arXiv subjects

Takashi Hayakawa

Publications and source records attributed to Takashi Hayakawa.

4 recordsLinked to original sources

arXiv2025

Fast Riemannian-manifold Hamiltonian Monte Carlo for hierarchical Gaussian-process models

Hierarchical Bayesian models based on Gaussian processes are considered useful for describing complex nonlinear statistical dependencies among variables in real-world data. However, effective Monte Carlo algorithms for inference with these models have not yet been established, except for several simple cases. In this study, we show that, compared with the slow inference achieved with existing program libraries, the performance of Riemannian-manifold Hamiltonian Monte Carlo (RMHMC) can be drastically improved by optimising the computation order according to the model structure and dynamically programming the eigendecomposition. This improvement cannot be achieved when using an existing library based on a naive automatic differentiator. We numerically demonstrate that RMHMC effectively samples from the posterior, allowing the calculation of model evidence, in a Bayesian logistic regression on simulated data and in the estimation of propensity functions for the American national medical expenditure data using several Bayesian multiple-kernel models. These results lay a foundation for implementing effective Monte Carlo algorithms for analysing real-world data with Gaussian processes, and highlight the need to develop a customisable library set that allows users to incorporate dynamically programmed objects and finely optimises the mode of automatic differentiation depending on the model structure.

stat.ML↗

arXiv2025

Debiased maximum-likelihood estimators for hazard ratios under kernel-based machine-learning adjustment

Previous studies have shown that hazard ratios between treatment groups estimated with the Cox model are uninterpretable because the unspecified baseline hazard of the model fails to identify temporal change in the risk set composition due to treatment assignment and unobserved factors among multiple, contradictory scenarios. To alleviate this problem, especially in studies based on observational data with uncontrolled dynamic treatment and real-time measurement of many covariates, we propose abandoning the baseline hazard and using kernel-based machine learning to explicitly model the change in the risk set with or without latent variables. For this framework, we clarify the context in which hazard ratios can be causally interpreted, and then develop a method based on Neyman orthogonality to compute debiased maximum-likelihood estimators of hazard ratios, proving necessary convergence results. Numerical simulations confirm that the proposed method identifies the true hazard ratios with minimal bias. These results lay the foundation for developing a useful, alternative method for causal inference with uncontrolled, observational data in modern epidemiology.

stat.ML↗

arXiv2019

Spontaneous and stimulus-induced coherent states of critically balanced neuronal networks

How the information microscopically processed by individual neurons is integrated and used in organizing the behavior of an animal is a central question in neuroscience. The coherence of neuronal dynamics over different scales has been suggested as a clue to the mechanisms underlying this integration. Balanced excitation and inhibition may amplify microscopic fluctuations to a macroscopic level, thus providing a mechanism for generating coherent multiscale dynamics. Previous theories of brain dynamics, however, were restricted to cases in which inhibition dominated excitation and suppressed fluctuations in the macroscopic population activity. In the present study, we investigate the dynamics of neuronal networks at a critical point between excitation-dominant and inhibition-dominant states. In these networks, the microscopic fluctuations are amplified by the strong excitation and inhibition to drive the macroscopic dynamics, while the macroscopic dynamics determine the statistics of the microscopic fluctuations. Developing a novel type of mean-field theory applicable to this class of interscale interactions, we show that the amplification mechanism generates spontaneous, irregular macroscopic rhythms similar to those observed in the brain. Through the same mechanism, microscopic inputs to a small number of neurons effectively entrain the dynamics of the whole network. These network dynamics undergo a probabilistic transition to a coherent state, as the magnitude of either the balanced excitation and inhibition or the external inputs is increased. Our mean-field theory successfully predicts the behavior of this model. Furthermore, we numerically demonstrate that the coherent dynamics can be used for state-dependent read-out of information from the network. These results show a novel form of neuronal information processing that connects neuronal dynamics on different scales.

cond-mat.dis-nn↗

arXiv2015

Learning in Neural Networks Based on a Generalized Fluctuation Theorem

Information maximization has been investigated as a possible mechanism of learning governing the self-organization that occurs within the neural systems of animals. Within the general context of models of neural systems bidirectionally interacting with environments, however, the role of information maximization remains to be elucidated. For bidirectionally interacting physical systems, universal laws describing the fluctuation they exhibit and the information they possess have recently been discovered. These laws are termed fluctuation theorems. In the present study, we formulate a theory of learning in neural networks bidirectionally interacting with environments based on the principle of information maximization. Our formulation begins with the introduction of a generalized fluctuation theorem, employing an interpretation appropriate for the present application, which differs from the original thermodynamic interpretation. We analytically and numerically demonstrate that the learning mechanism presented in our theory allows neural networks to efficiently explore their environments and optimally encode information about them.

cond-mat.dis-nn↗