Despite the remarkable success of low-rank estimation in data mining, its effectiveness diminishes when applied to data that inherently lacks low-rank structure. To address this limitation, in this paper, we focus on non-negative sparse matrices and aim to investigate the intrinsic low-rank characteristics of the rectified linear unit (ReLU) activation function. We first propose a novel nonlinear matrix decomposition framework incorporating a comprehensive regularization term designed to simultaneously promote useful structures in clustering and compression tasks, such as low-rankness, sparsity, and non-negativity in the resulting factors. This formulation presents significant computational challenges due to its multi-block structure, non-convexity, non-smoothness, and the absence of global gradient Lipschitz continuity. To address these challenges, we develop an accelerated alternating partial Bregman proximal gradient method (AAPB), whose distinctive feature lies in its capability to enable simultaneous updates of multiple variables. Under mild and theoretically justified assumptions, we establish both sublinear and global convergence properties of the proposed algorithm. Through careful selection of kernel generating distances tailored to various regularization terms, we derive corresponding closed-form solutions while maintaining the $L$-smooth adaptable property always holds for any $L\ge 1$. Numerical experiments, on graph regularized clustering and sparse NMF basis compression confirm the effectiveness of our model and algorithm.

Simultaneous Localization and Mapping (SLAM) allows mobile robots to navigate without external positioning systems or pre-existing maps. Radar is emerging as a valuable sensing tool, especially in vision-obstructed environments, as it is less affected by particles than lidars or cameras. Modern 4D imaging radars provide three-dimensional geometric information and relative velocity measurements, but they bring challenges, such as a small field of view and sparse, noisy point clouds. Detecting loop closures in SLAM is critical for reducing trajectory drift and maintaining map accuracy. However, the directional nature of 4D radar data makes identifying loop closures, especially from reverse viewpoints, difficult due to limited scan overlap. This article explores using 4D radar for loop closure in SLAM, focusing on similar and opposing viewpoints. We generate submaps for a denser environment representation and use introspective measures to reject false detections in feature-degenerate environments. Our experiments show accurate loop closure detection in geometrically diverse settings for both similar and opposing viewpoints, improving trajectory estimation with up to 82 % improvement in ATE and rejecting false positives in self-similar environments.

A main bottleneck of learning-based robotic scene understanding methods is the heavy reliance on extensive annotated training data, which often limits their generalization ability. In LiDAR panoptic segmentation, this challenge becomes even more pronounced due to the need to simultaneously address both semantic and instance segmentation from complex, high-dimensional point cloud data. In this work, we address the challenge of LiDAR panoptic segmentation with very few labeled samples by leveraging recent advances in label-efficient vision panoptic segmentation. To this end, we propose a novel method, Limited-Label LiDAR Panoptic Segmentation (L3PS), which requires only a minimal amount of labeled data. Our approach first utilizes a label-efficient 2D network to generate panoptic pseudo-labels from a small set of annotated images, which are subsequently projected onto point clouds. We then introduce a novel 3D refinement module that capitalizes on the geometric properties of point clouds. By incorporating clustering techniques, sequential scan accumulation, and ground point separation, this module significantly enhances the accuracy of the pseudo-labels, improving segmentation quality by up to +10.6 PQ and +7.9 mIoU. We demonstrate that these refined pseudo-labels can be used to effectively train off-the-shelf LiDAR segmentation networks. Through extensive experiments, we show that L3PS not only outperforms existing methods but also substantially reduces the annotation burden. We release the code of our work at https://l3ps.cs.uni-freiburg.de.

The performance of machine learning models depends to a great extent on the data quality and, in particular, the reliability of the labels. Label noise is one of the concerning issues that has a tremendous impact on the outcome of learning methods and receives attention from researchers in the community. Among different classes of learning methods, semi-supervised learning is a class of methods that utilize information from unlabeled data in addition to the labeled data, and they are often used in the context where labeled data is scarce or costly [Zhu and Goldberg, 2009]. By counterbalancing the effect of possibly noisy labeled data with information from unlabeled data, these methods also have the potential of mitigating the issue of label noise, on top of its advantage in the scenario where labeled samples are given in a limited amount. A particular class of semi-supervised methods that we are interested in is the class of network-flow based, or graph based, methods in which minimum cut solution of a graph representation of the data provides label prediction of unlabeled samples. Unlabeled samples assist the method through their connectivity with labeled samples, as well as that among themselves.

The injection molding process is a traditional technique for making products in various industries such as electronics and automobiles via solidifying liquid resin into certain molds. Although the process is not related to creating the main part of engines or semiconductors, this manufacturing methodology sets the final form of the products. Re-cently, research has continued to reduce the defect rate of the injection molding process. This study proposes an optimal injection molding process control system to reduce the defect rate of injection molding products with XAI (eXplainable Artificial Intelligence) ap-proaches. Boosting algorithms (XGBoost and LightGBM) are used as tree-based classifiers for predicting whether each product is normal or defective. The main features to control the process for improving the product are extracted by SHapley Additive exPlanations, while the individual conditional expectation analyzes the optimal control range of these extracted features. To validate the methodology presented in this work, the actual injection molding AI manufacturing dataset provided by KAMP (Korea AI Manufacturing Platform) is employed for the case study. The results reveal that the defect rate decreases from 1.00% (Original defect rate) to 0.21% with XGBoost and 0.13% with LightGBM, respectively.

Route choice models are one of the most important foundations for transportation research. Traditionally, theory-based models have been utilized for their great interpretability, such as logit models and Recursive logit models. More recently, machine learning approaches have gained attentions for their better prediction accuracy. In this study, we propose novel hybrid models that integrate the Recursive logit model with Graph Neural Networks (GNNs) to enhance both predictive performance and model interpretability. To the authors' knowldedge, GNNs have not been utilized for route choice modeling, despite their proven effectiveness in capturing road network features and their widespread use in other transportation research areas. We mathematically show that our use of GNN is not only beneficial for enhancing the prediction performance, but also relaxing the Independence of Irrelevant Alternatives property without relying on strong assumptions. This is due to the fact that a specific type of GNN can efficiently capture multiple cross-effect patterns on networks from data. By applying the proposed models to one-day travel trajectory data in Tokyo, we confirmed their higher prediction accuracy compared to the existing models.

Machine unlearning aims to remove the influence of problematic training data after a model has been trained. The primary challenge in machine unlearning is ensuring that the process effectively removes specified data without compromising the model's overall performance on the remaining dataset. Many existing machine unlearning methods address this challenge by carefully balancing gradient ascent on the unlearn data with the gradient descent on a retain set representing the training data. Here, we propose OrthoGrad, a novel approach that mitigates interference between the unlearn set and the retain set rather than competing ascent and descent processes. Our method projects the gradient of the unlearn set onto the subspace orthogonal to all gradients in the retain batch, effectively avoiding any gradient interference. We demonstrate the effectiveness of OrthoGrad on multiple machine unlearning benchmarks, including automatic speech recognition, outperforming competing methods.

This study reviews popular stochastic gradient-based schemes based on large least-square problems. These schemes, often called optimizers in machine learning, play a crucial role in finding better model parameters. Hence, this study focuses on viewing such optimizers with different hyper-parameters and analyzing them based on least square problems. Codes that produced results in this work are available on https://github.com/q-viper/gradients-based-methods-on-large-least-square.

This article provides a practical introduction to kernel discrepancies, focusing on the Maximum Mean Discrepancy (MMD), the Hilbert-Schmidt Independence Criterion (HSIC), and the Kernel Stein Discrepancy (KSD). Various estimators for these discrepancies are presented, including the commonly-used V-statistics and U-statistics, as well as several forms of the more computationallyefficient incomplete U-statistics. The importance of the choice of kernel bandwidth is stressed, showing how it affects the behaviour of the discrepancy estimation. Adaptive estimators are introduced, which combine multiple estimators with various kernels, addressing the problem of kernel selection. This paper corresponds to the introduction of my PhD thesis (Schrab, 2025a, Chapter 2) and is presented as a standalone article to introduce the reader to kernel discrepancies estimators. First, in Section 1, we define kernels, Reproducing Kernel Hilbert Spaces, mean embeddings and cross-covariance operators, and present kernel properties such as characteristicity, universality and translation invariance. Then, in Section 2, we introduce the Maximum Mean Discprecancy, the Hilbert-Schmidt Independence Criterion, and the Kernel Stein Discrepancy, as well as their estimators, and we discuss the importance of the choice of kernel for such measures. We then introduce a collection of statistics in Section 3, including the commonly-used complete statistics, as well as their incomplete counterparts which trade accuracy for computational efficiency. Finally, in Section 4, we construct adaptive estimators combining multiple statistics with various kernels, which is one method to address the problem of kernel selection.

Posterior sampling with the spike-and-slab prior [MB88], a popular multimodal distribution used to model uncertainty in variable selection, is considered the theoretical gold standard method for Bayesian sparse linear regression [CPS09, Roc18]. However, designing provable algorithms for performing this sampling task is notoriously challenging. Existing posterior samplers for Bayesian sparse variable selection tasks either require strong assumptions about the signal-to-noise ratio (SNR) [YWJ16], only work when the measurement count grows at least linearly in the dimension [MW24], or rely on heuristic approximations to the posterior. We give the first provable algorithms for spike-and-slab posterior sampling that apply for any SNR, and use a measurement count sublinear in the problem dimension. Concretely, assume we are given a measurement matrix $\mathbf{X} \in \mathbb{R}^{n\times d}$ and noisy observations $\mathbf{y} = \mathbf{X}\mathbf{\theta}^\star + \mathbf{\xi}$ of a signal $\mathbf{\theta}^\star$ drawn from a spike-and-slab prior $\pi$ with a Gaussian diffuse density and expected sparsity k, where $\mathbf{\xi} \sim \mathcal{N}(\mathbb{0}_n, \sigma^2\mathbf{I}_n)$. We give a polynomial-time high-accuracy sampler for the posterior $\pi(\cdot \mid \mathbf{X}, \mathbf{y})$, for any SNR $\sigma^{-1}$ > 0, as long as $n \geq k^3 \cdot \text{polylog}(d)$ and $X$ is drawn from a matrix ensemble satisfying the restricted isometry property. We further give a sampler that runs in near-linear time $\approx nd$ in the same setting, as long as $n \geq k^5 \cdot \text{polylog}(d)$. To demonstrate the flexibility of our framework, we extend our result to spike-and-slab posterior sampling with Laplace diffuse densities, achieving similar guarantees when $\sigma = O(\frac{1}{k})$ is bounded.