arXiv subjects

Daichi Mochihashi

Publications and source records attributed to Daichi Mochihashi.

12 recordsLinked to original sources

arXiv2026

Spatially Dependent Indian Buffet Processes

We develop a new stochastic process called spatially dependent Indian buffet processes (sIBP) for binary feature matrices of unbounded columns with spatial correlations between subjects, and propose general spatial factor models for various multivariate response variables. We introduce spatial dependency through the stick-breaking representation of the original Indian buffet process (IBP; Griffiths and Ghahramani, 2005, 2011) and latent Gaussian process for the logit-transformed breaking proportions to capture underlying spatial correlation. We show that sIBP retains the sparsity and finite-feature behavior of the original IBP, while its joint feature allocation probabilities are affected by spatial correlation. Using binomial expansion and Polya-gamma data augmentation, we provide an efficient Gibbs sampler for posterior computation. The usefulness of our sIBP is demonstrated through simulation studies and two applications for large-dimensional multinomial data of areal dialects and geographical distribution of multiple tree species.

stat.ME↗

arXiv2026

Dynamical Non-compensatory Multidimensional IRT Model Using Variational Approximation

Multidimensional item response theory (MIRT) is a statistical test theory that precisely estimates multiple latent skills of learners from the responses in a test. Both compensatory and non-compensatory models have been proposed for MIRT: the former assumes that each skill can complement other skills, whereas the latter assumes they cannot. This non-compensatory assumption is convincing in many tests that measure multiple skills; therefore, applying non-compensatory models to such data is crucial for achieving unbiased and accurate estimation. In contrast to tests, latent skills will change over time in daily learning. To monitor the growth of skills, dynamical extensions of MIRT models have been investigated. However, most of them assumed compensatory models, and a model that can reproduce continuous latent states of skills under the non-compensatory assumption has not been proposed thus far. To enable accurate skill tracing under the non-compensatory assumption, we propose a dynamical extension of non-compensatory MIRT models by combining a linear dynamical system and a non-compensatory model. This results in a complicated posterior of skills, which we approximate with a Gaussian distribution by minimizing the Kullback-Leibler divergence between the approximated posterior and the true posterior. The learning algorithm for the model parameters is derived through Monte Carlo expectation maximization. Simulation studies verify that the proposed method is able to reproduce latent skills accurately, whereas the dynamical compensatory model suffers from significant underestimation errors. Furthermore, experiments on an actual data set demonstrate that our dynamical non-compensatory model can infer practical skill tracing and clarify differences in skill tracing between non-compensatory and compensatory models.

stat.ME↗

arXiv2026

Contrastive Bayesian Inference for Unnormalized Models

Unnormalized (or energy-based) models provide a flexible framework for capturing the characteristics of data with complex dependency structures. However, the application of standard Bayesian inference methods has been severely limited because the parameter-dependent normalizing constant is either analytically intractable or computationally prohibitive to evaluate. A promising approach is score-based generalized Bayesian inference, which avoids evaluating the normalizing constant by replacing the likelihood with a scoring rule. However, this approach still requires careful tuning of the likelihood information, and it may fail to yield valid inference without appropriate control. To overcome this difficulty, we propose a fully Bayesian framework for inference on unnormalized models that does not require such tuning. We build on noise-contrastive estimation, which recasts inference as a binary classification problem between observed and noise samples, and treat the normalizing constant as an additional unknown parameter within the resulting likelihood. For exponential families, the classification likelihood becomes conditionally Gaussian via Pólya-Gamma data augmentation, leading to a simple Gibbs sampler. We further establish posterior concentration and a Bernstein-von Mises theorem for our proposed method, providing theoretical justification for its uncertainty quantification. We demonstrate the proposed approach through two models: time-varying density models of temporal point processes and sparse torus graph models of multivariate circular data. Through simulation studies and real-data analyses, our proposed method provides accurate point estimates and principled uncertainty quantification.

stat.ME↗

arXiv2026

Holographic Neural PCFG for Unsupervised Parsing

Unsupervised constituency parsing aims to accurately induce latent tree structures from raw text alone. Recent neural parameterizations of PCFGs achieve strong performance in both supervised and unsupervised parsing, yet rely on high-capacity black-box networks for rule scoring -- as exemplified by the Neural PCFG family -- leaving rule probabilities without an interpretable mathematical form. In this paper, we propose Holographic Neural PCFG (Hol-PCFG), which recasts PCFG rule scoring as algebraic relation modeling among grammar-symbol embeddings. Hol-PCFG adapts Holographic Embeddings (Nickel et al., 2016), which scores knowledge-graph triples via circular correlation, to the left-child, right-child, and lexical-emission relations over torus-constrained embeddings, giving every rule probability a closed form that carries the intrinsic structure of grammar rules by construction. Hol-PCFG achieves state-of-the-art parsing performance in six languages while cutting rule-scoring parameters by 99.94% relative to the baseline model and training more stably. Additionally, we demonstrate that Hol-PCFG can parse Japanese directly from characters without any morphological segmentation, retaining nearly the same morpheme-level performance.

cs.CL↗

arXiv2025

Sequential Adaptive Priors for Orthogonal Functions

We propose a novel class of prior distributions for sequences of orthogonal functions, which are frequently required in various statistical models such as functional principal component analysis (FPCA). Our approach constructs priors sequentially by imposing adaptive orthogonality constraints through a hierarchical formulation of conditionally normal distributions. The orthogonality is controlled via hyperparameters, allowing for flexible trade-offs between exactness and smoothness, which can be learned from the observed data. We illustrate the properties of the proposed prior and show that it leads to nearly orthogonal posterior estimates. The proposed prior is employed in Bayesian FPCA, providing more interpretable principal functions and efficient low-rank representations. Through simulation studies and analysis of human mobility data in Tokyo, we demonstrate the superior performance of our approach in inducing orthogonality and improving functional component estimation.

stat.ME↗

arXiv2025

Tracking Temporal Dynamics of Vector Sets with Gaussian Process

Understanding the temporal evolution of sets of vectors is a fundamental challenge across various domains, including ecology, crime analysis, and linguistics. For instance, ecosystem structures evolve due to interactions among plants, herbivores, and carnivores; the spatial distribution of crimes shifts in response to societal changes; and word embedding vectors reflect cultural and semantic trends over time. However, analyzing such time-varying sets of vectors is challenging due to their complicated structures, which also evolve over time. In this work, we propose a novel method for modeling the distribution underlying each set of vectors using infinite-dimensional Gaussian processes. By approximating the latent function in the Gaussian process with Random Fourier Features, we obtain compact and comparable vector representations over time. This enables us to track and visualize temporal transitions of vector sets in a low-dimensional space. We apply our method to both sociological data (crime distributions) and linguistic data (word embeddings), demonstrating its effectiveness in capturing temporal dynamics. Our results show that the proposed approach provides interpretable and robust representations, offering a powerful framework for analyzing structural changes in temporally indexed vector sets across diverse domains.

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

Scalable Unsupervised Segmentation via Random Fourier Feature-based Gaussian Process

In this paper, we propose RFF-GP-HSMM, a fast unsupervised time-series segmentation method that incorporates random Fourier features (RFF) to address the high computational cost of the Gaussian process hidden semi-Markov model (GP-HSMM). GP-HSMM models time-series data using Gaussian processes, requiring inversion of an N times N kernel matrix during training, where N is the number of data points. As the scale of the data increases, matrix inversion incurs a significant computational cost. To address this, the proposed method approximates the Gaussian process with linear regression using RFF, preserving expressive power while eliminating the need for inversion of the kernel matrix. Experiments on the Carnegie Mellon University (CMU) motion-capture dataset demonstrate that the proposed method achieves segmentation performance comparable to that of conventional methods, with approximately 278 times faster segmentation on time-series data comprising 39,200 frames.

cs.LG↗

arXiv2025

Analyzing Continuous Semantic Shifts with Diachronic Word Similarity Matrices

The meanings and relationships of words shift over time. This phenomenon is referred to as semantic shift. Research focused on understanding how semantic shifts occur over multiple time periods is essential for gaining a detailed understanding of semantic shifts. However, detecting change points only between adjacent time periods is insufficient for analyzing detailed semantic shifts, and using BERT-based methods to examine word sense proportions incurs a high computational cost. To address those issues, we propose a simple yet intuitive framework for how semantic shifts occur over multiple time periods by leveraging a similarity matrix between the embeddings of the same word through time. We compute a diachronic word similarity matrix using fast and lightweight word embeddings across arbitrary time periods, making it deeper to analyze continuous semantic shifts. Additionally, by clustering the similarity matrices for different words, we can categorize words that exhibit similar behavior of semantic shift in an unsupervised manner.

cs.CL↗

arXiv2020

Unbounded Slice Sampling

Slice sampling is an efficient Markov Chain Monte Carlo algorithm to sample from an unnormalized density with acceptance ratio always $1$. However, when the variable to sample is unbounded, its "stepping-out" heuristic works only locally, making it difficult to uniformly explore possible candidates. This paper proposes a simple change-of-variable method to slice sample an unbounded variable equivalently from [0,1).

stat.CO↗

arXiv2020

How LSTM Encodes Syntax: Exploring Context Vectors and Semi-Quantization on Natural Text

Long Short-Term Memory recurrent neural network (LSTM) is widely used and known to capture informative long-term syntactic dependencies. However, how such information are reflected in its internal vectors for natural text has not yet been sufficiently investigated. We analyze them by learning a language model where syntactic structures are implicitly given. We empirically show that the context update vectors, i.e. outputs of internal gates, are approximately quantized to binary or ternary values to help the language model to count the depth of nesting accurately, as Suzgun et al. (2019) recently show for synthetic Dyck languages. For some dimensions in the context vector, we show that their activations are highly correlated with the depth of phrase structures, such as VP and NP. Moreover, with an $L_1$ regularization, we also found that it can accurately predict whether a word is inside a phrase structure or not from a small number of components of the context vector. Even for the case of learning from raw text, context vectors are shown to still correlate well with the phrase structures. Finally, we show that natural clusters of the functional words and the part of speeches that trigger phrases are represented in a small but principal subspace of the context-update vector of LSTM.

cs.CL↗

arXiv2011

Restricted Collapsed Draw: Accurate Sampling for Hierarchical Chinese Restaurant Process Hidden Markov Models

We propose a restricted collapsed draw (RCD) sampler, a general Markov chain Monte Carlo sampler of simultaneous draws from a hierarchical Chinese restaurant process (HCRP) with restriction. Models that require simultaneous draws from a hierarchical Dirichlet process with restriction, such as infinite Hidden markov models (iHMM), were difficult to enjoy benefits of \markerg{the} HCRP due to combinatorial explosion in calculating distributions of coupled draws. By constructing a proposal of seating arrangements (partitioning) and stochastically accepts the proposal by the Metropolis-Hastings algorithm, the RCD sampler makes accurate sampling for complex combination of draws while retaining efficiency of HCRP representation. Based on the RCD sampler, we developed a series of sophisticated sampling algorithms for iHMMs, including blocked Gibbs sampling, beam sampling, and split-merge sampling, that outperformed conventional iHMM samplers in experiments

stat.ML↗