Deep neural networks learn structured features from complex, non-Gaussian inputs, but the mechanisms behind this process remain poorly understood. Our work is motivated by the observation that the first-layer filters learnt by deep convolutional neural networks from natural images resemble those learnt by independent component analysis (ICA), a simple unsupervised method that seeks the most non-Gaussian projections of its inputs. This similarity suggests that ICA provides a simple, yet principled model for studying feature learning. Here, we leverage this connection to investigate the interplay between data structure and optimisation in feature learning for the most popular ICA algorithm, FastICA, and stochastic gradient descent (SGD), which is used to train deep networks. We rigorously establish that FastICA requires at least $n\gtrsim d^4$ samples to recover a single non-Gaussian direction from $d$-dimensional inputs on a simple synthetic data model. We show that vanilla online SGD outperforms FastICA, and prove that the optimal sample complexity $n \gtrsim d^2$ can be reached by smoothing the loss, albeit in a data-dependent way. We finally demonstrate the existence of a search phase for FastICA on ImageNet, and discuss how the strong non-Gaussianity of said images compensates for the poor sample complexity of FastICA.

Best subset selection in linear regression is well known to be nonconvex and computationally challenging to solve, as the number of possible subsets grows rapidly with increasing dimensionality of the problem. As a result, finding the global optimal solution via an exact optimization method for a problem with dimensions of 1000s may take an impractical amount of CPU time. This suggests the importance of finding suboptimal procedures that can provide good approximate solutions using much less computational effort than exact methods. In this work, we introduce a new procedure and compare it with other popular suboptimal algorithms to solve the best subset selection problem. Extensive computational experiments using synthetic and real data have been performed. The results provide insights into the performance of these methods in different data settings. The new procedure is observed to be a competitive suboptimal algorithm for solving the best subset selection problem for high-dimensional data.

Convex clustering is a modern clustering framework that guarantees globally optimal solutions and performs comparably to other advanced clustering methods. However, obtaining a complete dendrogram (clusterpath) for large-scale datasets remains computationally challenging due to the extensive costs associated with iterative optimization approaches. To address this limitation, we develop a novel convex clustering algorithm called Tree-Guided $L_1$-Convex Clustering (TGCC). We first focus on the fact that the loss function of $L_1$-convex clustering with tree-structured weights can be efficiently optimized using a dynamic programming approach. We then develop an efficient cluster fusion algorithm that utilizes the tree structure of the weights to accelerate the optimization process and eliminate the issue of cluster splits commonly observed in convex clustering. By combining the dynamic programming approach with the cluster fusion algorithm, the TGCC algorithm achieves superior computational efficiency without sacrificing clustering performance. Remarkably, our TGCC algorithm can construct a complete clusterpath for $10^6$ points in $\mathbb{R}^2$ within 15 seconds on a standard laptop without the need for parallel or distributed computing frameworks. Moreover, we extend the TGCC algorithm to develop biclustering and sparse convex clustering algorithms.

Electricity demand forecasting is key to ensuring that supply meets demand lest the grid would blackout. Reliable short-term forecasts may be obtained by combining a Generalized Additive Models (GAM) with a State-Space model (Obst et al., 2021), leading to an adaptive (or online) model. A GAM is an over-parameterized linear model defined by a formula and a state-space model involves hyperparameters. Both the formula and adaptation parameters have to be fixed before model training and have a huge impact on the model's predictive performance. We propose optimizing them using the DRAGON package of Keisler (2025), originally designed for neural architecture search. This work generalizes it for automated online generalized additive model selection by defining an efficient modeling of the search space (namely, the space of the GAM formulae and adaptation parameters). Its application to short-term French electricity demand forecasting demonstrates the relevance of the approach

We propose a flexible Semi-Automatic Labeling Tool (SALT) for general LiDAR point clouds with cross-scene adaptability and 4D consistency. Unlike recent approaches that rely on camera distillation, SALT operates directly on raw LiDAR data, automatically generating pre-segmentation results. To achieve this, we propose a novel zero-shot learning paradigm, termed data alignment, which transforms LiDAR data into pseudo-images by aligning with the training distribution of vision foundation models. Additionally, we design a 4D-consistent prompting strategy and 4D non-maximum suppression module to enhance SAM2, ensuring high-quality, temporally consistent presegmentation. SALT surpasses the latest zero-shot methods by 18.4% PQ on SemanticKITTI and achieves nearly 40-50% of human annotator performance on our newly collected low-resolution LiDAR data and on combined data from three LiDAR types, significantly boosting annotation efficiency. We anticipate that SALT's open-sourcing will catalyze substantial expansion of current LiDAR datasets and lay the groundwork for the future development of LiDAR foundation models. Code is available at https://github.com/Cavendish518/SALT.

Data generated in perturbation experiments link perturbations to the changes they elicit and therefore contain information relevant to numerous biological discovery tasks -- from understanding the relationships between biological entities to developing therapeutics. However, these data encompass diverse perturbations and readouts, and the complex dependence of experimental outcomes on their biological context makes it challenging to integrate insights across experiments. Here, we present the Large Perturbation Model (LPM), a deep-learning model that integrates multiple, heterogeneous perturbation experiments by representing perturbation, readout, and context as disentangled dimensions. LPM outperforms existing methods across multiple biological discovery tasks, including in predicting post-perturbation transcriptomes of unseen experiments, identifying shared molecular mechanisms of action between chemical and genetic perturbations, and facilitating the inference of gene-gene interaction networks.

Face recognition is a crucial topic in data science and biometric security, with applications spanning military, finance, and retail industries. This paper explores the implementation of sparse Principal Component Analysis (PCA) using the Proximal Gradient method (also known as ISTA) and the Runge - Kutta numerical methods. To address the face recognition problem, we integrate sparse PCA with either the k - nearest neighbor method or the kernel ridge regression method. Experimental results demonstrate that combining sparse PCA -- solved via the Proximal Gradient method or the Runge - Kutta numerical approach -- with a classification system yields higher accuracy compared to standard PCA. Additionally, we observe that the Runge - Kutta - based sparse PCA computation consistently outperforms the Proximal Gradient method in terms of speed.

Machine learning has been successfully used in critical domains, such as medicine. However, extracting meaningful insights from biomedical data is often constrained by the lack of their available disease labels. In this research, we demonstrate how machine learning can be leveraged to enhance explainability and uncover biologically meaningful associations, even when predictive improvements in disease modeling are limited. We train LightGBM models from scratch on our dataset (10K) to impute metabolomics features and apply them to the UK Biobank (UKBB) for downstream analysis. The imputed metabolomics features are then used in survival analysis to assess their impact on disease-related risk factors. As a result, our approach successfully identified biologically relevant connections that were not previously known to the predictive models. Additionally, we applied a genome-wide association study (GWAS) on key metabolomics features, revealing a link between vascular dementia and smoking. Although being a well-established epidemiological relationship, this link was not embedded in the model's training data, which validated the method's ability to extract meaningful signals. Furthermore, by integrating survival models as inputs in the 10K data, we uncovered associations between metabolic substances and obesity, demonstrating the ability to infer disease risk for future patients without requiring direct outcome labels. These findings highlight the potential of leveraging external bio-banks to extract valuable biomedical insights, even in data-limited scenarios. Our results demonstrate that machine learning models trained on smaller datasets can still be used to uncover real biological associations when carefully integrated with survival analysis and genetic studies.

Global localization is a critical problem in autonomous navigation, enabling precise positioning without reliance on GPS. Modern global localization techniques often depend on dense LiDAR maps, which, while precise, require extensive storage and computational resources. Recent approaches have explored alternative methods, such as sparse maps and learned features, but they suffer from poor robustness and generalization. We propose SparseLoc, a global localization framework that leverages vision-language foundation models to generate sparse, semantic-topometric maps in a zero-shot manner. It combines this map representation with a Monte Carlo localization scheme enhanced by a novel late optimization strategy, ensuring improved pose estimation. By constructing compact yet highly discriminative maps and refining localization through a carefully designed optimization schedule, SparseLoc overcomes the limitations of existing techniques, offering a more efficient and robust solution for global localization. Our system achieves over a 5X improvement in localization accuracy compared to existing sparse mapping techniques. Despite utilizing only 1/500th of the points of dense mapping methods, it achieves comparable performance, maintaining an average global localization error below 5m and 2 degrees on KITTI sequences.

Improving Indoor Localization Accuracy by Using an Efficient Implicit Neural Map Representation Haofei Kuang Y ue Pan Xingguang Zhong Louis Wiesmann Jens Behley Cyrill Stachniss Abstract -- Globally localizing a mobile robot in a known map is often a foundation for enabling robots to navigate and operate autonomously. In indoor environments, traditional Monte Carlo localization based on occupancy grid maps is considered the gold standard, but its accuracy is limited by the representation capabilities of the occupancy grid map. In this paper, we address the problem of building an effective map representation that allows to accurately perform probabilistic global localization. T o this end, we propose an implicit neural map representation that is able to capture positional and directional geometric features from 2D LiDAR scans to efficiently represent the environment and learn a neural network that is able to predict both, the non-projective signed distance and a direction-aware projective distance for an arbitrary point in the mapped environment. This combination of neural map representation with a lightweight neural network allows us to design an efficient observation model within a conventional Monte Carlo localization framework for pose estimation of a robot in real time. We evaluated our approach to indoor localization on a publicly available dataset for global localization and the experimental results indicate that our approach is able to more accurately localize a mobile robot than other localization approaches employing occupancy or existing neural map representations. In contrast to other approaches employing an implicit neural map representation for 2D LiDAR localization, our approach allows to perform real-time pose tracking after convergence and near real-time global localization. The code of our approach is available at: https://github.com/PRBonn/enm-mcl .