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Sewon Park

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Machine Learning Artificial Intelligence Methodology

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preprint2026arXiv

Posterior Contraction of Lévy Adaptive B-spline Regression in Besov Spaces

We investigate the asymptotic properties of the Lévy Adaptive B-spline (LABS) regression model, a Bayesian nonparametric method that incorporates B-spline kernels into the Lévy Adaptive Regression Kernel (LARK) model. LABS applies splines of varying degrees with independently defined knots, yielding a flexible model class capable of adapting to irregular and locally structured features of the true function. Within the nonparametric regression framework with univariate random design and Gaussian errors, we establish that the LABS posterior contracts around the true function in Besov classes at nearly minimax-optimal rates, up to a logarithmic factor, while adapting automatically to unknown smoothness. This study contributes to filling a gap in the literature, where theoretical results on posterior contraction of the LARK model in Besov spaces remain scarce. Simulation experiments on standard test functions in Besov spaces, including Blocks, Bumps, HeaviSine, and Doppler, complement the theoretical results and demonstrate the practical utility of LABS.

preprint2023arXiv

Regular Time-series Generation using SGM

Score-based generative models (SGMs) are generative models that are in the spotlight these days. Time-series frequently occurs in our daily life, e.g., stock data, climate data, and so on. Especially, time-series forecasting and classification are popular research topics in the field of machine learning. SGMs are also known for outperforming other generative models. As a result, we apply SGMs to synthesize time-series data by learning conditional score functions. We propose a conditional score network for the time-series generation domain. Furthermore, we also derive the loss function between the score matching and the denoising score matching in the time-series generation domain. Finally, we achieve state-of-the-art results on real-world datasets in terms of sampling diversity and quality.

preprint2022arXiv

SOS: Score-based Oversampling for Tabular Data

Score-based generative models (SGMs) are a recent breakthrough in generating fake images. SGMs are known to surpass other generative models, e.g., generative adversarial networks (GANs) and variational autoencoders (VAEs). Being inspired by their big success, in this work, we fully customize them for generating fake tabular data. In particular, we are interested in oversampling minor classes since imbalanced classes frequently lead to sub-optimal training outcomes. To our knowledge, we are the first presenting a score-based tabular data oversampling method. Firstly, we re-design our own score network since we have to process tabular data. Secondly, we propose two options for our generation method: the former is equivalent to a style transfer for tabular data and the latter uses the standard generative policy of SGMs. Lastly, we define a fine-tuning method, which further enhances the oversampling quality. In our experiments with 6 datasets and 10 baselines, our method outperforms other oversampling methods in all cases.

preprint2021arXiv

Lévy Adaptive B-spline Regression via Overcomplete Systems

The estimation of functions with varying degrees of smoothness is a challenging problem in the nonparametric function estimation. In this paper, we propose the LABS (Lévy Adaptive B-Spline regression) model, an extension of the LARK models, for the estimation of functions with varying degrees of smoothness. LABS model is a LARK with B-spline bases as generating kernels. The B-spline basis consists of piecewise k degree polynomials with k-1 continuous derivatives and can express systematically functions with varying degrees of smoothness. By changing the orders of the B-spline basis, LABS can systematically adapt the smoothness of functions, i.e., jump discontinuities, sharp peaks, etc. Results of simulation studies and real data examples support that this model catches not only smooth areas but also jumps and sharp peaks of functions. The proposed model also has the best performance in almost all examples. Finally, we provide theoretical results that the mean function for the LABS model belongs to the certain Besov spaces based on the orders of the B-spline basis and that the prior of the model has the full support on the Besov spaces.