations by considering the entropy of the optimal function value instead of the optimal input point. We show that, in our multi-fidelity MES (MF-MES), most of additional computations, compared with usual MES, is reduced to analytical computations. Although an additional numerical integration is necessary for the information across different fidelities, this is only in one dimensional space, which can be performed efficiently and accurately. Further, we also propose parallelization of MF-MES. Since there exist a variety of different sampling costs, queries typically occur asynchronously in MFBO. We show that similar simple computations can be derived for asynchronous parallel MFBO. We demonstrate effectiveness of our approach by using benchmark datasets and a real-world application to materials science data.

Eugene Ndiaye, Tam Le, Olivier Fercoq et al.

Popular machine learning estimators involve regularization parameters that can be challenging to tune, and standard strategies rely on grid search for this task. In this paper, we revisit the techniques of approximating the regularization path up to predefined tolerance $ε$ in a unified framework and show that its complexity is $O(1/\sqrt[d]ε)$ for uniformly convex loss of order $d \geq 2$ and $O(1/\sqrtε)$ for Generalized Self-Concordant functions. This framework encompasses least-squares but also logistic regression, a case that as far as we know was not handled as precisely in previous works. We leverage our technique to provide refined bounds on the validation error as well as a practical algorithm for hyperparameter tuning. The latter has global convergence guarantee when targeting a prescribed accuracy on the validation set. Last but not least, our approach helps relieving the practitioner from the (often neglected) task of selecting a stopping criterion when optimizing over the training set: our method automatically calibrates this criterion based on the targeted accuracy on the validation set.

Hiroki Kato, Hiroyuki Hanada, Ichiro Takeuchi

We consider the problem of learning a sparse rule model, a prediction model in the form of a sparse linear combination of rules, where a rule is an indicator function defined over a hyper-rectangle in the input space. Since the number of all possible such rules is extremely large, it has been computationally intractable to select the optimal set of active rules. In this paper, to solve this difficulty for learning the optimal sparse rule model, we propose Safe RuleFit (SRF). Our basic idea is to develop meta safe screening (mSS), which is a non-trivial extension of well-known safe screening (SS) techniques. While SS is used for screening out one feature, mSS can be used for screening out multiple features by exploiting the inclusion-relations of hyper-rectangles in the input space. SRF provides a general framework for fitting sparse rule models for regression and classification, and it can be extended to handle more general sparse regularizations such as group regularization. We demonstrate the advantages of SRF through intensive numerical experiments.

Hiroyuki Hanada, Toshiyuki Takada, Jun Sakuma et al.

The problem of machine learning with missing values is common in many areas. A simple approach is to first construct a dataset without missing values simply by discarding instances with missing entries or by imputing a fixed value for each missing entry, and then train a prediction model with the new dataset. A drawback of this naive approach is that the uncertainty in the missing entries is not properly incorporated in the prediction. In order to evaluate prediction uncertainty, the multiple imputation (MI) approach has been studied, but the performance of MI is sensitive to the choice of the probabilistic model of the true values in the missing entries, and the computational cost of MI is high because multiple models must be trained. In this paper, we propose an alternative approach called the Interval-based Prediction Uncertainty Bounding (IPUB) method. The IPUB method represents the uncertainties due to missing entries as intervals, and efficiently computes the lower and upper bounds of the prediction results when all possible training sets constructed by imputing arbitrary values in the intervals are considered. The IPUB method can be applied to a wide class of convex learning algorithms including penalized least-squares regression, support vector machine (SVM), and logistic regression. We demonstrate the advantages of the IPUB method by comparing it with an existing method in numerical experiment with benchmark datasets.

Makoto Yamada, Denny Wu, Yao-Hung Hubert Tsai et al.

Measuring divergence between two distributions is essential in machine learning and statistics and has various applications including binary classification, change point detection, and two-sample test. Furthermore, in the era of big data, designing divergence measure that is interpretable and can handle high-dimensional and complex data becomes extremely important. In the paper, we propose a post selection inference (PSI) framework for divergence measure, which can select a set of statistically significant features that discriminate two distributions. Specifically, we employ an additive variant of maximum mean discrepancy (MMD) for features and introduce a general hypothesis test for PSI. A novel MMD estimator using the incomplete U-statistics, which has an asymptotically Normal distribution (under mild assumptions) and gives high detection power in PSI, is also proposed and analyzed theoretically. Through synthetic and real-world feature selection experiments, we show that the proposed framework can successfully detect statistically significant features. Last, we propose a sample selection framework for analyzing different members in the Generative Adversarial Networks (GANs) family.

Yao-Hung Hubert Tsai, Makoto Yamada, Denny Wu et al.

"Which Generative Adversarial Networks (GANs) generates the most plausible images?" has been a frequently asked question among researchers. To address this problem, we first propose an \emph{incomplete} U-statistics estimate of maximum mean discrepancy $\mathrm{MMD}_{inc}$ to measure the distribution discrepancy between generated and real images. $\mathrm{MMD}_{inc}$ enjoys the advantages of asymptotic normality, computation efficiency, and model agnosticity. We then propose a GANs analysis framework to select and test the "best" member in GANs family using the Post Selection Inference (PSI) with $\mathrm{MMD}_{inc}$. In the experiments, we adopt the proposed framework on 7 GANs variants and compare their $\mathrm{MMD}_{inc}$ scores.

Tomoki Yoshida, Ichiro Takeuchi, Masayuki Karasuyama

We study safe screening for metric learning. Distance metric learning can optimize a metric over a set of triplets, each one of which is defined by a pair of same class instances and an instance in a different class. However, the number of possible triplets is quite huge even for a small dataset. Our safe triplet screening identifies triplets which can be safely removed from the optimization problem without losing the optimality. Compared with existing safe screening studies, triplet screening is particularly significant because of (1) the huge number of possible triplets, and (2) the semi-definite constraint in the optimization. We derive several variants of screening rules, and analyze their relationships. Numerical experiments on benchmark datasets demonstrate the effectiveness of safe triplet screening.

Yuta Umezu, Ichiro Takeuchi

We study the problem of detecting change points (CPs) that are characterized by a subset of dimensions in a multi-dimensional sequence. A method for detecting those CPs can be formulated as a two-stage method: one for selecting relevant dimensions, and another for selecting CPs. It has been difficult to properly control the false detection probability of these CP detection methods because selection bias in each stage must be properly corrected. Our main contribution in this paper is to formulate a CP detection problem as a selective inference problem, and show that exact (non-asymptotic) inference is possible for a class of CP detection methods. We demonstrate the performances of the proposed selective inference framework through numerical simulations and its application to our motivating medical data analysis problem.

Atsushi Shibagaki, Ichiro Takeuchi

We study primal-dual type stochastic optimization algorithms with non-uniform sampling. Our main theoretical contribution in this paper is to present a convergence analysis of Stochastic Primal Dual Coordinate (SPDC) Method with arbitrary sampling. Based on this theoretical framework, we propose Optimality Violation-based Sampling SPDC (ovsSPDC), a non-uniform sampling method based on Optimality Violation. We also propose two efficient heuristic variants of ovsSPDC called ovsSDPC+ and ovsSDPC++. Through intensive numerical experiments, we demonstrate that the proposed method and its variants are faster than other state-of-the-art primal-dual type stochastic optimization methods.

Makoto Yamada, Yuta Umezu, Kenji Fukumizu et al.

We propose a novel kernel based post selection inference (PSI) algorithm, which can not only handle non-linearity in data but also structured output such as multi-dimensional and multi-label outputs. Specifically, we develop a PSI algorithm for independence measures, and propose the Hilbert-Schmidt Independence Criterion (HSIC) based PSI algorithm (hsicInf). The novelty of the proposed algorithm is that it can handle non-linearity and/or structured data through kernels. Namely, the proposed algorithm can be used for wider range of applications including nonlinear multi-class classification and multi-variate regressions, while existing PSI algorithms cannot handle them. Through synthetic experiments, we show that the proposed approach can find a set of statistically significant features for both regression and classification problems. Moreover, we apply the hsicInf algorithm to a real-world data, and show that hsicInf can successfully identify important features.

Hiroyuki Hanada, Atsushi Shibagaki, Jun Sakuma et al.

We study large-scale classification problems in changing environments where a small part of the dataset is modified, and the effect of the data modification must be quickly incorporated into the classifier. When the entire dataset is large, even if the amount of the data modification is fairly small, the computational cost of re-training the classifier would be prohibitively large. In this paper, we propose a novel method for efficiently incorporating such a data modification effect into the classifier without actually re-training it. The proposed method provides bounds on the unknown optimal classifier with the cost only proportional to the size of the data modification. We demonstrate through numerical experiments that the proposed method provides sufficiently tight bounds with negligible computational costs, especially when a small part of the dataset is modified in a large-scale classification problem.

Shinya Suzumura, Kazuya Nakagawa, Mahito Sugiyama et al.

Discovering statistically significant patterns from databases is an important challenging problem. The main obstacle of this problem is in the difficulty of taking into account the selection bias, i.e., the bias arising from the fact that patterns are selected from extremely large number of candidates in databases. In this paper, we introduce a new approach for predictive pattern mining problems that can address the selection bias issue. Our approach is built on a recently popularized statistical inference framework called selective inference. In selective inference, statistical inferences (such as statistical hypothesis testing) are conducted based on sampling distributions conditional on a selection event. If the selection event is characterized in a tractable way, statistical inferences can be made without minding selection bias issue. However, in pattern mining problems, it is difficult to characterize the entire selection process of mining algorithms. Our main contribution in this paper is to solve this challenging problem for a class of predictive pattern mining problems by introducing a novel algorithmic framework. We demonstrate that our approach is useful for finding statistically significant patterns from databases.

Toshiyuki Takada, Hiroyuki Hanada, Yoshiji Yamada et al.

Privacy concern has been increasingly important in many machine learning (ML) problems. We study empirical risk minimization (ERM) problems under secure multi-party computation (MPC) frameworks. Main technical tools for MPC have been developed based on cryptography. One of limitations in current cryptographically private ML is that it is computationally intractable to evaluate non-linear functions such as logarithmic functions or exponential functions. Therefore, for a class of ERM problems such as logistic regression in which non-linear function evaluations are required, one can only obtain approximate solutions. In this paper, we introduce a novel cryptographically private tool called secure approximation guarantee (SAG) method. The key property of SAG method is that, given an arbitrary approximate solution, it can provide a non-probabilistic assumption-free bound on the approximation quality under cryptographically secure computation framework. We demonstrate the benefit of the SAG method by applying it to several problems including a practical privacy-preserving data analysis task on genomic and clinical information.

Kazuya Nakagawa, Shinya Suzumura, Masayuki Karasuyama et al.

In this paper we study predictive pattern mining problems where the goal is to construct a predictive model based on a subset of predictive patterns in the database. Our main contribution is to introduce a novel method called safe pattern pruning (SPP) for a class of predictive pattern mining problems. The SPP method allows us to efficiently find a superset of all the predictive patterns in the database that are needed for the optimal predictive model. The advantage of the SPP method over existing boosting-type method is that the former can find the superset by a single search over the database, while the latter requires multiple searches. The SPP method is inspired by recent development of safe feature screening. In order to extend the idea of safe feature screening into predictive pattern mining, we derive a novel pruning rule called safe pattern pruning (SPP) rule that can be used for searching over the tree defined among patterns in the database. The SPP rule has a property that, if a node corresponding to a pattern in the database is pruned out by the SPP rule, then it is guaranteed that all the patterns corresponding to its descendant nodes are never needed for the optimal predictive model. We apply the SPP method to graph mining and item-set mining problems, and demonstrate its computational advantage.

Atsushi Shibagaki, Masayuki Karasuyama, Kohei Hatano et al.

The problem of learning a sparse model is conceptually interpreted as the process of identifying active features/samples and then optimizing the model over them. Recently introduced safe screening allows us to identify a part of non-active features/samples. So far, safe screening has been individually studied either for feature screening or for sample screening. In this paper, we introduce a new approach for safely screening features and samples simultaneously by alternatively iterating feature and sample screening steps. A significant advantage of considering them simultaneously rather than individually is that they have a synergy effect in the sense that the results of the previous safe feature screening can be exploited for improving the next safe sample screening performances, and vice-versa. We first theoretically investigate the synergy effect, and then illustrate the practical advantage through intensive numerical experiments for problems with large numbers of features and samples.

Shinya Suzumura, Kohei Ogawa, Masashi Sugiyama et al.

In support vector machine (SVM) applications with unreliable data that contains a portion of outliers, non-robustness of SVMs often causes considerable performance deterioration. Although many approaches for improving the robustness of SVMs have been studied, two major challenges remain in robust SVM learning. First, robust learning algorithms are essentially formulated as non-convex optimization problems. It is thus important to develop a non-convex optimization method for robust SVM that can find a good local optimal solution. The second practical issue is how one can tune the hyperparameter that controls the balance between robustness and efficiency. Unfortunately, due to the non-convexity, robust SVM solutions with slightly different hyper-parameter values can be significantly different, which makes model selection highly unstable. In this paper, we address these two issues simultaneously by introducing a novel homotopy approach to non-convex robust SVM learning. Our basic idea is to introduce parametrized formulations of robust SVM which bridge the standard SVM and fully robust SVM via the parameter that represents the influence of outliers. We characterize the necessary and sufficient conditions of the local optimal solutions of robust SVM, and develop an algorithm that can trace a path of local optimal solutions when the influence of outliers is gradually decreased. An advantage of our homotopy approach is that it can be interpreted as simulated annealing, a common approach for finding a good local optimal solution in non-convex optimization problems. In addition, our homotopy method allows stable and efficient model selection based on the path of local optimal solutions. Empirical performances of the proposed approach are demonstrated through intensive numerical experiments both on robust classification and regression problems.