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 Statistical Learning


Depth-discriminative Metric Learning for Monocular 3D Object Detection

Neural Information Processing Systems

These observations suggest that monocular 3D object detection heavily relies on object depth quality; nevertheless, conventional methods yield unsatisfactory results due to the extraction of less-discriminative features for object depth inference.




Jaccard Metric Losses: Optimizing the Jaccard Index with Soft Labels Zifu Wang

Neural Information Processing Systems

Leveraging IoU losses as part of the loss function have demonstrated superior performance in semantic segmentation tasks compared to optimizing pixel-wise losses such as the cross-entropy loss alone.


Exponential Lasso: robust sparse penalization under heavy-tailed noise and outliers with exponential-type loss

arXiv.org Machine Learning

In high-dimensional statistics, the Lasso is a cornerstone method for simultaneous variable selection and parameter estimation. However, its reliance on the squared loss function renders it highly sensitive to outliers and heavy-tailed noise, potentially leading to unreliable model selection and biased estimates. To address this limitation, we introduce the Exponential Lasso, a novel robust method that integrates an exponential-type loss function within the Lasso framework. This loss function is designed to achieve a smooth trade-off between statistical efficiency under Gaussian noise and robustness against data contamination. Unlike other methods that cap the influence of large residuals, the exponential loss smoothly redescends, effectively downweighting the impact of extreme outliers while preserving near-quadratic behavior for small errors. We establish theoretical guarantees showing that the Exponential Lasso achieves strong statistical convergence rates, matching the classical Lasso under ideal conditions while maintaining its robustness in the presence of heavy-tailed contamination. Computationally, the estimator is optimized efficiently via a Majorization-Minimization (MM) algorithm that iteratively solves a series of weighted Lasso subproblems. Numerical experiments demonstrate that the proposed method is highly competitive, outperforming the classical Lasso in contaminated settings and maintaining strong performance even under Gaussian noise. Our method is implemented in the \texttt{R} package \texttt{heavylasso} available on Github: https://github.com/tienmt/heavylasso


Reservoir Computing via Multi-Scale Random Fourier Features for Forecasting Fast-Slow Dynamical Systems

arXiv.org Artificial Intelligence

Forecasting nonlinear time series with multi-scale temporal structures remains a central challenge in complex systems modeling. We present a novel reservoir computing framework that combines delay embedding with random Fourier feature (RFF) mappings to capture such dynamics. Two formulations are investigated: a single-scale RFF reservoir, which employs a fixed kernel bandwidth, and a multi-scale RFF reservoir, which integrates multiple bandwidths to represent both fast and slow temporal dependencies. The framework is applied to a diverse set of canonical systems: neuronal models such as the Rulkov map, Izhikevich model, Hindmarsh-Rose model, and Morris-Lecar model, which exhibit spiking, bursting, and chaotic behaviors arising from fast-slow interactions; and ecological models including the predator-prey dynamics and Ricker map with seasonal forcing, which display multi-scale oscillations and intermittency. Across all cases, the multi-scale RFF reservoir consistently outperforms its single-scale counterpart, achieving lower normalized root mean square error (NRMSE) and more robust long-horizon predictions. These results highlight the effectiveness of explicitly incorporating multi-scale feature mappings into reservoir computing architectures for modeling complex dynamical systems with intrinsic fast-slow interactions.


A Unified Framework for Provably Efficient Algorithms to Estimate Shapley Values

arXiv.org Artificial Intelligence

Shapley values have emerged as a critical tool for explaining which features impact the decisions made by machine learning models. However, computing exact Shapley values is difficult, generally requiring an exponential (in the feature dimension) number of model evaluations. To address this, many model-agnostic randomized estimators have been developed, the most influential and widely used being the KernelSHAP method (Lundberg & Lee, 2017). While related estimators such as unbiased KernelSHAP (Covert & Lee, 2021) and LeverageSHAP (Musco & Witter, 2025) are known to satisfy theoretical guarantees, bounds for KernelSHAP have remained elusive. We describe a broad and unified framework that encompasses KernelSHAP and related estimators constructed using both with and without replacement sampling strategies. We then prove strong non-asymptotic theoretical guarantees that apply to all estimators from our framework. This provides, to the best of our knowledge, the first theoretical guarantees for KernelSHAP and sheds further light on tradeoffs between existing estimators. Through comprehensive benchmarking on small and medium dimensional datasets for Decision-Tree models, we validate our approach against exact Shapley values, consistently achieving low mean squared error with modest sample sizes. Furthermore, we make specific implementation improvements to enable scalability of our methods to high-dimensional datasets. Our methods, tested on datasets such MNIST and CIFAR10, provide consistently better results compared to the KernelSHAP library.


B+ANN: A Fast Billion-Scale Disk-based Nearest-Neighbor Index

arXiv.org Artificial Intelligence

Storing and processing of embedding vectors by specialized Vector databases (VDBs) has become the linchpin in building modern AI pipelines. Most current VDBs employ variants of a graph-based ap- proximate nearest-neighbor (ANN) index algorithm, HNSW, to an- swer semantic queries over stored vectors. Inspite of its wide-spread use, the HNSW algorithm suffers from several issues: in-memory design and implementation, random memory accesses leading to degradation in cache behavior, limited acceleration scope due to fine-grained pairwise computations, and support of only semantic similarity queries. In this paper, we present a novel disk-based ANN index, B+ANN, to address these issues: it first partitions input data into blocks containing semantically similar items, then builds an B+ tree variant to store blocks both in-memory and on disks, and finally, enables hybrid edge- and block-based in-memory traversals. As demonstrated by our experimantal evaluation, the proposed B+ANN disk-based index improves both quality (Recall value), and execution performance (Queries per second/QPS) over HNSW, by improving spatial and temporal locality for semantic operations, reducing cache misses (19.23% relative gain), and decreasing the memory consumption and disk-based build time by 24x over the DiskANN algorithm. Finally, it enables dissimilarity queries, which are not supported by similarity-oriented ANN indices.


PCARNN-DCBF: Minimal-Intervention Geofence Enforcement for Ground Vehicles

arXiv.org Artificial Intelligence

Runtime geofencing for ground vehicles is rapidly emerging as a critical technology for enforcing Operational Design Domains (ODDs). However, existing solutions struggle to reconcile high-fidelity learning with the structural requirements of verifiable control. We address this by introducing PCARNN-DCBF, a novel pipeline integrating a Physics-encoded Control-Affine Residual Neural Network with a preview-based Discrete Control Barrier Function. Unlike generic learned models, PCARNN explicitly preserves the control-affine structure of vehicle dynamics, ensuring the linearity required for reliable optimization. This enables the DCBF to enforce polygonal keep-in constraints via a real-time Quadratic Program (QP) that handles high relative degree and mitigates actuator saturation. Experiments in CARLA across electric and combustion platforms demonstrate that this structure-preserving approach significantly outperforms analytical and unstructured neural baselines.


LLM-MemCluster: Empowering Large Language Models with Dynamic Memory for Text Clustering

arXiv.org Artificial Intelligence

Large Language Models (LLMs) are reshaping unsupervised learning by offering an unprecedented ability to perform text clustering based on their deep semantic understanding. However, their direct application is fundamentally limited by a lack of stateful memory for iterative refinement and the difficulty of managing cluster granularity. As a result, existing methods often rely on complex pipelines with external modules, sacrificing a truly end-to-end approach. We introduce LLM-MemCluster, a novel framework that reconceptualizes clustering as a fully LLM-native task. It leverages a Dynamic Memory to instill state awareness and a Dual-Prompt Strategy to enable the model to reason about and determine the number of clusters. Evaluated on several benchmark datasets, our tuning-free framework significantly and consistently outperforms strong baselines. LLM-MemCluster presents an effective, interpretable, and truly end-to-end paradigm for LLM-based text clustering.