arXiv subjects

Hiroki Masuda

Publications and source records attributed to Hiroki Masuda.

At least 37 records · Page 2Linked to original sources

arXiv2023

Case-based Similar Image Retrieval for Weakly Annotated Large Histopathological Images of Malignant Lymphoma Using Deep Metric Learning

In the present study, we propose a novel case-based similar image retrieval (SIR) method for hematoxylin and eosin (H&E)-stained histopathological images of malignant lymphoma. When a whole slide image (WSI) is used as an input query, it is desirable to be able to retrieve similar cases by focusing on image patches in pathologically important regions such as tumor cells. To address this problem, we employ attention-based multiple instance learning, which enables us to focus on tumor-specific regions when the similarity between cases is computed. Moreover, we employ contrastive distance metric learning to incorporate immunohistochemical (IHC) staining patterns as useful supervised information for defining appropriate similarity between heterogeneous malignant lymphoma cases. In the experiment with 249 malignant lymphoma patients, we confirmed that the proposed method exhibited higher evaluation measures than the baseline case-based SIR methods. Furthermore, the subjective evaluation by pathologists revealed that our similarity measure using IHC staining patterns is appropriate for representing the similarity of H&E-stained tissue images for malignant lymphoma.

cs.CV↗

arXiv2023

Transformer-based Personalized Attention Mechanism for Medical Images with Clinical Records

In medical image diagnosis, identifying the attention region, i.e., the region of interest for which the diagnosis is made, is an important task. Various methods have been developed to automatically identify target regions from given medical images. However, in actual medical practice, the diagnosis is made based not only on the images but also on a variety of clinical records. This means that pathologists examine medical images with some prior knowledge of the patients and that the attention regions may change depending on the clinical records. In this study, we propose a method called the Personalized Attention Mechanism (PersAM), by which the attention regions in medical images are adaptively changed according to the clinical records. The primary idea of the PersAM method is to encode the relationships between the medical images and clinical records using a variant of Transformer architecture. To demonstrate the effectiveness of the PersAM method, we applied it to a large-scale digital pathology problem of identifying the subtypes of 842 malignant lymphoma patients based on their gigapixel whole slide images and clinical records.

eess.IV↗

arXiv2023

Optimal stable Ornstein-Uhlenbeck regression

We prove some efficient inference results concerning estimation of a Ornstein-Uhlenbeck regression model, which is driven by a non-Gaussian stable Levy process and where the output process is observed at high-frequency over a fixed time period. Local asymptotics for the likelihood function is presented, followed by a way to construct an asymptotically efficient estimator through a suboptimal yet very simple preliminary estimator.

math.ST↗

arXiv2022

Estimation of ergodic square-root diffusion under high-frequency sampling

Gaussian quasi-likelihood estimation of the parameter $θ$ in the square-root diffusion process is studied under high frequency sampling. Different from the previous study of Overbeck and Rydén(1998) under low-frequency sampling, high-frequency of data provides very simple form of the asymptotic covariance matrix. Through easy-to-compute preliminary contrast functions, a practical two-stage manner without numerical optimization is formulated in order to conduct not only an asymptotically efficient estimation of the drift parameters, but also high-precision estimator of the diffusion parameter. Simulation experiments are given to illustrate the results.

math.ST↗

arXiv2022

Noise Inference For Ergodic Lévy Driven SDE

We study inference for the driving Lévy noise of an ergodic stochastic differential equation (SDE) model, when the process is observed at high-frequency and long time and when the drift and scale coefficients contain finite-dimensional unknown parameters. By making use of the Gaussian quasi-likelihood function for the coefficients, we derive a stochastic expansion for functionals of the unit-time residuals, which clarifies some quantitative effect of plugging-in the estimators of the coefficients, thereby enabling us to take several inference procedures for the driving-noise characteristics into account. We also present new classes and methods available in YUIMA for the simulation and the estimation of a Lévy SDE model. We highlight the flexibility of these new advances in YUIMA using simulated and real data.

stat.ME↗

arXiv2019

Analyzing Trade-offs in Reversible Linear and Binary Search Algorithms

Reversible algorithms are algorithms in which each step represents a partial injective function; they are useful for performance optimization in reversible systems. In this study, using Janus, a reversible imperative high-level programming language, we have developed reversible linear and binary search algorithms. We have analyzed the non-trivial space-time trade-offs between them, focusing on the memory usage disregarding original inputs and outputs, the size of the output garbage disregarding the original inputs, and the maximum amount of traversal of the input. The programs in this study can easily be adapted to other reversible programming languages. Our analysis reveals that the change of the output data and/or the data structure affects the design of efficient reversible algorithms. For example, the number of input data traversals depends on whether the search has succeeded or failed, while it expectedly never changes in corresponding irreversible linear and binary searches. Our observations indicate the importance of the selection of data structures and what is regarded as the output with the aim of the reversible algorithm design.

cs.DS↗

arXiv2019

Estimating Diffusion With Compound Poisson Jumps Based On Self-normalized Residuals

We consider parametric estimation of the continuous part of a class of ergodic diffusions with jumps based on high-frequency samples. Various papers previously proposed threshold based methods, which enable us to distinguish whether observed increments have jumps or not at each small-time interval, hence to estimate the unknown parameters separately. However, a data-adapted and quantitative choice of the threshold parameter is known to be a subtle and sensitive problem. In this paper, we present a simple alternative based on the Jarque-Bera normality test for the Euler residuals. Different from the threshold based method, the proposed method does not require any sensitive fine tuning, hence is of practical value. It is shown that under suitable conditions the proposed estimator is asymptotically equivalent to an estimator constructed by the unobserved fluctuation of the continuous part of the solution process, hence is asymptotically efficient. Some numerical experiments are conducted to observe finite-sample performance of the proposed method.

stat.ME↗

arXiv2019

Data driven time scale in Gaussian quasi-likelihood inference

We study parametric estimation of ergodic diffusions observed at high frequency. Different from the previous studies, we suppose that sampling stepsize is unknown, thereby making the conventional Gaussian quasi-likelihood not directly applicable. In this situation, we construct estimators of both model parameters and sampling stepsize in a fully explicit way, and prove that they are jointly asymptotically normally distributed. The $L^{q}$-boundedness of the obtained estimator is also derived. Further, we propose the Schwarz (BIC) type statistics for model selection and show its model-selection consistency. We conducted some numerical experiments and found that the observed finite-sample performance well supports our theoretical findings. Also provided is a real data example.

math.ST↗

arXiv2018

Robust relative error estimation

Relative error estimation has been recently used in regression analysis. A crucial issue of the existing relative error estimation procedures is that they are sensitive to outliers. To address this issue, we employ the $γ$-likelihood function, which is constructed through $γ$-cross entropy with keeping the original statistical model in use. The estimating equation has a redescending property, a desirable property in robust statistics, for a broad class of noise distributions. To find a minimizer of the negative $γ$-likelihood function, a majorize-minimization (MM) algorithm is constructed. The proposed algorithm is guaranteed to decrease the negative $γ$-likelihood function at each iteration. We also derive asymptotic normality of the corresponding estimator together with a simple consistent estimator of the asymptotic covariance matrix, so that we can readily construct approximate confidence sets. Monte Carlo simulation is conducted to investigate the effectiveness of the proposed procedure. Real data analysis illustrates the usefulness of our proposed procedure.

stat.ME↗

arXiv2018

Non-Gaussian quasi-likelihood estimation of SDE driven by locally stable Lévy process

We address estimation of parametric coefficients of a pure-jump Lévy driven univariate stochastic differential equation (SDE) model, which is observed at high frequency over a fixed time period. It is known from the previous study Masuda (2013) that adopting the conventional Gaussian quasi-maximum likelihood estimator then leads to an inconsistent estimator. In this paper, under the assumption that the driving Lévy process is locally stable, we extend the Gaussian framework into a non-Gaussian counterpart, by introducing a novel quasi-likelihood function formally based on the small-time stable approximation of the unknown transition density. The resulting estimator turns out to be asymptotically mixed normally distributed without ergodicity and finite moments for a wide range of the driving pure-jump Lévy process, showing much better theoretical performance compared with the Gaussian quasi-maximum likelihood estimator. Extensive simulations are carried out to show good estimation accuracy. The case of large-time asymptotics under ergodicity is briefly mentioned as well, where we can deduce an analogous asymptotic normality result.

math.ST↗

arXiv2017

Bayesian inference for Stable Levy driven Stochastic Differential Equations with high-frequency data

In this article we consider parametric Bayesian inference for stochastic differential equations (SDE) driven by a pure-jump stable Levy process, which is observed at high frequency. In most cases of practical interest, the likelihood function is not available, so we use a quasi-likelihood and place an associated prior on the unknown parameters. It is shown under regularity conditions that there is a Bernstein-von Mises theorem associated to the posterior. We then develop a Markov chain Monte Carlo (MCMC) algorithm for Bayesian inference and assisted by our theoretical results, we show how to scale Metropolis-Hastings proposals when the frequency of the data grows, in order to prevent the acceptance ratio going to zero in the large data limit. Our algorithm is presented on numerical examples that help to verify our theoretical findings.

math.ST↗

arXiv2017

Moment convergence in regularized estimation under multiple and mixed-rates asymptotics

In $M$-estimation under standard asymptotics, the weak convergence combined with the polynomial type large deviation estimate of the associated statistical random field Yoshida (2011) provides us with not only the asymptotic distribution of the associated $M$-estimator but also the convergence of its moments, the latter playing an important role in theoretical statistics. In this paper, we study the above program for statistical random fields of multiple and also possibly mixed-rates type in the sense of Radchenko (2008) where the associated statistical random fields may be non-differentiable and may fail to be locally asymptotically quadratic. Consequently, a very strong mode of convergence of a wide range of regularized $M$-estimators is ensured. The results are applied to regularized estimation of an ergodic diffusion observed at high frequency.

math.ST↗

arXiv2016

Schwarz type model comparison for LAQ models

For model-specification purpose, we study asymptotic behavior of the marginal quasi-log likelihood associated with a family of locally asymptotically quadratic (LAQ) statistical experiments. Our result entails a far-reaching extension of applicable scope of the classical approximate Bayesian model comparison due to Schwarz, with frequentist-view theoretical foundation. In particular, the proposed statistics can deal with both ergodic and non-ergodic stochastic-process models, where the corresponding $M$-estimator is of multi-scaling type and the asymptotic quasi-information matrix is random. Focusing on the ergodic diffusion model, we also deduce the consistency of the multistage optimal-model selection where we may select an optimal sub-model structure step by step, so that computational cost can be much reduced. We illustrate the proposed method by the Gaussian quasi-likelihood for diffusion-type models in details, together with several numerical experiments.

math.ST↗

arXiv2016

Two-step estimation of ergodic Lévy driven SDE

We consider high frequency samples from ergodic Lévy driven stochastic differential equation (SDE) with drift coefficient $a(x,α)$ and scale coefficient $c(x,γ)$ involving unknown parameters $α$ and $γ$. We suppose that the Lévy measure $ν_{0}$, has all order moments but is not fully specified. We will prove the joint asymptotic normality of some estimators of $α$, $γ$ and a class of functional parameter $\intφ(z)ν_0(dz)$, which are constructed in a two-step manner: first, we use the Gaussian quasi-likelihood for estimation of $(α,γ)$, and then, for estimating $\intφ(z)ν_0(dz)$ we makes use of the method of moments based on the Euler-type residual with the the previously obtained quasi-likelihood estimator.

math.ST↗

arXiv2015

AIC for Non-concave Penalized Likelihood Method

Non-concave penalized maximum likelihood methods, such as the Bridge, the SCAD, and the MCP, are widely used because they not only do parameter estimation and variable selection simultaneously but also have a high efficiency as compared to the Lasso. They include a tuning parameter which controls a penalty level, and several information criteria have been developed for selecting it. While these criteria assure the model selection consistency and so have a high value, it is a severe problem that there are no appropriate rules to choose the one from a class of information criteria satisfying such a preferred asymptotic property. In this paper, we derive an information criterion based on the original definition of the AIC by considering the minimization of the prediction error rather than the model selection consistency. Concretely speaking, we derive a function of the score statistic which is asymptotically equivalent to the non-concave penalized maximum likelihood estimator, and then we provide an asymptotically unbiased estimator of the Kullback-Leibler divergence between the true distribution and the estimated distribution based on the function. Furthermore, through simulation studies, we check that the performance of the proposed information criterion gives almost the same as or better than that of the cross-validation.

stat.ME↗

arXiv2015

Uniform LAN property of locally stable Lévy process observed at high frequency

Suppose we have a high-frequency sample from the Lévy process of the form $X_t^θ=βt+γZ_t+U_t$, where $Z$ is a possibly asymmetric locally $α$-stable Lévy process, and $U$ is a nuisance Lévy process less active than $Z$. We prove the LAN property about the explicit parameter $θ=(β,γ)$ under very mild conditions without specific form of the Lévy measure of $Z$, thereby generalizing the LAN result of A\"ıt-Sahalia and Jacod (2007). In particular, it is clarified that a non-diagonal norming may be necessary in the truly asymmetric case. Due to the special nature of the local $α$-stable property, the asymptotic Fisher information matrix takes a clean-cut form.

math.PR↗

arXiv2014

Parametric estimation of Lévy processes

The main purpose of this chapter is to present some theoretical aspects of parametric estimation of Lévy processes based on high-frequency sampling, with a focus on infinite activity pure-jump models. Asymptotics for several classes of explicit estimating functions are discussed. In addition to the asymptotic normality at several rates of convergence, a uniform tail-probability estimate for statistical random fields is given. As specific cases, we discuss method of moments for the stable Lévy processes in much greater detail, with briefly mentioning locally stable Lévy processes too. Also discussed is, due to its theoretical importance, a brief review of how the classical likelihood approach works or does not, beyond the fact that the likelihood function is not explicit.

math.ST↗

arXiv2013

Convergence of Gaussian quasi-likelihood random fields for ergodic Lévy driven SDE observed at high frequency

This paper investigates the Gaussian quasi-likelihood estimation of an exponentially ergodic multidimensional Markov process, which is expressed as a solution to a Lévy driven stochastic differential equation whose coefficients are known except for the finite-dimensional parameters to be estimated, where the diffusion coefficient may be degenerate or even null. We suppose that the process is discretely observed under the rapidly increasing experimental design with step size $h_n$. By means of the polynomial-type large deviation inequality, convergence of the corresponding statistical random fields is derived in a mighty mode, which especially leads to the asymptotic normality at rate $\sqrt{nh_n}$ for all the target parameters, and also to the convergence of their moments. As our Gaussian quasi-likelihood solely looks at the local-mean and local-covariance structures, efficiency loss would be large in some instances. Nevertheless, it has the practically important advantages: first, the computation of estimates does not require any fine tuning, and hence it is straightforward; second, the estimation procedure can be adopted without full specification of the Lévy measure.

math.ST↗