arXiv subjects

Toshinari Morimoto

Publications and source records attributed to Toshinari Morimoto.

5 recordsLinked to original sources

arXiv2026

Function-On-Function Regression Through Separable Neural Operators

This paper investigates the estimation of the regression operator in function-on-function regression models. While traditional research has predominantly focused on linear models or their immediate nonlinear extensions, we propose a neural operator approach to accommodate general regression operators under mild smoothness assumptions. Operator learning has emerged as an active area of machine learning, particularly for solving physical models governed by partial differential equations. Using this paradigm, our methodology introduces the separable neural operator, a neural-operator architecture that represents the regression operator through input-dependent coefficient functions and output-dependent basis functions. Beyond adapting this architecture to the regression operator estimation problem, we establish the consistency of the estimator under relatively mild smoothness and sampling conditions, allowing functional data to be observed on dense, possibly irregular, discrete grids. We also apply the proposed approach to the BGC Argo data and demonstrate its potential for oceanographic research.

math.ST↗

arXiv2026

Blurring Mean Shift for Clustering Functional Data: A Scalable Algorithm and Convergence Analysis

This paper extends the blurring mean shift algorithm from vector-valued data to functional data, enabling effective clustering in infinite-dimensional settings without requiring specification of the number of clusters. To address the computational challenges posed by large-scale datasets, we introduce a fast stochastic variant that significantly reduces computational complexity. We provide a rigorous convergence analysis for the full blurring functional mean shift procedure, establishing theoretical guarantees for its iterative behavior. For the stochastic variant, we provide partial theoretical justification by showing that, when the subset size is sufficiently large, its one-step update is well approximated by the corresponding update of the full algorithm. The proposed method is demonstrated through real-data applications, including hourly Taiwan PM$_{2.5}$ measurements and Argo oceanographic profiles. Our key contributions include: (1) extending the blurring mean shift algorithm to functional data in a Hilbert-space setting; (2) developing a scalable stochastic variant based on random partitioning for large-scale data; (3) establishing convergence results for the full blurring functional mean shift algorithm; and (4) demonstrating the scalability and practical usefulness of the proposed method through simulation and real-data applications.

stat.ME↗

arXiv2026

Generative and Nonparametric Approaches for Conditional Distribution Estimation: Methods, Perspectives, and Comparative Evaluations

The inference of conditional distributions is a fundamental problem in statistics, essential for prediction, uncertainty quantification, and probabilistic modeling. A wide range of methodologies have been developed for this task. This article reviews and compares several representative approaches spanning classical nonparametric methods and modern generative models. We begin with the single-index method of Hall and Yao (2005), which estimates the conditional distribution through a dimension-reducing index and nonparametric smoothing of the resulting one-dimensional cumulative conditional distribution function. We then examine the basis-expansion approaches, including FlexCode (Izbicki and Lee, 2017) and DeepCDE (Dalmasso et al., 2020), which convert conditional density estimation into a set of nonparametric regression problems. In addition, we discuss two recent generative simulation-based methods that leverage modern deep generative architectures: the generative conditional distribution sampler (Zhou et al., 2023) and the conditional denoising diffusion probabilistic model (Fu et al., 2024; Yang et al., 2025). A systematic numerical comparison of these approaches is provided using a unified evaluation framework that ensures fairness and reproducibility. The performance metrics used for the estimated conditional distribution include the mean-squared errors of conditional mean and standard deviation, as well as the Wasserstein distance. We also discuss their flexibility and computational costs, highlighting the distinct advantages and limitations of each approach.

stat.ML↗

arXiv2024

TensorProjection Layer: A Tensor-Based Dimension Reduction Method in Deep Neural Networks

In this paper, we propose a dimension reduction method specifically designed for tensor-structured feature data in deep neural networks. The method is implemented as a hidden layer, called the TensorProjection layer, which transforms input tensors into output tensors with reduced dimensions through mode-wise projections. The projection directions are treated as model parameters of the layer and are optimized during model training. Our method can serve as an alternative to pooling layers for summarizing image data, or to convolutional layers as a technique for reducing the number of channels. We conduct experiments on tasks such as medical image classification and segmentation, integrating the TensorProjection layer into commonly used baseline architectures to evaluate its effectiveness. Numerical experiments indicate that the proposed method can outperform traditional downsampling methods, such as pooling layers, in our tasks, suggesting it as a promising alternative for feature summarization.

stat.ML↗

arXiv2024

Information Criterion-Based Rank Estimation Methods for Factor Analysis: A Unified Selection Consistency Theorem and Numerical Comparison

Over the years, numerous rank estimators for factor models have been proposed in the literature. This article focuses on information criterion-based rank estimators and investigates their consistency in rank selection. The gap conditions serve as necessary and sufficient conditions for rank estimators to achieve selection consistency under the general assumptions of random matrix theory. We establish a unified theorem on selection consistency, presenting the gap conditions for information criterion-based rank estimators with a unified formulation. To validate the theorem's assertion that rank selection consistency is solely determined by the gap conditions, we conduct extensive numerical simulations across various settings. Additionally, we undertake supplementary simulations to explore the strengths and limitations of information criterion-based estimators by comparing them with other types of rank estimators.

math.ST↗