arXiv subjects

Masahiro Kato

Publications and source records attributed to Masahiro Kato.

At least 55 records · Page 3Linked to original sources

arXiv2025

Conformal Predictive Portfolio Selection

This study examines portfolio selection using predictive models for portfolio returns. Portfolio selection is a fundamental task in finance, and a variety of methods have been developed to achieve this goal. For instance, the mean-variance approach constructs portfolios by balancing the trade-off between the mean and variance of asset returns, while the quantile-based approach optimizes portfolios by considering tail risk. These methods often depend on distributional information estimated from historical data using predictive models, each of which carries its own uncertainty. To address this, we propose a framework for predictive portfolio selection via conformal prediction , called \emph{Conformal Predictive Portfolio Selection} (CPPS). Our approach forecasts future portfolio returns, computes the corresponding prediction intervals, and selects the portfolio of interest based on these intervals. The framework is flexible and can accommodate a wide range of predictive models, including autoregressive (AR) models, random forests, and neural networks. We demonstrate the effectiveness of the CPPS framework by applying it to an AR model and validate its performance through empirical studies, showing that it delivers superior returns compared to simpler strategies.

q-fin.PM↗

arXiv2025

Generalized Neyman Allocation for Locally Minimax Optimal Best-Arm Identification

This study investigates an asymptotically locally minimax optimal algorithm for fixed-budget best-arm identification (BAI). We propose the Generalized Neyman Allocation (GNA) algorithm and demonstrate that its worst-case upper bound on the probability of misidentifying the best arm aligns with the worst-case lower bound under the small-gap regime, where the gap between the expected outcomes of the best and suboptimal arms is small. Our lower and upper bounds are tight, matching exactly including constant terms within the small-gap regime. The GNA algorithm generalizes the Neyman allocation for two-armed bandits (Neyman, 1934; Kaufmann et al., 2016) and refines existing BAI algorithms, such as those proposed by Glynn & Juneja (2004). By proposing an asymptotically minimax optimal algorithm, we address the longstanding open issue in BAI (Kaufmann, 2020) and treatment choice (Kasy & Sautmann, 202) by restricting a class of distributions to the small-gap regimes.

cs.LG↗

arXiv2025

A Note on Doubly Robust Estimator in Regression Discontinuity Designs

This note introduces a doubly robust (DR) estimator for regression discontinuity (RD) designs. RD designs provide a quasi-experimental framework for estimating treatment effects, where treatment assignment depends on whether a running variable surpasses a predefined cutoff. A common approach in RD estimation is the use of nonparametric regression methods, such as local linear regression. However, the validity of these methods still relies on the consistency of the nonparametric estimators. In this study, we propose the DR-RD estimator, which combines two distinct estimators for the conditional expected outcomes. The primary advantage of the DR-RD estimator lies in its ability to ensure the consistency of the treatment effect estimation as long as at least one of the two estimators is consistent. Consequently, our DR-RD estimator enhances robustness of treatment effect estimators in RD designs.

econ.EM↗

arXiv2025

Bayesian Spatial Predictive Synthesis

Due to spatial dependence -- often characterized as complex and non-linear -- model misspecification is a prevalent and critical issue in spatial data analysis and prediction. As the data, and thus model performance, is heterogeneous, typical model selection and ensemble methods that assume homogeneity are not suitable. We address the issue of model uncertainty for spatial data by proposing a novel Bayesian ensemble methodology that captures spatially-varying model uncertainty and performance heterogeneity of multiple spatial predictions, and synthesizes them for improved predictions, which we call Bayesian spatial predictive synthesis. Our proposal is defined by specifying a latent factor spatially-varying coefficient model as the synthesis function, which enables spatial characteristics of each model to be learned and ensemble coefficients to vary over regions to achieve flexible predictions. We derive our method from the theoretically best approximation of the data generating process, and show that it provides a finite sample theoretical guarantee for its predictive performance, specifically that the predictions are exact minimax. Two MCMC strategies are implemented for full uncertainty quantification, as well as a variational inference strategy for fast point inference. We also extend the estimation strategy for general responses. Through simulation examples and two real data applications in real estate and ecology, our proposed Bayesian spatial predictive synthesis outperforms standard spatial models and ensemble methods, and advanced machine learning methods, in terms of predictive accuracy and uncertainty quantification, while maintaining interpretability of the prediction mechanism.

stat.ME↗

arXiv2025

Minimax Optimal Simple Regret in Two-Armed Best-Arm Identification

This study investigates an asymptotically minimax optimal algorithm in the two-armed fixed-budget best-arm identification (BAI) problem. Given two treatment arms, the objective is to identify the arm with the highest expected outcome through an adaptive experiment. We focus on the Neyman allocation, where treatment arms are allocated following the ratio of their outcome standard deviations. Our primary contribution is to prove the minimax optimality of the Neyman allocation for the simple regret, defined as the difference between the expected outcomes of the true best arm and the estimated best arm. Specifically, we first derive a minimax lower bound for the expected simple regret, which characterizes the worst-case performance achievable under the location-shift distributions, including Gaussian distributions. We then show that the simple regret of the Neyman allocation asymptotically matches this lower bound, including the constant term, not just the rate in terms of the sample size, under the worst-case distribution. Notably, our optimality result holds without imposing locality restrictions on the distribution, such as the local asymptotic normality. Furthermore, we demonstrate that the Neyman allocation reduces to the uniform allocation, i.e., the standard randomized controlled trial, under Bernoulli distributions.

stat.ML↗

arXiv2024

Debiased Regression for Root-N-Consistent Conditional Mean Estimation

This study introduces a debiasing method for regression estimators, including high-dimensional and nonparametric regression estimators. For example, nonparametric regression methods allow for the estimation of regression functions in a data-driven manner with minimal assumptions; however, these methods typically fail to achieve $\sqrt{n}$-consistency in their convergence rates, and many, including those in machine learning, lack guarantees that their estimators asymptotically follow a normal distribution. To address these challenges, we propose a debiasing technique for nonparametric estimators by adding a bias-correction term to the original estimators, extending the conventional one-step estimator used in semiparametric analysis. Specifically, for each data point, we estimate the conditional expected residual of the original nonparametric estimator, which can, for instance, be computed using kernel (Nadaraya-Watson) regression, and incorporate it as a bias-reduction term. Our theoretical analysis demonstrates that the proposed estimator achieves $\sqrt{n}$-consistency and asymptotic normality under a mild convergence rate condition for both the original nonparametric estimator and the conditional expected residual estimator. Notably, this approach remains model-free as long as the original estimator and the conditional expected residual estimator satisfy the convergence rate condition. The proposed method offers several advantages, including improved estimation accuracy and simplified construction of confidence intervals.

stat.ML↗

arXiv2024

Mean-Variance Efficient Reinforcement Learning with Applications to Dynamic Financial Investment

This study investigates the mean-variance (MV) trade-off in reinforcement learning (RL), an instance of the sequential decision-making under uncertainty. Our objective is to obtain MV-efficient policies whose means and variances are located on the Pareto efficient frontier with respect to the MV trade-off; under the condition, any increase in the expected reward would necessitate a corresponding increase in variance, and vice versa. To this end, we propose a method that trains our policy to maximize the expected quadratic utility, defined as a weighted sum of the first and second moments of the rewards obtained through our policy. We subsequently demonstrate that the maximizer indeed qualifies as an MV-efficient policy. Previous studies that employed constrained optimization to address the MV trade-off have encountered computational challenges. However, our approach is more computationally efficient as it eliminates the need for gradient estimation of variance, a contributing factor to the double sampling issue observed in existing methodologies. Through experimentation, we validate the efficacy of our approach.

cs.LG↗

arXiv2024

Double Debiased Covariate Shift Adaptation Robust to Density-Ratio Estimation

Consider a scenario where we have access to train data with both covariates and outcomes while test data only contains covariates. In this scenario, our primary aim is to predict the missing outcomes of the test data. With this objective in mind, we train parametric regression models under a covariate shift, where covariate distributions are different between the train and test data. For this problem, existing studies have proposed covariate shift adaptation via importance weighting using the density ratio. This approach averages the train data losses, each weighted by an estimated ratio of the covariate densities between the train and test data, to approximate the test-data risk. Although it allows us to obtain a test-data risk minimizer, its performance heavily relies on the accuracy of the density ratio estimation. Moreover, even if the density ratio can be consistently estimated, the estimation errors of the density ratio also yield bias in the estimators of the regression model's parameters of interest. To mitigate these challenges, we introduce a doubly robust estimator for covariate shift adaptation via importance weighting, which incorporates an additional estimator for the regression function. Leveraging double machine learning techniques, our estimator reduces the bias arising from the density ratio estimation errors. We demonstrate the asymptotic distribution of the regression parameter estimator. Notably, our estimator remains consistent if either the density ratio estimator or the regression function is consistent, showcasing its robustness against potential errors in density ratio estimation. Finally, we confirm the soundness of our proposed method via simulation studies.

stat.ME↗

arXiv2024

A Policy Gradient Primal-Dual Algorithm for Constrained MDPs with Uniform PAC Guarantees

We study a primal-dual (PD) reinforcement learning (RL) algorithm for online constrained Markov decision processes (CMDPs). Despite its widespread practical use, the existing theoretical literature on PD-RL algorithms for this problem only provides sublinear regret guarantees and fails to ensure convergence to optimal policies. In this paper, we introduce a novel policy gradient PD algorithm with uniform probably approximate correctness (Uniform-PAC) guarantees, simultaneously ensuring convergence to optimal policies, sublinear regret, and polynomial sample complexity for any target accuracy. Notably, this represents the first Uniform-PAC algorithm for the online CMDP problem. In addition to the theoretical guarantees, we empirically demonstrate in a simple CMDP that our algorithm converges to optimal policies, while baseline algorithms exhibit oscillatory performance and constraint violation.

cs.LG↗

arXiv2024

Active Adaptive Experimental Design for Treatment Effect Estimation with Covariate Choices

This study designs an adaptive experiment for efficiently estimating average treatment effects (ATEs). In each round of our adaptive experiment, an experimenter sequentially samples an experimental unit, assigns a treatment, and observes the corresponding outcome immediately. At the end of the experiment, the experimenter estimates an ATE using the gathered samples. The objective is to estimate the ATE with a smaller asymptotic variance. Existing studies have designed experiments that adaptively optimize the propensity score (treatment-assignment probability). As a generalization of such an approach, we propose optimizing the covariate density as well as the propensity score. First, we derive the efficient covariate density and propensity score that minimize the semiparametric efficiency bound and find that optimizing both covariate density and propensity score minimizes the semiparametric efficiency bound more effectively than optimizing only the propensity score. Next, we design an adaptive experiment using the efficient covariate density and propensity score sequentially estimated during the experiment. Lastly, we propose an ATE estimator whose asymptotic variance aligns with the minimized semiparametric efficiency bound.

stat.ME↗

arXiv2024

General Bayesian Predictive Synthesis

This study investigates Bayesian ensemble learning for improving the quality of decision-making. We consider a decision-maker who selects an action from a set of candidates based on a policy trained using observations. In our setting, we assume the existence of experts who provide predictive distributions based on their own policies. Our goal is to integrate these predictive distributions within the Bayesian framework. Our proposed method, which we refer to as General Bayesian Predictive Synthesis (GBPS), is characterized by a loss minimization framework and does not rely on parameter estimation, unlike existing studies. Inspired by Bayesian predictive synthesis and general Bayes frameworks, we evaluate the performance of our proposed method through simulation studies.

stat.ME↗

arXiv2024

Locally Optimal Fixed-Budget Best Arm Identification in Two-Armed Gaussian Bandits with Unknown Variances

We address the problem of best arm identification (BAI) with a fixed budget for two-armed Gaussian bandits. In BAI, given multiple arms, we aim to find the best arm, an arm with the highest expected reward, through an adaptive experiment. Kaufmann et al. (2016) develops a lower bound for the probability of misidentifying the best arm. They also propose a strategy, assuming that the variances of rewards are known, and show that it is asymptotically optimal in the sense that its probability of misidentification matches the lower bound as the budget approaches infinity. However, an asymptotically optimal strategy is unknown when the variances are unknown. For this open issue, we propose a strategy that estimates variances during an adaptive experiment and draws arms with a ratio of the estimated standard deviations. We refer to this strategy as the Neyman Allocation (NA)-Augmented Inverse Probability weighting (AIPW) strategy. We then demonstrate that this strategy is asymptotically optimal by showing that its probability of misidentification matches the lower bound when the budget approaches infinity, and the gap between the expected rewards of two arms approaches zero (small-gap regime). Our results suggest that under the worst-case scenario characterized by the small-gap regime, our strategy, which employs estimated variance, is asymptotically optimal even when the variances are unknown.

cs.LG↗

arXiv2024

Worst-Case Optimal Multi-Armed Gaussian Best Arm Identification with a Fixed Budget

This study investigates the experimental design problem for identifying the arm with the highest expected outcome, referred to as best arm identification (BAI). In our experiments, the number of treatment-allocation rounds is fixed. During each round, a decision-maker allocates an arm and observes a corresponding outcome, which follows a Gaussian distribution with variances that can differ among the arms. At the end of the experiment, the decision-maker recommends one of the arms as an estimate of the best arm. To design an experiment, we first discuss lower bounds for the probability of misidentification. Our analysis highlights that the available information on the outcome distribution, such as means (expected outcomes), variances, and the choice of the best arm, significantly influences the lower bounds. Because available information is limited in actual experiments, we develop a lower bound that is valid under the unknown means and the unknown choice of the best arm, which are referred to as the worst-case lower bound. We demonstrate that the worst-case lower bound depends solely on the variances of the outcomes. Then, under the assumption that the variances are known, we propose the Generalized-Neyman-Allocation (GNA)-empirical-best-arm (EBA) strategy, an extension of the Neyman allocation proposed by Neyman (1934). We show that the GNA-EBA strategy is asymptotically optimal in the sense that its probability of misidentification aligns with the lower bounds as the sample size increases infinitely and the differences between the expected outcomes of the best and other suboptimal arms converge to the same values across arms. We refer to such strategies as asymptotically worst-case optimal.

math.ST↗

arXiv2024

Triple/Debiased Lasso for Statistical Inference of Conditional Average Treatment Effects

This study investigates the estimation and the statistical inference about Conditional Average Treatment Effects (CATEs), which have garnered attention as a metric representing individualized causal effects. In our data-generating process, we assume linear models for the outcomes associated with binary treatments and define the CATE as a difference between the expected outcomes of these linear models. This study allows the linear models to be high-dimensional, and our interest lies in consistent estimation and statistical inference for the CATE. In high-dimensional linear regression, one typical approach is to assume sparsity. However, in our study, we do not assume sparsity directly. Instead, we consider sparsity only in the difference of the linear models. We first use a doubly robust estimator to approximate this difference and then regress the difference on covariates with Lasso regularization. Although this regression estimator is consistent for the CATE, we further reduce the bias using the techniques in double/debiased machine learning (DML) and debiased Lasso, leading to $\sqrt{n}$-consistency and confidence intervals. We refer to the debiased estimator as the triple/debiased Lasso (TDL), applying both DML and debiased Lasso techniques. We confirm the soundness of our proposed method through simulation studies.

stat.ME↗

arXiv2024

The Role of Contextual Information in Best Arm Identification

We study the best-arm identification problem with fixed confidence when contextual (covariate) information is available in stochastic bandits. Although we can use contextual information in each round, we are interested in the marginalized mean reward over the contextual distribution. Our goal is to identify the best arm with a minimal number of samplings under a given value of the error rate. We show the instance-specific sample complexity lower bounds for the problem. Then, we propose a context-aware version of the "Track-and-Stop" strategy, wherein the proportion of the arm draws tracks the set of optimal allocations and prove that the expected number of arm draws matches the lower bound asymptotically. We demonstrate that contextual information can be used to improve the efficiency of the identification of the best marginalized mean reward compared with the results of Garivier & Kaufmann (2016). We experimentally confirm that context information contributes to faster best-arm identification.

cs.LG↗

arXiv2023

Best-of-Both-Worlds Linear Contextual Bandits

This study investigates the problem of $K$-armed linear contextual bandits, an instance of the multi-armed bandit problem, under an adversarial corruption. At each round, a decision-maker observes an independent and identically distributed context and then selects an arm based on the context and past observations. After selecting an arm, the decision-maker incurs a loss corresponding to the selected arm. The decision-maker aims to minimize the cumulative loss over the trial. The goal of this study is to develop a strategy that is effective in both stochastic and adversarial environments, with theoretical guarantees. We first formulate the problem by introducing a novel setting of bandits with adversarial corruption, referred to as the contextual adversarial regime with a self-bounding constraint. We assume linear models for the relationship between the loss and the context. Then, we propose a strategy that extends the RealLinExp3 by Neu & Olkhovskaya (2020) and the Follow-The-Regularized-Leader (FTRL). The regret of our proposed algorithm is shown to be upper-bounded by $O\left(\min\left\{\frac{(\log(T))^3}{Δ_{*}} + \sqrt{\frac{C(\log(T))^3}{Δ_{*}}},\ \ \sqrt{T}(\log(T))^2\right\}\right)$, where $T \in\mathbb{N}$ is the number of rounds, $Δ_{*} > 0$ is the constant minimum gap between the best and suboptimal arms for any context, and $C\in[0, T] $ is an adversarial corruption parameter. This regret upper bound implies $O\left(\frac{(\log(T))^3}{Δ_{*}}\right)$ in a stochastic environment and by $O\left( \sqrt{T}(\log(T))^2\right)$ in an adversarial environment. We refer to our strategy as the Best-of-Both-Worlds (BoBW) RealFTRL, due to its theoretical guarantees in both stochastic and adversarial regimes.

cs.LG↗

arXiv2023

CATE Lasso: Conditional Average Treatment Effect Estimation with High-Dimensional Linear Regression

In causal inference about two treatments, Conditional Average Treatment Effects (CATEs) play an important role as a quantity representing an individualized causal effect, defined as a difference between the expected outcomes of the two treatments conditioned on covariates. This study assumes two linear regression models between a potential outcome and covariates of the two treatments and defines CATEs as a difference between the linear regression models. Then, we propose a method for consistently estimating CATEs even under high-dimensional and non-sparse parameters. In our study, we demonstrate that desirable theoretical properties, such as consistency, remain attainable even without assuming sparsity explicitly if we assume a weaker assumption called implicit sparsity originating from the definition of CATEs. In this assumption, we suppose that parameters of linear models in potential outcomes can be divided into treatment-specific and common parameters, where the treatment-specific parameters take difference values between each linear regression model, while the common parameters remain identical. Thus, in a difference between two linear regression models, the common parameters disappear, leaving only differences in the treatment-specific parameters. Consequently, the non-zero parameters in CATEs correspond to the differences in the treatment-specific parameters. Leveraging this assumption, we develop a Lasso regression method specialized for CATE estimation and present that the estimator is consistent. Finally, we confirm the soundness of the proposed method by simulation studies.

econ.EM↗

arXiv2023

Rate-optimal Bayesian Simple Regret in Best Arm Identification

We consider best arm identification in the multi-armed bandit problem. Assuming certain continuity conditions of the prior, we characterize the rate of the Bayesian simple regret. Differing from Bayesian regret minimization (Lai, 1987), the leading term in the Bayesian simple regret derives from the region where the gap between optimal and suboptimal arms is smaller than $\sqrt{\frac{\log T}{T}}$. We propose a simple and easy-to-compute algorithm with its leading term matching with the lower bound up to a constant factor; simulation results support our theoretical findings.

cs.LG↗