arXiv subjects

Masahiro Kato

Publications and source records attributed to Masahiro Kato.

At least 73 records · Page 4Linked to original sources

arXiv2023

Asymptotically Optimal Fixed-Budget Best Arm Identification with Variance-Dependent Bounds

We investigate the problem of fixed-budget best arm identification (BAI) for minimizing expected simple regret. In an adaptive experiment, a decision maker draws one of multiple treatment arms based on past observations and observes the outcome of the drawn arm. After the experiment, the decision maker recommends the treatment arm with the highest expected outcome. We evaluate the decision based on the expected simple regret, which is the difference between the expected outcomes of the best arm and the recommended arm. Due to inherent uncertainty, we evaluate the regret using the minimax criterion. First, we derive asymptotic lower bounds for the worst-case expected simple regret, which are characterized by the variances of potential outcomes (leading factor). Based on the lower bounds, we propose the Two-Stage (TS)-Hirano-Imbens-Ridder (HIR) strategy, which utilizes the HIR estimator (Hirano et al., 2003) in recommending the best arm. Our theoretical analysis shows that the TS-HIR strategy is asymptotically minimax optimal, meaning that the leading factor of its worst-case expected simple regret matches our derived worst-case lower bound. Additionally, we consider extensions of our method, such as the asymptotic optimality for the probability of misidentification. Finally, we validate the proposed method's effectiveness through simulations.

cs.LG↗

arXiv2023

Automatic Debiased Learning from Positive, Unlabeled, and Exposure Data

We address the issue of binary classification from positive and unlabeled data (PU classification) with a selection bias in the positive data. During the observation process, (i) a sample is exposed to a user, (ii) the user then returns the label for the exposed sample, and (iii) we however can only observe the positive samples. Therefore, the positive labels that we observe are a combination of both the exposure and the labeling, which creates a selection bias problem for the observed positive samples. This scenario represents a conceptual framework for many practical applications, such as recommender systems, which we refer to as ``learning from positive, unlabeled, and exposure data'' (PUE classification). To tackle this problem, we initially assume access to data with exposure labels. Then, we propose a method to identify the function of interest using a strong ignorability assumption and develop an ``Automatic Debiased PUE'' (ADPUE) learning method. This algorithm directly debiases the selection bias without requiring intermediate estimates, such as the propensity score, which is necessary for other learning methods. Through experiments, we demonstrate that our approach outperforms traditional PU learning methods on various semi-synthetic datasets.

cs.LG↗

arXiv2023

Best Arm Identification with Contextual Information under a Small Gap

We study the best-arm identification (BAI) problem with a fixed budget and contextual (covariate) information. In each round of an adaptive experiment, after observing contextual information, we choose a treatment arm using past observations and current context. Our goal is to identify the best treatment arm, which is a treatment arm with the maximal expected reward marginalized over the contextual distribution, with a minimal probability of misidentification. In this study, we consider a class of nonparametric bandit models that converge to location-shift models when the gaps go to zero. First, we derive lower bounds of the misidentification probability for a certain class of strategies and bandit models (probabilistic models of potential outcomes) under a small-gap regime. A small-gap regime is a situation where gaps of the expected rewards between the best and suboptimal treatment arms go to zero, which corresponds to one of the worst cases in identifying the best treatment arm. We then develop the ``Random Sampling (RS)-Augmented Inverse Probability weighting (AIPW) strategy,'' which is asymptotically optimal in the sense that the probability of misidentification under the strategy matches the lower bound when the budget goes to infinity in the small-gap regime. The RS-AIPW strategy consists of the RS rule tracking a target sample allocation ratio and the recommendation rule using the AIPW estimator.

cs.LG↗

arXiv2022

Optimal Best Arm Identification in Two-Armed Bandits with a Fixed Budget under a Small Gap

We consider fixed-budget best-arm identification in two-armed Gaussian bandit problems. One of the longstanding open questions is the existence of an optimal strategy under which the probability of misidentification matches a lower bound. We show that a strategy following the Neyman allocation rule (Neyman, 1934) is asymptotically optimal when the gap between the expected rewards is small. First, we review a lower bound derived by Kaufmann et al. (2016). Then, we propose the "Neyman Allocation (NA)-Augmented Inverse Probability weighting (AIPW)" strategy, which consists of the sampling rule using the Neyman allocation with an estimated standard deviation and the recommendation rule using an AIPW estimator. Our proposed strategy is optimal because the upper bound matches the lower bound when the budget goes to infinity and the gap goes to zero.

stat.ML↗

arXiv2022

Learning Causal Models from Conditional Moment Restrictions by Importance Weighting

We consider learning causal relationships under conditional moment restrictions. Unlike causal inference under unconditional moment restrictions, conditional moment restrictions pose serious challenges for causal inference, especially in high-dimensional settings. To address this issue, we propose a method that transforms conditional moment restrictions to unconditional moment restrictions through importance weighting, using a conditional density ratio estimator. Using this transformation, we successfully estimate nonparametric functions defined under conditional moment restrictions. Our proposed framework is general and can be applied to a wide range of methods, including neural networks. We analyze the estimation error, providing theoretical support for our proposed method. In experiments, we confirm the soundness of our proposed method.

econ.EM↗

arXiv2022

Learning Classifiers under Delayed Feedback with a Time Window Assumption

We consider training a binary classifier under delayed feedback (\emph{DF learning}). For example, in the conversion prediction in online ads, we initially receive negative samples that clicked the ads but did not buy an item; subsequently, some samples among them buy an item then change to positive. In the setting of DF learning, we observe samples over time, then learn a classifier at some point. We initially receive negative samples; subsequently, some samples among them change to positive. This problem is conceivable in various real-world applications such as online advertisements, where the user action takes place long after the first click. Owing to the delayed feedback, naive classification of the positive and negative samples returns a biased classifier. One solution is to use samples that have been observed for more than a certain time window assuming these samples are correctly labeled. However, existing studies reported that simply using a subset of all samples based on the time window assumption does not perform well, and that using all samples along with the time window assumption improves empirical performance. We extend these existing studies and propose a method with the unbiased and convex empirical risk that is constructed from all samples under the time window assumption. To demonstrate the soundness of the proposed method, we provide experimental results on a synthetic and open dataset that is the real traffic log datasets in online advertising.

cs.LG↗

arXiv2022

Benign-Overfitting in Conditional Average Treatment Effect Prediction with Linear Regression

We study the benign overfitting theory in the prediction of the conditional average treatment effect (CATE), with linear regression models. As the development of machine learning for causal inference, a wide range of large-scale models for causality are gaining attention. One problem is that suspicions have been raised that the large-scale models are prone to overfitting to observations with sample selection, hence the large models may not be suitable for causal prediction. In this study, to resolve the suspicious, we investigate on the validity of causal inference methods for overparameterized models, by applying the recent theory of benign overfitting (Bartlett et al., 2020). Specifically, we consider samples whose distribution switches depending on an assignment rule, and study the prediction of CATE with linear models whose dimension diverges to infinity. We focus on two methods: the T-learner, which based on a difference between separately constructed estimators with each treatment group, and the inverse probability weight (IPW)-learner, which solves another regression problem approximated by a propensity score. In both methods, the estimator consists of interpolators that fit the samples perfectly. As a result, we show that the T-learner fails to achieve the consistency except the random assignment, while the IPW-learner converges the risk to zero if the propensity score is known. This difference stems from that the T-learner is unable to preserve eigenspaces of the covariances, which is necessary for benign overfitting in the overparameterized setting. Our result provides new insights into the usage of causal inference methods in the overparameterizated setting, in particular, doubly robust estimators.

econ.EM↗

arXiv2022

Unified Perspective on Probability Divergence via Maximum Likelihood Density Ratio Estimation: Bridging KL-Divergence and Integral Probability Metrics

This paper provides a unified perspective for the Kullback-Leibler (KL)-divergence and the integral probability metrics (IPMs) from the perspective of maximum likelihood density-ratio estimation (DRE). Both the KL-divergence and the IPMs are widely used in various fields in applications such as generative modeling. However, a unified understanding of these concepts has still been unexplored. In this paper, we show that the KL-divergence and the IPMs can be represented as maximal likelihoods differing only by sampling schemes, and use this result to derive a unified form of the IPMs and a relaxed estimation method. To develop the estimation problem, we construct an unconstrained maximum likelihood estimator to perform DRE with a stratified sampling scheme. We further propose a novel class of probability divergences, called the Density Ratio Metrics (DRMs), that interpolates the KL-divergence and the IPMs. In addition to these findings, we also introduce some applications of the DRMs, such as DRE and generative adversarial networks. In experiments, we validate the effectiveness of our proposed methods.

cs.LG↗

arXiv2021

Policy Choice and Best Arm Identification: Asymptotic Analysis of Exploration Sampling

We consider the "policy choice" problem -- otherwise known as best arm identification in the bandit literature -- proposed by Kasy and Sautmann (2021) for adaptive experimental design. Theorem 1 of Kasy and Sautmann (2021) provides three asymptotic results that give theoretical guarantees for exploration sampling developed for this setting. We first show that the proof of Theorem 1 (1) has technical issues, and the proof and statement of Theorem 1 (2) are incorrect. We then show, through a counterexample, that Theorem 1 (3) is false. For the former two, we correct the statements and provide rigorous proofs. For Theorem 1 (3), we propose an alternative objective function, which we call posterior weighted policy regret, and derive the asymptotic optimality of exploration sampling.

econ.EM↗

arXiv2021

Non-Negative Bregman Divergence Minimization for Deep Direct Density Ratio Estimation

Density ratio estimation (DRE) is at the core of various machine learning tasks such as anomaly detection and domain adaptation. In existing studies on DRE, methods based on Bregman divergence (BD) minimization have been extensively studied. However, BD minimization when applied with highly flexible models, such as deep neural networks, tends to suffer from what we call train-loss hacking, which is a source of overfitting caused by a typical characteristic of empirical BD estimators. In this paper, to mitigate train-loss hacking, we propose a non-negative correction for empirical BD estimators. Theoretically, we confirm the soundness of the proposed method through a generalization error bound. Through our experiments, the proposed methods show a favorable performance in inlier-based outlier detection.

cs.LG↗

arXiv2021

The Adaptive Doubly Robust Estimator for Policy Evaluation in Adaptive Experiments and a Paradox Concerning Logging Policy

The doubly robust (DR) estimator, which consists of two nuisance parameters, the conditional mean outcome and the logging policy (the probability of choosing an action), is crucial in causal inference. This paper proposes a DR estimator for dependent samples obtained from adaptive experiments. To obtain an asymptotically normal semiparametric estimator from dependent samples with non-Donsker nuisance estimators, we propose adaptive-fitting as a variant of sample-splitting. We also report an empirical paradox that our proposed DR estimator tends to show better performances compared to other estimators utilizing the true logging policy. While a similar phenomenon is known for estimators with i.i.d. samples, traditional explanations based on asymptotic efficiency cannot elucidate our case with dependent samples. We confirm this hypothesis through simulation studies.

cs.LG↗

arXiv2021

Scalable Personalised Item Ranking through Parametric Density Estimation

Learning from implicit feedback is challenging because of the difficult nature of the one-class problem: we can observe only positive examples. Most conventional methods use a pairwise ranking approach and negative samplers to cope with the one-class problem. However, such methods have two main drawbacks particularly in large-scale applications; (1) the pairwise approach is severely inefficient due to the quadratic computational cost; and (2) even recent model-based samplers (e.g. IRGAN) cannot achieve practical efficiency due to the training of an extra model. In this paper, we propose a learning-to-rank approach, which achieves convergence speed comparable to the pointwise counterpart while performing similarly to the pairwise counterpart in terms of ranking effectiveness. Our approach estimates the probability densities of positive items for each user within a rich class of distributions, viz. \emph{exponential family}. In our formulation, we derive a loss function and the appropriate negative sampling distribution based on maximum likelihood estimation. We also develop a practical technique for risk approximation and a regularisation scheme. We then discuss that our single-model approach is equivalent to an IRGAN variant under a certain condition. Through experiments on real-world datasets, our approach outperforms the pointwise and pairwise counterparts in terms of effectiveness and efficiency.

cs.LG↗

arXiv2021

Adaptive Doubly Robust Estimator from Non-stationary Logging Policy under a Convergence of Average Probability

Adaptive experiments, including efficient average treatment effect estimation and multi-armed bandit algorithms, have garnered attention in various applications, such as social experiments, clinical trials, and online advertisement optimization. This paper considers estimating the mean outcome of an action from samples obtained in adaptive experiments. In causal inference, the mean outcome of an action has a crucial role, and the estimation is an essential task, where the average treatment effect estimation and off-policy value estimation are its variants. In adaptive experiments, the probability of choosing an action (logging policy) is allowed to be sequentially updated based on past observations. Due to this logging policy depending on the past observations, the samples are often not independent and identically distributed (i.i.d.), making developing an asymptotically normal estimator difficult. A typical approach for this problem is to assume that the logging policy converges in a time-invariant function. However, this assumption is restrictive in various applications, such as when the logging policy fluctuates or becomes zero at some periods. To mitigate this limitation, we propose another assumption that the average logging policy converges to a time-invariant function and show the doubly robust (DR) estimator's asymptotic normality. Under the assumption, the logging policy itself can fluctuate or be zero for some actions. We also show the empirical properties by simulations.

stat.ME↗

arXiv2021

Density-Ratio Based Personalised Ranking from Implicit Feedback

Learning from implicit user feedback is challenging as we can only observe positive samples but never access negative ones. Most conventional methods cope with this issue by adopting a pairwise ranking approach with negative sampling. However, the pairwise ranking approach has a severe disadvantage in the convergence time owing to the quadratically increasing computational cost with respect to the sample size; it is problematic, particularly for large-scale datasets and complex models such as neural networks. By contrast, a pointwise approach does not directly solve a ranking problem, and is therefore inferior to a pairwise counterpart in top-K ranking tasks; however, it is generally advantageous in regards to the convergence time. This study aims to establish an approach to learn personalised ranking from implicit feedback, which reconciles the training efficiency of the pointwise approach and ranking effectiveness of the pairwise counterpart. The key idea is to estimate the ranking of items in a pointwise manner; we first reformulate the conventional pointwise approach based on density ratio estimation and then incorporate the essence of ranking-oriented approaches (e.g. the pairwise approach) into our formulation. Through experiments on three real-world datasets, we demonstrate that our approach not only dramatically reduces the convergence time (one to two orders of magnitude faster) but also significantly improving the ranking performance.

cs.IR↗

arXiv2020

ATRO: Adversarial Training with a Rejection Option

This paper proposes a classification framework with a rejection option to mitigate the performance deterioration caused by adversarial examples. While recent machine learning algorithms achieve high prediction performance, they are empirically vulnerable to adversarial examples, which are slightly perturbed data samples that are wrongly classified. In real-world applications, adversarial attacks using such adversarial examples could cause serious problems. To this end, various methods are proposed to obtain a classifier that is robust against adversarial examples. Adversarial training is one of them, which trains a classifier to minimize the worst-case loss under adversarial attacks. In this paper, in order to acquire a more reliable classifier against adversarial attacks, we propose the method of Adversarial Training with a Rejection Option (ATRO). Applying the adversarial training objective to both a classifier and a rejection function simultaneously, classifiers trained by ATRO can choose to abstain from classification when it has insufficient confidence to classify a test data point. We examine the feasibility of the framework using the surrogate maximum hinge loss and establish a generalization bound for linear models. Furthermore, we empirically confirmed the effectiveness of ATRO using various models and real-world datasets.

cs.LG↗

arXiv2020

A Practical Guide of Off-Policy Evaluation for Bandit Problems

Off-policy evaluation (OPE) is the problem of estimating the value of a target policy from samples obtained via different policies. Recently, applying OPE methods for bandit problems has garnered attention. For the theoretical guarantees of an estimator of the policy value, the OPE methods require various conditions on the target policy and policy used for generating the samples. However, existing studies did not carefully discuss the practical situation where such conditions hold, and the gap between them remains. This paper aims to show new results for bridging the gap. Based on the properties of the evaluation policy, we categorize OPE situations. Then, among practical applications, we mainly discuss the best policy selection. For the situation, we propose a meta-algorithm based on existing OPE estimators. We investigate the proposed concepts using synthetic and open real-world datasets in experiments.

cs.LG↗

arXiv2020

Off-Policy Evaluation of Bandit Algorithm from Dependent Samples under Batch Update Policy

The goal of off-policy evaluation (OPE) is to evaluate a new policy using historical data obtained via a behavior policy. However, because the contextual bandit algorithm updates the policy based on past observations, the samples are not independent and identically distributed (i.i.d.). This paper tackles this problem by constructing an estimator from a martingale difference sequence (MDS) for the dependent samples. In the data-generating process, we do not assume the convergence of the policy, but the policy uses the same conditional probability of choosing an action during a certain period. Then, we derive an asymptotically normal estimator of the value of an evaluation policy. As another advantage of our method, the batch-based approach simultaneously solves the deficient support problem. Using benchmark and real-world datasets, we experimentally confirm the effectiveness of the proposed method.

cs.LG↗

arXiv2020

Off-Policy Evaluation and Learning for External Validity under a Covariate Shift

We consider evaluating and training a new policy for the evaluation data by using the historical data obtained from a different policy. The goal of off-policy evaluation (OPE) is to estimate the expected reward of a new policy over the evaluation data, and that of off-policy learning (OPL) is to find a new policy that maximizes the expected reward over the evaluation data. Although the standard OPE and OPL assume the same distribution of covariate between the historical and evaluation data, a covariate shift often exists, i.e., the distribution of the covariate of the historical data is different from that of the evaluation data. In this paper, we derive the efficiency bound of OPE under a covariate shift. Then, we propose doubly robust and efficient estimators for OPE and OPL under a covariate shift by using a nonparametric estimator of the density ratio between the historical and evaluation data distributions. We also discuss other possible estimators and compare their theoretical properties. Finally, we confirm the effectiveness of the proposed estimators through experiments.

stat.ML↗