47 citations · 411 across the 42 of their papers we have counts for
42 papers
Estimating nested expectations without inner conditional sampling and application to value of information analysis
Tomohiko Hironaka, Takashi Goda
Motivated by various computational applications, we investigate the problem of estimating nested expectations. Building upon recent work by the authors, we propose a novel Monte Ca…
Strong tractability for multivariate integration in a subspace of the Wiener algebra
Takashi Goda
Building upon recent work by the author, we prove that multivariate integration in the following subspace of the Wiener algebra over is strongly polynomially tractable: \…
Randomizing the trapezoidal rule gives the optimal RMSE rate in Gaussian Sobolev spaces
Takashi Goda, Yoshihito Kazashi, Yuya Suzuki
Randomized quadratures for integrating functions in Sobolev spaces of order , where the integrability condition is with respect to the Gaussian measure, are considered. In…
Polynomial tractability for integration in an unweighted function space with absolutely convergent Fourier series
Takashi Goda
In this note, we prove that the following function space with absolutely convergent Fourier series \[ F_d:=\left\{ f\in L^2([0,1)^d)\:\middle| \: \|f\|:=\sum_{\boldsymbol{k}\in \ma…
Improved bounds on the gain coefficients for digital nets in prime power base
Takashi Goda, Kosuke Suzuki
We study randomized quasi-Monte Carlo integration by scrambled nets. The scrambled net quadrature has long gained its popularity because it is an unbiased estimator of the true int…
Constructing unbiased gradient estimators with finite variance for conditional stochastic optimization
Takashi Goda, Wataru Kitade
We study stochastic gradient descent for solving conditional stochastic optimization problems, in which an objective to be minimized is given by a parametric nested expectation wit…
Sub-optimality of Gauss--Hermite quadrature and optimality of the trapezoidal rule for functions with finite smoothness
Yoshihito Kazashi, Yuya Suzuki, Takashi Goda
The sub-optimality of Gauss--Hermite quadrature and the optimality of the trapezoidal rule are proved in the weighted Sobolev spaces of square integrable functions of order , wh…
Construction-free median quasi-Monte Carlo rules for function spaces with unspecified smoothness and general weights
Takashi Goda, Pierre L'Ecuyer
We study quasi-Monte Carlo (QMC) integration of smooth functions defined over the multi-dimensional unit cube. Inspired by a recent work of Pan and Owen, we study a new constructio…
An efficient estimation of nested expectations without conditional sampling
Tomohiko Hironaka, Takashi Goda
Estimating nested expectations is an important task in computational mathematics and statistics. In this paper we propose a new Monte Carlo method using post-stratification to esti…
Component-by-component construction of randomized rank-1 lattice rules achieving almost the optimal randomized error rate
Josef Dick, Takashi Goda, Kosuke Suzuki
We study a randomized quadrature algorithm to approximate the integral of periodic functions defined over the high-dimensional unit cube. Recent work by Kritzer, Kuo, Nuyens and Ul…
A note on concatenation of quasi-Monte Carlo and plain Monte Carlo rules in high dimensions
Takashi Goda
In this note, we study a concatenation of quasi-Monte Carlo and plain Monte Carlo rules for high-dimensional numerical integration in weighted function spaces. In particular, we co…
A simple algorithm for global sensitivity analysis with Shapley effects
Takashi Goda
Global sensitivity analysis aims at measuring the relative importance of different variables or groups of variables for the variability of a quantity of interest. Among several sen…
Unbiased MLMC stochastic gradient-based optimization of Bayesian experimental designs
Takashi Goda, Tomohiko Hironaka, Wataru Kitade +1
In this paper we propose an efficient stochastic optimization algorithm to search for Bayesian experimental designs such that the expected information gain is maximized. The gradie…
Toeplitz Monte Carlo
Josef Dick, Takashi Goda, Hiroya Murata
Motivated mainly by applications to partial differential equations with random coefficients, we introduce a new class of Monte Carlo estimators, called Toeplitz Monte Carlo (TMC) e…
Efficient Debiased Evidence Estimation by Multilevel Monte Carlo Sampling
Kei Ishikawa, Takashi Goda
In this paper, we propose a new stochastic optimization algorithm for Bayesian inference based on multilevel Monte Carlo (MLMC) methods. In Bayesian statistics, biased estimators o…
Multilevel Monte Carlo estimation of log marginal likelihood
Takashi Goda, Kei Ishikawa
In this short note we provide an unbiased multilevel Monte Carlo estimator of the log marginal likelihood and discuss its application to variational Bayes.
Stability of lattice rules and polynomial lattice rules constructed by the component-by-component algorithm
Josef Dick, Takashi Goda
We study quasi-Monte Carlo (QMC) methods for numerical integration of multivariate functions defined over the high-dimensional unit cube. Lattice rules and polynomial lattice rules…
Multilevel Monte Carlo estimation of the expected value of sample information
Tomohiko Hironaka, Michael B. Giles, Takashi Goda +1
We study Monte Carlo estimation of the expected value of sample information (EVSI) which measures the expected benefit of gaining additional information for decision making under u…
Recent advances in higher order quasi-Monte Carlo methods
Takashi Goda, Kosuke Suzuki
In this article we review some of recent results on higher order quasi-Monte Carlo (HoQMC) methods. After a seminal work by Dick (2007, 2008) who originally introduced the concept…
Multilevel Monte Carlo estimation of expected information gains
Takashi Goda, Tomohiko Hironaka, Takeru Iwamoto
The expected information gain is an important quality criterion of Bayesian experimental designs, which measures how much the information entropy about uncertain quantity of intere…
Richardson extrapolation allows truncation of higher order digital nets and sequences
Takashi Goda
We study numerical integration of smooth functions defined over the -dimensional unit cube. A recent work by Dick et al. (2019) has introduced so-called extrapolated polynomial…
Lattice rules in non-periodic subspaces of Sobolev spaces
Takashi Goda, Kosuke Suzuki, Takehito Yoshiki
We investigate quasi-Monte Carlo (QMC) integration over the -dimensional unit cube based on rank-1 lattice point sets in weighted non-periodic Sobolev spaces $\mathcal{H}(K_{α,\…
Decision-making under uncertainty: using MLMC for efficient estimation of EVPPI
Michael B. Giles, Takashi Goda
In this paper we develop a very efficient approach to the Monte Carlo estimation of the expected value of partial perfect information (EVPPI) that measures the average benefit of k…
Richardson extrapolation of polynomial lattice rules
Josef Dick, Takashi Goda, Takehito Yoshiki
We study multivariate numerical integration of smooth functions in weighted Sobolev spaces with dominating mixed smoothness defined over the -dimensional unit cube. We…