arXiv subjects

Shunnosuke Ikeda

Publications and source records attributed to Shunnosuke Ikeda.

14 recordsLinked to original sources

arXiv2026

Safe screening rules for portfolio optimization with linear and cardinality constraints

In portfolio optimization, a cardinality constraint, which limits the number of assets held, plays a key role in cutting down monitoring and transaction costs. However, the resulting problem is NP-hard and becomes computationally difficult to solve globally as the number of candidate assets grows. Safe screening addresses this difficulty by fixing decision variables before optimization without excluding any globally optimal solution, thereby reducing the problem size while preserving optimality guarantees. We propose safe screening rules for cardinality-constrained portfolio optimization with a convex quadratic objective function and linear constraints. Using a perspective relaxation of the L2-regularization term and Fenchel duality, we derive asset-specific scores that incorporate the Lagrange multipliers of the linear constraints. Combined with a relaxation-based lower bound and a feasible-solution upper bound, these scores safely fix binary asset-selection variables to zero or one. Experiments on S&P 500 and Russell 2000 datasets show substantial computational improvements on challenging cases, particularly under moderate or strong regularization and less stringent return requirements. These results demonstrate the effectiveness of safe screening as an optimality-preserving preprocessing technique that greatly boosts computational efficiency in large-scale cardinality-constrained portfolio optimization.

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arXiv2026

Nonlinear Data Integration via Kernel Methods for Data Collaboration Analysis

Collaborative analysis of decentralized confidential datasets is important, but direct sharing of original datasets is often restricted by privacy and institutional constraints. Data collaboration (DC) analysis transforms each dataset into privacy-preserving intermediate representations via party-specific obfuscation functions and integrates them into common collaboration representations using an anchor dataset. However, many existing DC analysis methods rely on linear transformations for data obfuscation and integration, which may increase reconstruction risk. Although nonlinear dimensionality reduction can mitigate this risk, conventional linear integration methods cannot accurately align intermediate representations produced by nonlinear transformations. Moreover, existing integration methods mainly minimize discrepancies among parties and do not explicitly incorporate geometric or target-variable information useful for downstream analysis. To overcome these limitations, we first formulate linear target-normalized integration (LTI) as a linear integration method and then kernelize it to obtain kernel-based target-normalized integration (KTI). KTI admits a globally optimal solution via kernel ridge regression and an eigenvalue problem. We also introduce graph regularization and a centering constraint so that the target representation can capture geometric and target-variable information useful for downstream analysis. Experiments on image classification tasks demonstrate that KTI improves classification accuracy over existing linear integration methods under nonlinear dimensionality reduction, with further gains from target-variable-aware graph regularization and centering. The results also show that dimensionality reduction choices substantially affect both classification accuracy and reconstruction risk.

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arXiv2026

Cross-validation-based optimal feature selection for linear SVM classification

This paper addresses feature subset selection for Support Vector Machines (SVMs) based on the cross-validation criterion. Unlike statistical criteria such as the Akaike information criterion (AIC) and the Bayesian information criterion (BIC), cross-validation requires only the mild assumption that samples are independently and identically distributed (i.i.d.). For this reason, the cross-validation criterion is expected to work well across a wide range of prediction problems, and it has already demonstrated its usefulness as a feature subset selection method for regression. The objective of this paper is to extend the framework of best feature subset selection via the cross-validation criterion to SVM classification problems. This subset-selection problem can be formulated as a bilevel mixed-integer optimization problem. Because bilevel optimization problems are generally hard to solve, we introduce the Least Squares Support Vector Machine (LS-SVM), whose optimality conditions admit a closed-form expression, and reduce the problem to a single-level mixed-integer optimization problem. This reformulation allows us to solve the problem using standard optimization software. We evaluate the proposed framework through simulation experiments that compare it with a regularization-based method (L1-regularization), a sequential search method (recursive feature elimination), and mixed-integer optimization (MIO) based on statistical criteria. The results show that the proposed framework achieves favorable performance both in classification accuracy and feature selection accuracy.

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arXiv2026

Distributionally robust optimization for recommendation selection

Recommender systems play an essential role in online services by providing personalized item lists to support users' decision-making processes. While collaborative filtering methods can achieve high accuracy, it is crucial to consider not only accuracy but also the diversity of recommended items to improve user satisfaction. Although financial portfolio theory has been applied to balance these factors, existing models are often sensitive to estimation errors in rating statistics. To overcome these challenges, we establish a computational framework of distributionally robust optimization (DRO) for recommendation selection. We first formulate a cardinality-constrained DRO model based on moment-based ambiguity sets to select a specified number of items for each user. We then design a penalty alternating direction method (PADM) to efficiently compute high-quality solutions and prove its convergence properties. Computational experiments using three publicly available rating datasets demonstrate that our DRO model generates more diverse recommendations than existing models while maintaining the same level of accuracy. Additionally, our solution method computes these recommendations for each user in just a few seconds, proving its practical effectiveness. This study establishes a DRO framework that has the potential to enhance the recommendation quality of various collaborative filtering methods.

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arXiv2026

Interpretable clustering via optimal multi-way decision trees

Clustering is a fundamental unsupervised learning technique for uncovering data structures to facilitate knowledge discovery and decision-making. While clustering accuracy is crucial, interpretability significantly impacts the practical value of clustering results, particularly in high-risk decision-making contexts. Although decision-tree-based clustering methods offer high interpretability through explicit splitting rules, existing approaches often rely on local greedy search or require expensive computational costs limited to binary splits, resulting in deeper, less interpretable trees. To overcome these limitations, we establish a high-performance computational framework named Interpretable Clustering via Optimal Multi-way Trees (ICOMT). We make three primary contributions. First, we propose a new discretization method for numerical features using one-dimensional K-means clustering to capture data distributions. Second, we formulate a binary linear optimization (BLO) problem to guarantee tree optimality. Third, extensive validation on four public datasets demonstrates that our ICOMT method outperforms existing baselines, achieving superior clustering accuracy while maintaining shallow, concise tree structures.

cs.LG↗

arXiv2026

Buffered AUC maximization for scoring systems via mixed-integer optimization

A scoring system is a linear classifier composed of a small number of explanatory variables, each assigned a small integer coefficient. This system is highly interpretable and allows predictions to be made with simple manual calculations without the need for a calculator. Several previous studies have used mixed-integer optimization (MIO) techniques to develop scoring systems for binary classification; however, they have not focused on directly maximizing AUC (i.e., area under the receiver operating characteristic curve), even though AUC is recognized as an essential evaluation metric for scoring systems. Our goal herein is to establish an effective MIO framework for constructing scoring systems that directly maximize the buffered AUC (bAUC) as the tightest concave lower bound on AUC. Our optimization model is formulated as a mixed-integer linear optimization (MILO) problem that maximizes bAUC subject to a group sparsity constraint for limiting the number of questions in the scoring system. Computational experiments using publicly available real-world datasets demonstrate that our MILO method can build scoring systems with superior AUC values compared to the baseline methods based on regularization and stepwise regression. This research contributes to the advancement of MIO techniques for developing highly interpretable classification models.

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arXiv2025

Impossibility Results of Card-Based Protocols via Mathematical Optimization

This paper introduces mathematical optimization as a new method for proving impossibility results in the field of card-based cryptography. While previous impossibility proofs were often limited to cases involving a small number of cards, this new approach establishes results that hold for a large number of cards. The research focuses on single-cut full-open (SCFO) protocols, which consist of performing one random cut and then revealing all cards. The main contribution is that for any three-variable Boolean function, no new SCFO protocols exist beyond those already known, under the condition that all additional cards have the same color. The significance of this work is that it provides a new framework for proving impossibility results and delivers a proof that is valid for any number of cards, as long as all additional cards have the same color.

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arXiv2025

Estimating profitable price bounds for prescriptive price optimization

Pricing of products and services, which has a significant impact on consumer demand, is one of the most important factors in maximizing business profits. Prescriptive price optimization is a prominent data-driven pricing methodology consisting of two phases: demand forecasting and price optimization. In the practice of prescriptive price optimization, the price of each item is typically set within a predetermined range defined by lower and upper bounds. Narrow price ranges can lead to missed opportunities, while wide price ranges run the risk of proposing unrealistic prices; therefore, determining profitable price bounds while maintaining the reliability of the suggested prices is a critical challenge that directly affects the effectiveness of prescriptive price optimization. We propose two methods for estimating price bounds in prescriptive price optimization so that future total revenue derived from the optimized prices will be maximized. Our first method for price bounds estimation uses the bootstrap procedure to estimate confidence intervals for optimal prices. Our second method uses the Nelder--Mead simplex method for black-box price bounds optimization that maximizes total revenue estimated through $K$-fold cross-validation. Experimental results with synthetic price--demand datasets demonstrate that our methods successfully narrowed down the price range while maintaining high revenues, particularly when the number of items was small or the demand noise level was low. Moreover, as more data accumulated, the comparative advantage of our methods further increased.

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arXiv2024

Robust personalized pricing under uncertainty of purchase probabilities

This paper is concerned with personalized pricing models aimed at maximizing the expected revenues or profits for a single item. While it is essential for personalized pricing to predict the purchase probabilities for each consumer, these predicted values are inherently subject to unavoidable errors that can negatively impact the realized revenues and profits. To address this issue, we focus on robust optimization techniques that yield reliable solutions to optimization problems under uncertainty. Specifically, we propose a robust optimization model for personalized pricing that accounts for the uncertainty of predicted purchase probabilities. This model can be formulated as a mixed-integer linear optimization problem, which can be solved exactly using mathematical optimization solvers. We also develop a Lagrangian decomposition algorithm combined with line search to efficiently find high-quality solutions for large-scale optimization problems. Experimental results demonstrate the effectiveness of our robust optimization model and highlight the utility of our Lagrangian decomposition algorithm in terms of both computational efficiency and solution quality.

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arXiv2024

Fast solution to the fair ranking problem using the Sinkhorn algorithm

In two-sided marketplaces such as online flea markets, recommender systems for providing consumers with personalized item rankings play a key role in promoting transactions between providers and consumers. Meanwhile, two-sided marketplaces face the problem of balancing consumer satisfaction and fairness among items to stimulate activity of item providers. Saito and Joachims (2022) devised an impact-based fair ranking method for maximizing the Nash social welfare based on fair division; however, this method, which requires solving a large-scale constrained nonlinear optimization problem, is very difficult to apply to practical-scale recommender systems. We thus propose a fast solution to the impact-based fair ranking problem. We first transform the fair ranking problem into an unconstrained optimization problem and then design a gradient ascent method that repeatedly executes the Sinkhorn algorithm. Experimental results demonstrate that our algorithm provides fair rankings of high quality and is about 1000 times faster than application of commercial optimization software.

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arXiv2024

Robust portfolio optimization for recommender systems considering uncertainty of estimated statistics

This paper is concerned with portfolio optimization models for creating high-quality lists of recommended items to balance the accuracy and diversity of recommendations. However, the statistics (i.e., expectation and covariance of ratings) required for mean--variance portfolio optimization are subject to inevitable estimation errors. To remedy this situation, we focus on robust optimization techniques that derive reliable solutions to uncertain optimization problems. Specifically, we propose a robust portfolio optimization model that copes with the uncertainty of estimated statistics based on the cardinality-based uncertainty sets. This robust portfolio optimization model can be reduced to a mixed-integer linear optimization problem, which can be solved exactly using mathematical optimization solvers. Experimental results using two publicly available rating datasets demonstrate that our method can improve not only the recommendation accuracy but also the diversity of recommendations compared with conventional mean--variance portfolio optimization models. Notably, our method has the potential to improve the recommendation quality of various rating prediction algorithms.

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arXiv2024

Container pre-marshalling problem minimizing CV@R under uncertainty of ship arrival times

This paper is concerned with the container pre-marshalling problem, which involves relocating containers in the storage area so that they can be efficiently loaded onto ships without reshuffles. In reality, however, ship arrival times are affected by various external factors, which can cause the order of container retrieval to be different from the initial plan. To represent such uncertainty, we generate multiple scenarios from a multivariate probability distribution of ship arrival times. We derive a mixed-integer linear optimization model to find an optimal container layout such that the conditional value-at-risk is minimized for the number of misplaced containers responsible for reshuffles. Moreover, we devise an exact algorithm based on the cutting-plane method to handle large-scale problems. Numerical experiments using synthetic datasets demonstrate that our method can produce high-quality container layouts compared with the conventional robust optimization model. Additionally, our algorithm can speed up the computation of solving large-scale problems.

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arXiv2024

Privacy-preserving recommender system using the data collaboration analysis for distributed datasets

In order to provide high-quality recommendations for users, it is desirable to share and integrate multiple datasets held by different parties. However, when sharing such distributed datasets, we need to protect personal and confidential information contained in the datasets. To this end, we establish a framework for privacy-preserving recommender systems using the data collaboration analysis of distributed datasets. Numerical experiments with two public rating datasets demonstrate that our privacy-preserving method for rating prediction can improve the prediction accuracy for distributed datasets. This study opens up new possibilities for privacy-preserving techniques in recommender systems.

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arXiv2024

Interpretable Price Bounds Estimation with Shape Constraints in Price Optimization

This study addresses the interpretable estimation of price bounds in the context of price optimization. In recent years, price-optimization methods have become indispensable for maximizing revenue and profits. However, effective application of these methods to real-world pricing operations remains a significant challenge. It is crucial for operators responsible for setting prices to utilize reasonable price bounds that are not only interpretable but also acceptable. Despite this necessity, most studies assume that price bounds are given constant values, and few have explored reasonable determinations of these bounds. Therefore, we propose a comprehensive framework for determining price bounds that includes both the estimation and adjustment of these bounds. Specifically, we first estimate price bounds using three distinct approaches based on historical pricing data. Then, we adjust the estimated price bounds by solving an optimization problem that incorporates shape constraints. This method allows the implementation of price optimization under practical and reasonable price bounds suitable for real-world applications. We report the effectiveness of our proposed method through numerical experiments using historical pricing data from actual services.

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