arXiv subjects

Hideitsu Hino

Publications and source records attributed to Hideitsu Hino.

At least 19 recordsLinked to original sources

arXiv2026

Knowledge Distillation under Teacher Misspecification: An Order-Parameter Analysis of the Gap between Teacher Mimicry and Task Performance

Knowledge distillation trains a small student model to reproduce the outputs of a large teacher model, and its progress is typically monitored through the teacher--student discrepancy. The quantity of ultimate interest, however, is the student's error with respect to the true task. We study the relation between these two objectives in a minimal three-party model, a true teacher (generative model), a teacher, and a student, all soft committee machines, in which the true teacher contains a shared latent factor that the teacher cannot represent, with mismatch strength controlled by a single scalar $\dmiss$. Within an order-parameter description of online distillation, and exploiting closed-form (arcsine-type) expressions for all errors under error-function activations, we prove that the learning dynamics and the distillation error $\Ets$ are exactly invariant to $\dmiss$, whereas the true error $\Etzs$ and the gap $\Delta=\Etzs-\Ets$ are strictly increasing in $\dmiss$, with a rate that is amplified linearly by the complexity $M_0$ of the true teacher. Numerical phase diagrams over the plane spanned by true-teacher complexity and student capacity confirm the predicted deformation: the contours of $\Ets$ do not move while the landscape of $\Etzs$ rises systematically, and a teacher-miss regime, where mimicry succeeds but the task fails, expands with $\dmiss$. The results give a quantitative warning against evaluating distillation solely through teacher-mimicry metrics and identify the gap $\Delta$ as a minimal diagnostic for distinguishing teacher-miss from capacity-limited failure.

cs.LG↗

arXiv2026

Determinantal Point Process Approximation under Positive and Negative Dependence

Determinantal point processes (DPPs) are widely used as probabilistic models for diverse random subsets, but their approximation error under model misspecification has not been fully characterized. We study the population-level approximation of a strictly positive target distribution p* by DPPs under the forward Kullback-Leibler divergence. Using information-geometric analysis and the standard quality-diversity decomposition of an L-ensemble kernel, in which the diagonal quality component Q encodes item-specific weights and the diversity component D controls repulsive interactions among items, we show that the quality component can be chosen uniquely to match all first-order inclusion probabilities of p*. The DPP approximation problem therefore reduces to the optimization of the diversity component. This reduction yields a global optimality result for attractively dependent targets: under conditions including weak positive association, the independent product distribution with the same first-order marginals, corresponding to D=I, is an optimal DPP approximation. For more general target distributions, positively correlated pairs yield lower bounds on the approximation error. On the repulsive side, a matching of disjoint negatively correlated pairs yields an upper bound on the approximation error, or equivalently a guaranteed improvement over the independent approximation. We further study local optimality around D=I and, more generally, around block-diagonal diversity matrices by analyzing perturbations between their blocks.

math.ST↗

arXiv2026

Projective Maximum Entropy: Universality and Acceptance-Region Calibration

Maximum-entropy reference distributions are usually constructed on the normalized probability simplex. This formulation is less natural for unnormalized statistical models, in which positive multiples represent the same shape, and it does not directly explain how a prescribed admissible region should determine the deformation parameter of a bounded-support reference distribution. We formulate maximum entropy on the projective space of nonnegative measures and establish three results of statistical relevance. First, a universality theorem shows that every admissible monotone transform of the same normalized power functional has exactly the same optimizer under linear moment constraints. The result unifies the maximum-entropy implications of Tsallis and R\'enyi entropies, H\"older composite scores, pseudo-spherical scores, Bregman--H\"older constructions, and related homogeneous divergences without asserting a new distribution family. Second, the common optimizer is characterized as a $q$-exponential density; under mean and covariance constraints it is a compactly supported $q$-Gaussian for positive deformation and a Student-type density for negative deformation. Third, a prescribed Mahalanobis acceptance region with squared radius $R^2>d+2$ uniquely determines the deformation parameter $\gamma_R=2/(R^2-d-2)$. The resulting affine-equivariant reference density is the unique projective maximum-entropy solution, and its support coincides with the specified ellipsoid without an additional support constraint. This provides a principled method for constructing bounded-support statistical reference distributions from robust location and scatter estimates or from externally specified admissible regions.

math.ST↗

arXiv2026

LIG: Layer-wise Integrated Gradients for Within-Layer Flow Analysis in Transformers

Transformers achieve strong performance, but their internal computations remain opaque. We view each Transformer layer as a dynamic graph whose nodes are token representations and per-head attention outputs, with Multi-Head Attention (ATT) and MLP as module boundaries. On this graph we use LIG (Layer-wise Integrated Gradients), which applies set-to-set Integrated Gradients (IG) at nonlinear module boundaries. Set-to-set IG applies IG to a map from a set of input token representations to a set of output representations, evaluating token-to-token contributions, which is not standard in prior IG applications. This extends IG from the usual scalar-objective setting to set-to-set maps via an L2 scalarization, and composes within-layer contributions in the spirit of Layer-wise Relevance Propagation (LRP), with IG completeness playing the role of LRP-style conservation at each boundary. We use LIG to analyze (i) the agreement between module-wise composition and layer-whole attribution under an L2 criterion, and (ii) within-layer information flow by tracing separated ATT and MLP contributions. On BERT-base and PTB, configurations that best preserved within-layer consistency used the target token's embedding as the ATT baseline and either the ATT output at a=0 or Zero as the MLP baseline. We therefore present LIG as a diagnostic XAI tool at module-boundary granularity, without model-specific retraining or per-operation interpreter design. Code is available at https://github.com/eightsuzuki/layer-wise-integrated-gradients.

cs.LG↗

arXiv2026

From DPPs to $k$-DPPs: identifiability analysis via spectral decomposition

We study the geometry of determinantal point processes (DPPs) through the spectral decomposition $L=U\Lambda U^{\top}$. The spectrum $\Lambda$ governs the cardinality distribution via elementary symmetric polynomials, while the eigenspace orientation $U$ governs the conditional law within each fixed-cardinality stratum. Conditioning on cardinality $k$ yields the $k$-DPP, for which the identifiability structure changes fundamentally: the spectral parameter becomes identifiable only up to a common scale, and the eigenspace rotation parameter is identifiable only through squared minors of the eigenvector matrix. We characterize the identifiability gap precisely, via three explicit invariances (scale, sign similarity, and eigenspace rotation) and a dimension-counting theorem showing the existence of additional continuous non-identifiability whenever $\binom{N}{k}<N(N+1)/2$. In contrast, for the full DPP the non-identifiability comes only from the discrete sign similarity.

stat.ML↗

arXiv2026

Sobolev--Ricci Curvature

Ricci curvature is a fundamental concept in differential geometry for encoding local geometric structure, and its graph-based analogues have recently gained prominence as practical tools for reweighting, pruning, and reshaping network geometry. We propose Sobolev-Ricci Curvature (SRC), a graph Ricci curvature canonically induced by Sobolev transport geometry, which admits efficient evaluation via a tree-metric Sobolev structure on neighborhood measures. We establish two consistency behaviors that anchor SRC to classical transport curvature: (i) on trees endowed with the length measure, SRC recovers Ollivier-Ricci curvature (ORC) in the canonical W1 setting, and (ii) SRC vanishes in the Dirac limit, matching the flat case of measure-theoretic Ricci curvature. We demonstrate SRC as a reusable curvature primitive in two representative pipelines. We define Sobolev-Ricci Flow by replacing ORC with SRC in a Ricci-flow-style reweighting rule, and we use SRC for curvature-guided edge pruning aimed at preserving manifold structure. Overall, SRC provides a transport-based foundation for scalable curvature-driven graph transformation and manifold-oriented pruning.

cs.LG↗

arXiv2025

Generalized Sobolev IPM for Graph-Based Measures

We study the Sobolev IPM problem for measures supported on a graph metric space, where critic function is constrained to lie within the unit ball defined by Sobolev norm. While Le et al. (2025) achieved scalable computation by relating Sobolev norm to weighted $L^p$-norm, the resulting framework remains intrinsically bound to $L^p$ geometric structure, limiting its ability to incorporate alternative structural priors beyond the $L^p$ geometry paradigm. To overcome this limitation, we propose to generalize Sobolev IPM through the lens of \emph{Orlicz geometric structure}, which employs convex functions to capture nuanced geometric relationships, building upon recent advances in optimal transport theory -- particularly Orlicz-Wasserstein (OW) and generalized Sobolev transport -- that have proven instrumental in advancing machine learning methodologies. This generalization encompasses classical Sobolev IPM as a special case while accommodating diverse geometric priors beyond traditional $L^p$ structure. It however brings up significant computational hurdles that compound those already inherent in Sobolev IPM. To address these challenges, we establish a novel theoretical connection between Orlicz-Sobolev norm and Musielak norm which facilitates a novel regularization for the generalized Sobolev IPM (GSI). By further exploiting the underlying graph structure, we show that GSI with Musielak regularization (GSI-M) reduces to a simple \emph{univariate optimization} problem, achieving remarkably computational efficiency. Empirically, GSI-M is several-order faster than the popular OW in computation, and demonstrates its practical advantages in comparing probability measures on a given graph for document classification and several tasks in topological data analysis.

cs.LG↗

arXiv2025

Misspecifying non-compensatory as compensatory IRT: analysis of estimated skills and variance

Multidimensional item response theory is a statistical test theory used to estimate the latent skills of learners and the difficulty levels of problems based on test results. Both compensatory and non-compensatory models have been proposed in the literature. Previous studies have revealed the substantial underestimation of higher skills when the non-compensatory model is misspecified as the compensatory model. However, the underlying mechanism behind this phenomenon has not been fully elucidated. It remains unclear whether overestimation also occurs and whether issues arise regarding the variance of the estimated parameters. In this paper, we aim to provide a comprehensive understanding of both underestimation and overestimation through a theoretical approach. In addition to the previously identified underestimation of the skills, we newly discover that the overestimation of skills occurs around the origin. Furthermore, we investigate the extent to which the asymptotic variance of the estimated parameters differs when considering model misspecification compared to when it is not taken into account.

stat.ME↗

arXiv2025

Complex non-backtracking matrix for directed graphs

Graph representation matrices are essential tools in graph data analysis. Recently, Hermitian adjacency matrices have been proposed to investigate directed graph structures. Previous studies have demonstrated that these matrices can extract valuable information for clustering. In this paper, we propose the complex non-backtracking matrix that integrates the properties of the Hermitian adjacency matrix and the non-backtracking matrix. The proposed matrix has similar properties with the non-backtracking matrix of undirected graphs. We reveal relationships between the complex non-backtracking matrix and the Hermitian adjacency matrix. Also, we provide intriguing insights that this matrix representation holds cluster information, particularly for sparse directed graphs.

math.CO↗

arXiv2025

An $(\epsilon,\delta)$-accurate level set estimation with a stopping criterion

The level set estimation problem seeks to identify regions within a set of candidate points where an unknown and costly to evaluate function's value exceeds a specified threshold, providing an efficient alternative to exhaustive evaluations of function values. Traditional methods often use sequential optimization strategies to find $\epsilon$-accurate solutions, which permit a margin around the threshold contour but frequently lack effective stopping criteria, leading to excessive exploration and inefficiencies. This paper introduces an acquisition strategy for level set estimation that incorporates a stopping criterion, ensuring the algorithm halts when further exploration is unlikely to yield improvements, thereby reducing unnecessary function evaluations. We theoretically prove that our method satisfies $\epsilon$-accuracy with a confidence level of $1 - \delta$, addressing a key gap in existing approaches. Furthermore, we show that this also leads to guarantees on the lower bounds of performance metrics such as F-score. Numerical experiments demonstrate that the proposed acquisition function achieves comparable precision to existing methods while confirming that the stopping criterion effectively terminates the algorithm once adequate exploration is completed.

stat.ML↗

arXiv2025

Scalable Sobolev IPM for Probability Measures on a Graph

We investigate the Sobolev IPM problem for probability measures supported on a graph metric space. Sobolev IPM is an important instance of integral probability metrics (IPM), and is obtained by constraining a critic function within a unit ball defined by the Sobolev norm. In particular, it has been used to compare probability measures and is crucial for several theoretical works in machine learning. However, to our knowledge, there are no efficient algorithmic approaches to compute Sobolev IPM effectively, which hinders its practical applications. In this work, we establish a relation between Sobolev norm and weighted $L^p$-norm, and leverage it to propose a \emph{novel regularization} for Sobolev IPM. By exploiting the graph structure, we demonstrate that the regularized Sobolev IPM provides a \emph{closed-form} expression for fast computation. This advancement addresses long-standing computational challenges, and paves the way to apply Sobolev IPM for practical applications, even in large-scale settings. Additionally, the regularized Sobolev IPM is negative definite. Utilizing this property, we design positive-definite kernels upon the regularized Sobolev IPM, and provide preliminary evidences of their advantages for comparing probability measures on a given graph for document classification and topological data analysis.

stat.ML↗

arXiv2025

An Efficient Orlicz-Sobolev Approach for Transporting Unbalanced Measures on a Graph

We investigate optimal transport (OT) for measures on graph metric spaces with different total masses. To mitigate the limitations of traditional $L^p$ geometry, Orlicz-Wasserstein (OW) and generalized Sobolev transport (GST) employ Orlicz geometric structure, leveraging convex functions to capture nuanced geometric relationships and remarkably contribute to advance certain machine learning approaches. However, both OW and GST are restricted to measures with equal total mass, limiting their applicability to real-world scenarios where mass variation is common, and input measures may have noisy supports, or outliers. To address unbalanced measures, OW can either incorporate mass constraints or marginal discrepancy penalization, but this leads to a more complex two-level optimization problem. Additionally, GST provides a scalable yet rigid framework, which poses significant challenges to extend GST to accommodate nonnegative measures. To tackle these challenges, in this work we revisit the entropy partial transport (EPT) problem. By exploiting Caffarelli & McCann (2010)'s insights, we develop a novel variant of EPT endowed with Orlicz geometric structure, called Orlicz-EPT. We establish theoretical background to solve Orlicz-EPT using a binary search algorithmic approach. Especially, by leveraging the dual EPT and the underlying graph structure, we formulate a novel regularization approach that leads to the proposed Orlicz-Sobolev transport (OST). Notably, we demonstrate that OST can be efficiently computed by simply solving a univariate optimization problem, in stark contrast to the intensive computation needed for Orlicz-EPT. Building on this, we derive geometric structures for OST and draw its connections to other transport distances. We empirically illustrate that OST is several-order faster than Orlicz-EPT.

stat.ML↗

arXiv2024

A Family of Distributions of Random Subsets for Controlling Positive and Negative Dependence

Positive and negative dependence are fundamental concepts that characterize the attractive and repulsive behavior of random subsets. Although some probabilistic models are known to exhibit positive or negative dependence, it is challenging to seamlessly bridge them with a practicable probabilistic model. In this study, we introduce a new family of distributions, named the discrete kernel point process (DKPP), which includes determinantal point processes and parts of Boltzmann machines. We also develop some computational methods for probabilistic operations and inference with DKPPs, such as calculating marginal and conditional probabilities and learning the parameters. Our numerical experiments demonstrate the controllability of positive and negative dependence and the effectiveness of the computational methods for DKPPs.

stat.ML↗

arXiv2024

Duality induced by an embedding structure of determinantal point process

This paper investigates the information geometrical structure of a determinantal point process (DPP). It demonstrates that a DPP is embedded in the exponential family of log-linear models. The extent of deviation from an exponential family is analyzed using the $\mathrm{e}$-embedding curvature tensor, which identifies partially flat parameters of a DPP. On the basis of this embedding structure, the duality related to a marginal kernel and an $L$-ensemble kernel is discovered.

math.ST↗

arXiv2024

A Short Survey on Importance Weighting for Machine Learning

Importance weighting is a fundamental procedure in statistics and machine learning that weights the objective function or probability distribution based on the importance of the instance in some sense. The simplicity and usefulness of the idea has led to many applications of importance weighting. For example, it is known that supervised learning under an assumption about the difference between the training and test distributions, called distribution shift, can guarantee statistically desirable properties through importance weighting by their density ratio. This survey summarizes the broad applications of importance weighting in machine learning and related research.

cs.LG↗

arXiv2024

Gradual Domain Adaptation via Normalizing Flows

Standard domain adaptation methods do not work well when a large gap exists between the source and target domains. Gradual domain adaptation is one of the approaches used to address the problem. It involves leveraging the intermediate domain, which gradually shifts from the source domain to the target domain. In previous work, it is assumed that the number of intermediate domains is large and the distance between adjacent domains is small; hence, the gradual domain adaptation algorithm, involving self-training with unlabeled datasets, is applicable. In practice, however, gradual self-training will fail because the number of intermediate domains is limited and the distance between adjacent domains is large. We propose the use of normalizing flows to deal with this problem while maintaining the framework of unsupervised domain adaptation. The proposed method learns a transformation from the distribution of the target domain to the Gaussian mixture distribution via the source domain. We evaluate our proposed method by experiments using real-world datasets and confirm that it mitigates the above-explained problem and improves the classification performance.

stat.ML↗

arXiv2023

Scalable Counterfactual Distribution Estimation in Multivariate Causal Models

We consider the problem of estimating the counterfactual joint distribution of multiple quantities of interests (e.g., outcomes) in a multivariate causal model extended from the classical difference-in-difference design. Existing methods for this task either ignore the correlation structures among dimensions of the multivariate outcome by considering univariate causal models on each dimension separately and hence produce incorrect counterfactual distributions, or poorly scale even for moderate-size datasets when directly dealing with such multivariate causal model. We propose a method that alleviates both issues simultaneously by leveraging a robust latent one-dimensional subspace of the original high-dimension space and exploiting the efficient estimation from the univariate causal model on such space. Since the construction of the one-dimensional subspace uses information from all the dimensions, our method can capture the correlation structures and produce good estimates of the counterfactual distribution. We demonstrate the advantages of our approach over existing methods on both synthetic and real-world data.

stat.ML↗

arXiv2023

Information Geometrically Generalized Covariate Shift Adaptation

Many machine learning methods assume that the training and test data follow the same distribution. However, in the real world, this assumption is very often violated. In particular, the phenomenon that the marginal distribution of the data changes is called covariate shift, one of the most important research topics in machine learning. We show that the well-known family of covariate shift adaptation methods is unified in the framework of information geometry. Furthermore, we show that parameter search for geometrically generalized covariate shift adaptation method can be achieved efficiently. Numerical experiments show that our generalization can achieve better performance than the existing methods it encompasses.

cs.LG↗