The class imbalance is a major issue in classification, i.e., the sample size of a rare class (positive) is often a performance bottleneck. In real-world situations, however, “near-miss” positive instances, i.e., negative but nearly-positive instances, are sometimes plentiful. For example, natural disasters such as floods are rare, while there are relatively plentiful near-miss cases where actual floods did not occur but the water level approached the bank height. We show that even when the true positive cases are quite limited, such as in disaster forecasting, the accuracy can be improved by obtaining refined label-like side-information “positivity” (e.g., the water level of the river) to distinguish near-miss cases from other negatives. Conventional cost-sensitive classification cannot utilize such side-information, and the small size of the positive sample causes high estimation variance. Our approach is in line with learning using privileged information (LUPI), which exploits side-information for training without predicting the side-information itself. We theoretically prove that our method reduces the estimation variance, provided that near-miss positive instances are plentiful, in exchange for additional bias. Results of extensive experiments demonstrate that our method tends to outperform or compares favorably to existing approaches.

Unsupervised representation learning is one of the most important problems in machine learning. A recent promising approach is contrastive learning: A feature representation of data is learned by solving a pseudo classification problem where class labels are automatically generated from unlabelled data. However, it is not straightforward to understand what representation contrastive learning yields through the classification problem. In addition, most of practical methods for contrastive learning are based on the maximum likelihood estimation, which is often vulnerable to the contamination by outliers. In order to promote the understanding to contrastive learning, this paper first theoretically shows a connection to maximization of mutual information (MI). Our result indicates that density ratio estimation is necessary and sufficient for maximization of MI under some conditions. Since popular objective functions for classification can be regarded as estimating density ratios, contrastive learning related to density ratio estimation can be interpreted as maximizing MI. Next, in terms of density ratio estimation, we establish new recovery conditions for the latent source components in nonlinear independent component analysis (ICA). In contrast with existing work, the established conditions include a novel insight for the dimensionality of data, which is clearly supported by numerical experiments. Furthermore, inspired by nonlinear ICA, we propose a novel framework to estimate a nonlinear subspace for lower-dimensional latent source components, and some theoretical conditions for the subspace estimation are established with density ratio estimation. Motivated by the theoretical results, we propose a practical method through outlier-robust density ratio estimation, which can be seen as performing maximization of MI, nonlinear ICA or nonlinear subspace estimation. Moreover, a sample-efficient nonlinear ICA method is also proposed based on a variational lower-bound of MI. Then, we theoretically investigate outlier-robustness of the proposed methods. Finally, we numerically demonstrate usefulness of the proposed methods in nonlinear ICA and through application to a downstream task for linear classification.

Predicting which action (treatment) will lead to a better outcome is a central task in decision support systems. To build a prediction model in real situations, learning from observational data with a sampling bias is a critical issue due to the lack of randomized controlled trial (RCT) data. To handle such biased observational data, recent efforts in causal inference and counterfactual machine learning have focused on debiased estimation of the potential outcomes on a binary action space and the difference between them, namely, the individual treatment effect. When it comes to a large action space (e.g., selecting an appropriate combination of medicines for a patient), however, the regression accuracy of the potential outcomes is no longer sufficient in practical terms to achieve a good decision-making performance. This is because a high mean accuracy on the large action space does not guarantee the nonexistence of a single potential outcome misestimation that misleads the whole decision. Our proposed loss minimizes the classification error of whether or not the action is relatively good for the individual target among all feasible actions, which further improves the decision-making performance, as we demonstrate. We also propose a network architecture and a regularizer that extracts a debiased representation not only from the individual feature but also from the biased action for better generalization in large action spaces. Extensive experiments on synthetic and semi-synthetic datasets demonstrate the superiority of our method for large combinatorial action spaces.

This paper discusses the problem of weakly supervised classification, in which instances are given weak labels that are produced by some label-corruption process. The goal is to derive conditions under which loss functions for weak-label learning are proper and lower-bounded—two essential requirements for the losses used in class-probability estimation. To this end, we derive a representation theorem for proper losses in supervised learning, which dualizes the Savage representation. We use this theorem to characterize proper weak-label losses and find a condition for them to be lower-bounded. From these theoretical findings, we derive a novel regularization scheme called generalized logit squeezing, which makes any proper weak-label loss bounded from below, without losing properness. Furthermore, we experimentally demonstrate the effectiveness of our proposed approach, as compared to improper or unbounded losses. The results highlight the importance of properness and lower-boundedness.

The parameter estimation of unnormalized models is a challenging problem. The maximum likelihood estimation (MLE) is computationally infeasible for these models since normalizing constants are not explicitly calculated. Although some consistent estimators have been proposed earlier, the problem of statistical efficiency remains. In this study, we propose a unified, statistically efficient estimation framework for unnormalized models and several efficient estimators, whose asymptotic variance is the same as the MLE. The computational cost of these estimators is also reasonable and they can be employed whether the sample space is discrete or continuous. The loss functions of the proposed estimators are derived by combining the following two methods: (1) density-ratio matching using Bregman divergence, and (2) plugging-in nonparametric estimators. We also analyze the properties of the proposed estimators when the unnormalized models are misspecified. The experimental results demonstrate the advantages of our method over existing approaches.

Nonlinear independent component analysis (ICA) is a general framework for unsupervised representation learning, and aimed at recovering the latent variables in data. Recent practical methods perform nonlinear ICA by solving classification problems based on logistic regression. However, it is well-known that logistic regression is vulnerable to outliers, and thus the performance can be strongly weakened by outliers. In this paper, we first theoretically analyze nonlinear ICA models in the presence of outliers. Our analysis implies that estimation in nonlinear ICA can be seriously hampered when outliers exist on the tails of the (noncontaminated) target density, which happens in a typical case of contamination by outliers. We develop two robust nonlinear ICA methods based on the $\gamma$-divergence, which is a robust alternative to the KL-divergence in logistic regression. The proposed methods are theoretically shown to have desired robustness properties in the context of nonlinear ICA. We also experimentally demonstrate that the proposed methods are very robust and outperform existing methods in the presence of outliers. Finally, the proposed method is applied to ICA-based causal discovery and shown to find a plausible causal relationship on fMRI data.

We tackle a domain adaptation problem under partially zero-shot setting. In this setting, a certain subset of classes is missing in the unlabeled target data, while all classes appear in the labeled source data, and the goal is to discriminate all classes at the target domain. To solve this problem, we utilize an adversarial training scheme and adopt instance weighting to estimate the loss related to unavailable target data in the missing classes. The instance weight is computed on the basis of the prediction of deep neural networks, implying which instance would be similar to unseen data and having useful information for the loss estimation. This estimation makes it possible to explicitly consider all classes during the domain adaptation training even in the partially zero-shot setting, which leads to accurate adaptation between domains. Experimental results with several benchmark datasets validate the advantage of our method.

In this paper, we propose a novel domain adaptation method that can be applied without target data. We consider the situation where domain shift is caused by a prior change of a specific factor and assume that we know how the prior changes between source and target domains. We call this factor an attribute, and reformulate the domain adaptation problem to utilize the attribute prior instead of target data. In our method, the source data are reweighted with the sample-wise weight estimated by the attribute prior and the data themselves so that they are useful in the target domain. We theoretically reveal that our method provides more precise estimation of sample-wise transferability than a straightforward attribute-based reweighting approach. Experimental results with both toy datasets and benchmark datasets show that our method can perform well, though it does not use any target data.

In this paper, we focus on parameters estimation of probabilistic models in discrete space. A naive calculation of the normalization constant of the probabilistic model on discrete space is often infeasible and statistical inference based on such probabilistic models has difficulty. In this paper, we propose a novel estimator for probabilistic models on discrete space, which is derived from an empirically localized homogeneous divergence. The idea of the empirical localization makes it possible to ignore an unobserved domain on sample space, and the homogeneous divergence is a discrepancy measure between two positive measures and has a weak coincidence axiom. The proposed estimator can be constructed without calculating the normalization constant and is asymptotically consistent and Fisher efficient. We investigate statistical properties of the proposed estimator and reveal a relationship between the empirically localized homogeneous divergence and a mixture of the $\alpha$-divergence. The $\alpha$-divergence is a non- homogeneous discrepancy measure that is frequently discussed in the context of information geometry. Using the relationship, we also propose an asymptotically consistent estimator of the normalization constant. Experiments showed that the proposed estimator comparably performs to the maximum likelihood estimator but with drastically lower computational cost.

Non-negative Matrix Factorization (NMF) is a method of multivariate analysis which factorizes a non-negative matrix into two non-negative matrices. While conventional NMF algorithms use the Euclidian distance or the Kullback-Leibler divergence as cost functions, those methods fail to extract latent structure or interpretable information from the matrix when the target matrix is contaminated by noise. In this paper, we propose novel NMF algorithms based on the γ-divergence which is known to be robust, and investigate robustness of proposed methods with numerical experiments.

In this paper, we propose a novel parameter estimator for probabilistic models on discrete space. The proposed estimator is derived from minimization of homogeneous divergence and can be constructed without calculation of the normalization constant, which is frequently infeasible for models in the discrete space. We investigate statistical properties of the proposed estimator such as consistency and asymptotic normality, and reveal a relationship with the alpha-divergence. Small experiments show that the proposed estimator attains comparable performance to the MLE with drastically lower computational cost.

We propose a novel estimator for a specific class of probabilistic models on discrete spaces such as the Boltzmann machine. The proposed estimator is derived from minimization of a convex risk function and can be constructed without calculating the normalization constant, whose computational cost is exponential order. We investigate statistical properties of the proposed estimator such as consistency and asymptotic normality in the framework of the estimating function. Small experiments show that the proposed estimator can attain comparable performance to the maximum likelihood expectation at a much lower computational cost and is applicable to high-dimensional data.

While most proposed methods for solving classification problems focus on minimization of the classification error rate, we are interested in the receiver operating characteristic (ROC) curve, which provides more information about classification performance than the error rate does. The area under the ROC curve (AUC) is a natural measure for overall assessment of a classifier based on the ROC curve. We discuss a class of concave functions for AUC maximization in which a boosting-type algorithm including RankBoost is considered, and the Bayesian risk consistency and the lower bound of the optimum function are discussed. A procedure derived by maximizing a specific optimum function has high robustness, based on gross error sensitivity. Additionally, we focus on the partial AUC, which is the partial area under the ROC curve. For example, in medical screening, a high true-positive rate to the fixed lower false-positive rate is preferable and thus the partial AUC corresponding to lower false-positive rates is much more important than the remaining AUC. We extend the class of concave optimum functions for partial AUC optimality with the boosting algorithm. We investigated the validity of the proposed method through several experiments with data sets in the UCI repository.

In this paper, we study probabilistic modeling of heterogeneously attributed multi-dimensional arrays. The model can manage the heterogeneity by employing an individual exponential-family distribution for each attribute of the tensor array. These entries are connected by latent variables and are shared information across the different attributes. Because a Bayesian inference for our model is intractable, we cast the EM algorithm approximated by using the Lap lace method and Gaussian process. This approximation enables us to derive a predictive distribution for missing values in a consistent manner. Simulation experiments show that our method outperforms other methods such as PARAFAC and Tucker decomposition in missing-values prediction for cross-national statistics and is also applicable to discover anomalies in heterogeneous office-logging data.

In this letter, we present new methods of multiclass classification that combine multiple binary classifiers. Misclassification of each binary classifier is formulated as a bit inversion error with probabilistic models by making an analogy to the context of information transmission theory. Dependence between binary classifiers is incorporated into our model, which makes a decoder a type of Boltzmann machine. We performed experimental studies using a synthetic data set, data sets from the UCI repository, and bioinformatics data sets, and the results show that the proposed methods are superior to the existing multiclass classification methods.

We discuss robustness against mislabeling in multiclass labels for classification problems and propose two algorithms of boosting, the normalized Eta-Boost.M and Eta-Boost.M, based on the Eta-divergence. Those two boosting algorithms are closely related to models of mislabeling in which the label is erroneously exchanged for others. For the two boosting algorithms, theoretical aspects supporting the robustness for mislabeling are explored. We apply the proposed two boosting methods for synthetic and real data sets to investigate the performance of these methods, focusing on robustness, and confirm the validity of the proposed methods.

In this article, we propose a new method of multi-class classification in the framework of error-correcting output coding (ECOC). Misclassification of each binary classifier is formulated as a bit inversion error with a probabilistic model for each class and dependence between binary classifiers is incorporated into our model, which makes a decoder, a type of Boltzmann machine. Experimental studies using a synthetic dataset and datasets from UCI repository are performed, and the results show that the proposed method is superior to other existing multi-class classification methods.

Boosting is known as a gradient descent algorithm over loss functions. It is often pointed out that the typical boosting algorithm, Adaboost, is highly affected by outliers. In this letter, loss functions for robust boosting are studied. Based on the concept of robust statistics, we propose a transformation of loss functions that makes boosting algorithms robust against extreme outliers. Next, the truncation of loss functions is applied to contamination models that describe the occurrence of mislabels near decision boundaries. Numerical experiments illustrate that the proposed loss functions derived from the contamination models are useful for handling highly noisy data in comparison with other loss functions.

This paper proposes GroupAdaBoost as a variant of AdaBoost for statistical pattern recognition. The objective of the proposed algorithm is to solve the p /spl Gt/ n problem arisen in bioinformatics. Typically, p is the number of investigated genes and n is number of individuals in a microarray experiment for observing gene expressions in a problem to extract any speci c pattern of gene expressions related to a disease status. The ordinary method for predicting the genetic causes of diseases is apt to over-learn from any particular training dataset because of facing p /spl Gt/ n problem. We observed that GroupAdaBoost gave a robust performance for cases of the excess number of genes. In several real datasets, which are publicly available from Web-pages, we compared the analysis of results among the proposed method and others, and a small scale of simulation study to confirm the validity of the proposed method.

We aim at an extension of AdaBoost to U-Boost, in the paradigm to build a stronger classification machine from a set of weak learning machines. A geometric understanding of the Bregman divergence defined by a generic convex function U leads to the U-Boost method in the framework of information geometry extended to the space of the finite measures over a label set. We propose two versions of U-Boost learning algorithms by taking account of whether the domain is restricted to the space of probability functions. In the sequential step, we observe that the two adjacent and the initial classifiers are associated with a right triangle in the scale via the Bregman divergence, called the Pythagorean relation. This leads to a mild convergence property of the U-Boost algorithm as seen in the expectation-maximization algorithm. Statistical discussions for consistency and robustness elucidate the properties of the U-Boost methods based on a stochastic assumption for training data.

AdaBoost can be derived by sequential minimization of the exponential loss function. It implements the learning process by exponentially reweighting examples according to classification results. However, weights are often too sharply tuned, so that AdaBoost suffers from the nonrobustness and overlearning. Wepropose a new boosting method that is a slight modification of AdaBoost. The loss function is defined by a mixture of the exponential loss and naive error loss functions. As a result, the proposed method incorporates the effect of forgetfulness into AdaBoost. The statistical significance of our method is discussed, and simulations are presented for confirmation.