47 citations · 411 across the 42 of their papers we have counts for
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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…