arXiv subjects

Jungkwon Kim

Publications and source records attributed to Jungkwon Kim.

5 recordsLinked to original sources

arXiv2026

Mitigating Long-Tailed Anomaly Score Distributions with Importance-Weighted Loss

Anomaly detection is crucial in industrial applications for identifying rare and unseen patterns to ensure system reliability. Traditional models, trained on a single class of normal data, struggle with real-world distributions where normal data exhibit diverse patterns, leading to class imbalance and long-tailed anomaly score distributions (LTD). This imbalance skews model training and degrades detection performance, especially for minority instances. To address this issue, we propose a novel importance-weighted loss designed specifically for anomaly detection. Compared to the previous method for LTD in classification, our method does not require prior knowledge of normal data classes. Instead, we introduce a weighted loss function that incorporates importance sampling to align the distribution of anomaly scores with a target Gaussian, ensuring a balanced representation of normal data. Extensive experiments on three benchmark image datasets and three real-world hyperspectral imaging datasets demonstrate the robustness of our approach in mitigating LTD-induced bias. Our method improves anomaly detection performance by 0.043, highlighting its effectiveness in real-world applications.

stat.ML↗

arXiv2025

Anomaly Detection with Adaptive and Aggressive Rejection for Contaminated Training Data

Handling contaminated data poses a critical challenge in anomaly detection, as traditional models assume training on purely normal data. Conventional methods mitigate contamination by relying on fixed contamination ratios, but discrepancies between assumed and actual ratios can severely degrade performance, especially in noisy environments where normal and abnormal data distributions overlap. To address these limitations, we propose Adaptive and Aggressive Rejection (AAR), a novel method that dynamically excludes anomalies using a modified z-score and Gaussian mixture model-based thresholds. AAR effectively balances the trade-off between preserving normal data and excluding anomalies by integrating hard and soft rejection strategies. Extensive experiments on two image datasets and thirty tabular datasets demonstrate that AAR outperforms the state-of-the-art method by 0.041 AUROC. By providing a scalable and reliable solution, AAR enhances robustness against contaminated datasets, paving the way for broader real-world applications in domains such as security and healthcare.

cs.LG↗

arXiv2022

Endpoint Strichartz estimates with angular integrability and some applications

The endpoint Strichartz estimate $\|e^{itΔ} f\|_{L_t^2 L_x^\infty} \lesssim \|f\|_{L^2}$ is known to be false in two space dimensions. Taking averages spherically on the polar coordinates $x=ρω$, $ρ>0$, $ω\in\mathbb{S}^1$, Tao showed a substitute of the form $\|e^{itΔ} f\|_{L_t^2L_ρ^\infty L_ω^2} \lesssim \|f\|_{L^2}$. Here we address a weighted version of such spherically averaged estimates. As an application, the existence of solutions for the inhomogeneous nonlinear Schrödinger equation is shown for $L^2$ data.

math.AP↗

arXiv2021

On well-posedness for the inhomogeneous nonlinear Schrödinger equation in the critical case

In this paper we study the well-posedness for the inhomogeneous nonlinear Schrödinger equation $i\partial_{t}u+Δu=λ|x|^{-α}|u|^βu$ in Sobolev spaces $H^s$, $s\geq0$. The well-posedness theory for this model has been intensively studied in recent years, but much less is understood compared to the classical NLS model where $α=0$. The conventional approach does not work particularly for the critical cases $β=\frac{4-2α}{d-2s}$. It is still an open problem. The main contribution of this paper is to develop the well-posedness theory in this critical case (as well as non-critical cases). To this end, we approach to the matter in a new way based on a weighted $L^p$ setting which seems to be more suitable to perform a finer analysis for this model. This is because it makes it possible to handle the singularity $|x|^{-α}$ in the nonlinearity more effectively. This observation is a core of our approach that covers the critical case successfully.

math.AP↗

arXiv2020

On Morawetz estimates with time-dependent weights for the Klein-Gordon equation

We obtain some new Morawetz estimates for the Klein-Gordon flow of the form \begin{equation*} \big\||\nabla|^σ e^{it \sqrt{1-Δ}}f \big\|_{L^2_{x,t}(|(x,t)|^{-α})} \lesssim \|f\|_{H^s} \end{equation*} where $σ,s\geq0$ and $α>0$. The conventional approaches to Morawetz estimates with $|x|^{-α}$ are no longer available in the case of time-dependent weights $|(x,t)|^{-α}$. Here we instead apply the Littlewood-Paley theory with Muckenhoupt $A_2$ weights to frequency localized estimates thereof that are obtained by making use of the bilinear interpolation between their bilinear form estimates which need to carefully analyze some relevant oscillatory integrals according to the different scaling of $\sqrt{1-Δ}$ for low and high frequencies.

math.AP↗