Research Overview (a trial)

My research topics are the following:

• High-dimensional statistics and machine learning

• Statistics for stochastic processes

• Algorithms for statistics and machine learning

I summarize my previous studies on these topics. Some of them can be regarded as ones based on multiple topics of interest, but for readability, I classify them into one topic respectively.

High-dimensional statistics and machine learning

Benign overfitting

• Nakakita, S., and Imaizumi, M. (in press). Benign overfitting in time series linear models with over-parameterization. Bernoulli. 

Dimension-free concentration

• Nakakita, S. (2025). Sharp concentration of uniform generalization errors in binary linear classification. arXiv:2505.16713 [stat.ML]

• Nakakita, S. (2024). Dimension-free uniform concentration bound for logistic regression. arXiv:2405.18055 [math.ST]

• Nakakita, S., Alquier, P., and Imaizumi, M. (2024). Dimension-free Bounds for Sums of Dependent Matrices and Operators with Heavy-Tailed Distributions. Electronic Journal of Statistics, 18(1), 1130–1159.

Learning dynamics

• Yoshida, N., Nakakita, S., and Imaizumi, M. (2024). Effect of Random Learning Rate: Theoretical Analysis of SGD Dynamics in Non-Convex Optimization via Stationary Distribution. arXiv:2406.16038 [stat.ML]

Federated learning

• Nakakita, S., Kaneko, T., Takamaeda-Yamazaki, S., and Imaizumi, M. (2024). Federated Learning with Relative Fairness. arXiv:2411.01161 [stat.ML]

Statistics for stochastic processes

Computer-intensive statistics of stochastic processes

• Nakakita, S. (in press). Parametric estimation of stochastic differential equations via online gradient descent. Japanese Journal of Statistics and Data Science.

Inference for diffusion processes with noisy observations

• Nakakita, S. H., Kaino, Y., and Uchida, M. (2021). Quasi-likelihood analysis and Bayes-type estimators of an ergodic diffusion plus noise. Annals of the Institute of Statistical Mathematics, 73(1), 177–225.

• Nakakita, S. H., and Uchida, M. (2020). Inference for convolutionally observed diffusion processes. Entropy, 22(9), 1031.

• Kaino, Y., Nakakita, S. H., and Uchida, M. (2020). Hybrid estimation for ergodic diffusion processes based on noisy discrete observations. Statistical Inference for Stochastic Processes, 23(1), 171-198.

• Nakakita, S. H., and Uchida, M. (2019b). Adaptive test for ergodic diffusions plus noise. Journal of Statistical Planning and Inference, 203, 131–150.

• Nakakita, S. H., and Uchida, M. (2019a). Inference for ergodic diffusions plus noise. Scandinavian Journal of Statistics, 46(2), 470–516.

Algorithms for statistics and machine learning

Posterior sampling

• Nakakita, S. (2023). Non-asymptotic analysis of Langevin-type Monte Carlo algorithms. arXiv:2303.12407 [math.ST]