arXiv subjects

Dongmin Lee

Publications and source records attributed to Dongmin Lee.

6 recordsLinked to original sources

arXiv2026

On the Oracle Complexity of Interpolation-Based Gradient Descent

Recent work on first-order optimizers for empirical risk minimization (ERM) has suggested that smoothness of ERM loss functions in the training data, rather than in the optimization parameters, can be leveraged to improve the oracle complexity of gradient descent (GD) methods. In this paper, we propose an inexact gradient method, piecewise polynomial interpolation-based gradient descent (PPI-GD), which approximates the full gradient in each iteration by querying the first-order oracle at equidistant points in the data domain to construct polynomial interpolants of the resulting gradient samples over appropriately sized patches of the data domain. We analyze the oracle complexity of PPI-GD for strongly convex and non-convex loss functions when the data space dimension is bounded by a polylogarithmic function of the number of training samples, and find it to outperform several GD variants in key regimes when the loss function is sufficiently smooth. Furthermore, our analysis extends several techniques from the error analysis of bicubic spline interpolants to the setting of $d$-variate tensor product polynomial interpolants which may be of independent interest in interpolation analysis.

cs.LG↗

arXiv2026

Doeblin Curves

Recent research on Doeblin coefficients has shed light on their usefulness as a multi-way generalization of the Dobrushin contraction coefficient for TV distance, in a separate vein from their classic role in the theory of Markov chain ergodicity. However, strong conditions, such as being bounded away from 0, are typically necessary for Doeblin coefficients to establish the existence of information contraction. Building on recently formulated concepts of nonlinear information contraction, we aim to propose a finer-grained Doeblin-based characterization of multi-way contraction behavior which yields non-vacuous contraction guarantees even for channels whose Doeblin coefficient is 0. To this end, we introduce the notion of a Doeblin curve -- a nonlinear function which quantifies the contraction behavior of a Markov kernel on collections of input distributions at specific levels of divergence and power. Through the course of our analysis, we develop a new variational characterization of Doeblin coefficients, present several properties of Doeblin curves, define several versions of power-constrained Doeblin curves, and derive upper and lower bounds using our aforementioned variational characterization. We then utilize these results in diverse areas, including generalization bounds for noisy iterative optimization, error bounds for reliable computation with noisy circuits, and differential privacy guarantees for online iterative algorithms. In particular, we extend results in these areas to broader domains or group settings, leveraging Doeblin curves to reveal finer-grained contraction phenomena than Doeblin coefficients.

cs.IT↗

arXiv2026

Entrywise Error Bounds for Spectral Ranking with Semi-Random Adversaries

Bradley-Terry-Luce (BTL) model estimation is a well-established strategy to rank a collection of items given a dataset of pairwise comparisons. Although the theoretical performance of BTL estimation methods, such as spectral and maximum likelihood estimation, is well studied in the regime of uniformly sampled graphs, generalizing such results to a wider class of random graphs has proved challenging. In this work, we investigate the entry-wise error of spectral algorithms against a semi-random adversary that can arbitrarily boost the sampling probabilities of certain edges. We find that the performance of the unweighted spectral method is heavily dependent on the spectral properties of the generated graph. Furthermore, we show that asymptotic performance approaching that of uniformly sampled graphs can be recovered by appropriately reweighting the observed edges to counteract the adversary and restore the spectral gap. Finally, we provide numerical simulations that support our theoretical findings.

cs.LG↗

arXiv2026

Assessment of cloud and associated radiation fields from a GAN stochastic cloud subcolumn generator

Modern Earth System Models (ESMs) operate on horizontal scales far larger than typical cloud features, requiring stochastic subcolumn generators to represent subgrid horizontal and vertical cloud variability. Traditional physically-based generators often rely on analytical cloud overlap paradigms, such as exponential-random decorrelation, which can struggle to capture the complex, anti-correlated behavior of non-contiguous cloud layers. In this study, we introduce a novel two-stage machine learning subcolumn generator for the GEOS atmospheric model, utilizing a Conditional Variational Autoencoder combined with a Generative Adversarial Network (CVAE-GAN) and a U-Net architecture. Trained on a merged CloudSat-CALIPSO height-resolved cloud optical depth dataset, the ML generator creates 56 stochastic subcolumns representing cloud occurrence and optical depth profiles. Evaluated against the established R\"{a}is\"{a}nen, the ML approach accurately reproduces bimodal cloud overlap distributions, significantly reduces biases in grid-mean statistics, and halves the root-mean-square error in ISCCP-style cloud-top pressure and optical thickness joint histograms. The improvements brought by our deep generative models translate into more accurate offline radiative transfer calculations, reducing the global-mean shortwave top-of-atmosphere cloud radiative effect bias by a factor of three. Provided that the generator can be accelerated on CPUs, this offers a practical pathway to reduce structural errors at the cloud-radiation interface.

physics.ao-ph↗

arXiv2025

Tumor Detection, Segmentation and Classification Challenge on Automated 3D Breast Ultrasound: The TDSC-ABUS Challenge

Breast cancer is one of the most common causes of death among women worldwide. Early detection helps in reducing the number of deaths. Automated 3D Breast Ultrasound (ABUS) is a newer approach for breast screening, which has many advantages over handheld mammography such as safety, speed, and higher detection rate of breast cancer. Tumor detection, segmentation, and classification are key components in the analysis of medical images, especially challenging in the context of 3D ABUS due to the significant variability in tumor size and shape, unclear tumor boundaries, and a low signal-to-noise ratio. The lack of publicly accessible, well-labeled ABUS datasets further hinders the advancement of systems for breast tumor analysis. Addressing this gap, we have organized the inaugural Tumor Detection, Segmentation, and Classification Challenge on Automated 3D Breast Ultrasound 2023 (TDSC-ABUS2023). This initiative aims to spearhead research in this field and create a definitive benchmark for tasks associated with 3D ABUS image analysis. In this paper, we summarize the top-performing algorithms from the challenge and provide critical analysis for ABUS image examination. We offer the TDSC-ABUS challenge as an open-access platform at https://tdsc-abus2023.grand-challenge.org/ to benchmark and inspire future developments in algorithmic research.

eess.IV↗

arXiv2023

Exploring the magnetic properties of individual barcode nanowires using wide-field diamond microscopy

Barcode magnetic nanowires typically comprise a multilayer magnetic structure in a single body with more than one segment type. Interestingly, owing to selective functionalization and novel interactions between the layers, barcode magnetic nanowires have attracted significant attention, particularly in the field of bioengineering. However, an analysis of their magnetic properties at the individual nanowire level remains challenging. With this background, herein, we investigated the characterization of magnetic nanowires at room temperature under ambient conditions based on magnetic images obtained via wide-field quantum microscopy with nitrogen-vacancy centers in diamond. Consequently, we could extract critical magnetic properties, such as the saturation magnetization and coercivity, of single nanowires by comparing the experimental results with those of micromagnetic simulations. This study opens up the possibility for a versatile characterization method suited to individual magnetic nanowires.

quant-ph↗