Near-Optimal Lower Bounds on One-Bit Compressed Sensing of Approximately Sparse Signals

This paper provides the first near-optimal lower bounds for one-bit compressed sensing of approximately sparse signals lying in a scaled $\ell_1$ ball, which is a commonly adopted relaxation of the exactly $k$-sparse assumption. In prior works, the best known upper bounds on uniform Euclidean error are of order $\widetilde{O}((k/m)^{1/3})$, where $m$ is the number of measurements. Under sub-Gaussian matrices, we establish nearly matching lower bounds for both the canonical one-bit compressed sensing model and the uniformly dithered model. Our argument is to first embed a small Euclidean ball into the signal set, which is straightforward for the dithered model but relies on a lifting map for the canonical model, and then construct two signals in this small ball that are separated in Euclidean distance by at least $(k/m)^{1/3}$ (up to logarithmic factor) but are indistinguishable from the binary measurements. Moreover, our argument extends to approximately sparse signals that live in a properly scaled $\ell_q$ ball $(q\in [0,1])$, yielding a lower bound $\widetildeΩ((k/m)^{\frac{2-q}{2+q}})$ that smoothly bridges the cases of exact sparsity ($q=0$) and $\ell_1$ sparsity ($q=1$). Finally, we discuss the extensions of our lower bounds to sub-Weibull matrices, adversarial bit flipping, matrix recovery, and characterize the transition to the non-sparse case.

Deep Learning for Semen Analysis in Male Infertility: Computer Vision, Multimodal Fusion, and Clinical Translation

Male infertility contributes substantially to the global infertility burden, and sperm analysis remains central to diagnosis, treatment planning, and assisted reproductive technology. Conventional semen evaluation, however, is labor-intensive, operator-dependent, and limited by inter- and intra-observer variability, motivating the development of objective and reproducible computational approaches. This review provides a comprehensive and perspective-oriented synthesis of artificial intelligence-driven sperm analysis, with a focus on computer vision, deep learning, multimodal fusion, robustness, and clinical translation. We first review task-specific methods for sperm detection and counting, tracking-based motility assessment, semantic and instance segmentation, morphology and defect classification, functional assessment, and genetic integrity evaluation. We then summarize public datasets, benchmarks, evaluation metrics, and emerging multimodal strategies that integrate microscopic images, time-lapse videos, CASA-derived parameters, DNA integrity assays, and clinical metadata. Beyond algorithmic performance, we discuss key barriers to real-world deployment, including data scarcity, cross-center domain shift, annotation inconsistency, interpretability, uncertainty calibration, privacy-preserving learning, and workflow integration. Finally, we outline a staged clinical translation roadmap spanning technical standardization, multicenter retrospective validation, silent prospective evaluation, human-in-the-loop clinical testing, ART outcome validation, regulatory approval, and post-market monitoring. By organizing the field from task-specific visual recognition to trustworthy multimodal reproductive intelligence, this review highlights both the progress and the unresolved challenges required to translate AI-driven sperm analysis into clinically meaningful decision support.

Robust Matrix Estimation with Side Information

We introduce a flexible framework for high-dimensional matrix estimation to incorporate side information for both rows and columns. Existing approaches, such as inductive matrix completion, often impose restrictive structure-for example, an exact low-rank covariate interaction term, linear covariate effects, and limited ability to exploit components explained only by one side (row or column) or by neither-and frequently omit an explicit noise component. To address these limitations, we propose to decompose the underlying matrix as the sum of four complementary components: (possibly nonlinear) interaction between row and column characteristics; row characteristic-driven component, column characteristic-driven component, and residual low-rank structure unexplained by observed characteristics. By combining sieve-based projection with nuclear-norm penalization, each component can be estimated separately and these estimated components can then be aggregated to yield a final estimate. We derive convergence rates that highlight robustness across a range of model configurations depending on the informativeness of the side information. We further extend the method to partially observed matrices under both missing-at-random and missing-not-at-random mechanisms, including block-missing patterns motivated by causal panel data. Simulations and a real-data application to tobacco sales show that leveraging side information improves imputation accuracy and can enhance treatment-effect estimation relative to standard low-rank and spectral-based alternatives.

Knowledge-Embedded Latent Projection for Robust Representation Learning

Latent space models are widely used for analyzing high-dimensional discrete data matrices, such as patient-feature matrices in electronic health records (EHRs), by capturing complex dependence structures through low-dimensional embeddings. However, estimation becomes challenging in the imbalanced regime, where one matrix dimension is much larger than the other. In EHR applications, cohort sizes are often limited by disease prevalence or data availability, whereas the feature space remains extremely large due to the breadth of medical coding system. Motivated by the increasing availability of external semantic embeddings, such as pre-trained embeddings of clinical concepts in EHRs, we propose a knowledge-embedded latent projection model that leverages semantic side information to regularize representation learning. Specifically, we model column embeddings as smooth functions of semantic embeddings via a mapping in a reproducing kernel Hilbert space. We develop a computationally efficient two-step estimation procedure that combines semantically guided subspace construction via kernel principal component analysis with scalable projected gradient descent. We establish estimation error bounds that characterize the trade-off between statistical error and approximation error induced by the kernel projection. Furthermore, we provide local convergence guarantees for our non-convex optimization procedure. Extensive simulation studies and a real-world EHR application demonstrate the effectiveness of the proposed method.

TransST: Transfer Learning Embedded Spatial Factor Modeling of Spatial Transcriptomics Data

Background: Spatial transcriptomics have emerged as a powerful tool in biomedical research because of its ability to capture both the spatial contexts and abundance of the complete RNA transcript profile in organs of interest. However, limitations of the technology such as the relatively low resolution and comparatively insufficient sequencing depth make it difficult to reliably extract real biological signals from these data. To alleviate this challenge, we propose a novel transfer learning framework, referred to as TransST, to adaptively leverage the cell-labeled information from external sources in inferring cell-level heterogeneity of a target spatial transcriptomics data. Results: Applications in several real studies as well as a number of simulation settings show that our approach significantly improves existing techniques. For example, in the breast cancer study, TransST successfully identifies five biologically meaningful cell clusters, including the two subgroups of cancer in situ and invasive cancer; in addition, only TransST is able to separate the adipose tissues from the connective issues among all the studied methods. Conclusions: In summary, the proposed method TransST is both effective and robust in identifying cell subclusters and detecting corresponding driving biomarkers in spatial transcriptomics data.

DenseFormer: Learning Dense Depth Map from Sparse Depth and Image via Conditional Diffusion Model

The depth completion task is a critical problem in autonomous driving, involving the generation of dense depth maps from sparse depth maps and RGB images. Most existing methods employ a spatial propagation network to iteratively refine the depth map after obtaining an initial dense depth. In this paper, we propose DenseFormer, a novel method that integrates the diffusion model into the depth completion task. By incorporating the denoising mechanism of the diffusion model, DenseFormer generates the dense depth map by progressively refining an initial random depth distribution through multiple iterations. We propose a feature extraction module that leverages a feature pyramid structure, along with multi-layer deformable attention, to effectively extract and integrate features from sparse depth maps and RGB images, which serve as the guiding condition for the diffusion process. Additionally, this paper presents a depth refinement module that applies multi-step iterative refinement across various ranges to the dense depth results generated by the diffusion process. The module utilizes image features enriched with multi-scale information and sparse depth input to further enhance the accuracy of the predicted depth map. Extensive experiments on the KITTI outdoor scene dataset demonstrate that DenseFormer outperforms classical depth completion methods.

V2X-DGPE: Addressing Domain Gaps and Pose Errors for Robust Collaborative 3D Object Detection

In V2X collaborative perception, the domain gaps between heterogeneous nodes pose a significant challenge for effective information fusion. Pose errors arising from latency and GPS localization noise further exacerbate the issue by leading to feature misalignment. To overcome these challenges, we propose V2X-DGPE, a high-accuracy and robust V2X feature-level collaborative perception framework. V2X-DGPE employs a Knowledge Distillation Framework and a Feature Compensation Module to learn domain-invariant representations from multi-source data, effectively reducing the feature distribution gap between vehicles and roadside infrastructure. Historical information is utilized to provide the model with a more comprehensive understanding of the current scene. Furthermore, a Collaborative Fusion Module leverages a heterogeneous self-attention mechanism to extract and integrate heterogeneous representations from vehicles and infrastructure. To address pose errors, V2X-DGPE introduces a deformable attention mechanism, enabling the model to adaptively focus on critical parts of the input features by dynamically offsetting sampling points. Extensive experiments on the real-world DAIR-V2X dataset demonstrate that the proposed method outperforms existing approaches, achieving state-of-the-art detection performance. The code is available at https://github.com/wangsch10/V2X-DGPE.

XLD: A Cross-Lane Dataset for Benchmarking Novel Driving View Synthesis

Thoroughly testing autonomy systems is crucial in the pursuit of safe autonomous driving vehicles. It necessitates creating safety-critical scenarios that go beyond what can be safely collected from real-world data, as many of these scenarios occur infrequently on public roads. However, the evaluation of most existing NVS methods relies on sporadic sampling of image frames from the training data, comparing the rendered images with ground truth images using metrics. Unfortunately, this evaluation protocol falls short of meeting the actual requirements in closed-loop simulations. Specifically, the true application demands the capability to render novel views that extend beyond the original trajectory (such as cross-lane views), which are challenging to capture in the real world. To address this, this paper presents a novel driving view synthesis dataset and benchmark specifically designed for autonomous driving simulations. This dataset is unique as it includes testing images captured by deviating from the training trajectory by 1-4 meters. It comprises six sequences encompassing various time and weather conditions. Each sequence contains 450 training images, 150 testing images, and their corresponding camera poses and intrinsic parameters. Leveraging this novel dataset, we establish the first realistic benchmark for evaluating existing NVS approaches under front-only and multi-camera settings. The experimental findings underscore the significant gap that exists in current approaches, revealing their inadequate ability to fulfill the demanding prerequisites of cross-lane or closed-loop simulation. Our dataset is released publicly at the project page: https://3d-aigc.github.io/XLD/.

Tensor Methods in High Dimensional Data Analysis: Opportunities and Challenges

Large amount of multidimensional data represented by multiway arrays or tensors are prevalent in modern applications across various fields such as chemometrics, genomics, physics, psychology, and signal processing. The structural complexity of such data provides vast new opportunities for modeling and analysis, but efficiently extracting information content from them, both statistically and computationally, presents unique and fundamental challenges. Addressing these challenges requires an interdisciplinary approach that brings together tools and insights from statistics, optimization and numerical linear algebra among other fields. Despite these hurdles, significant progress has been made in the last decade. This review seeks to examine some of the key advancements and identify common threads among them, under eight different statistical settings.

Multiple Testing of Linear Forms for Noisy Matrix Completion

Many important tasks of large-scale recommender systems can be naturally cast as testing multiple linear forms for noisy matrix completion. These problems, however, present unique challenges because of the subtle bias-and-variance tradeoff of and an intricate dependence among the estimated entries induced by the low-rank structure. In this paper, we develop a general approach to overcome these difficulties by introducing new statistics for individual tests with sharp asymptotics both marginally and jointly, and utilizing them to control the false discovery rate (FDR) via a data splitting and symmetric aggregation scheme. We show that valid FDR control can be achieved with guaranteed power under nearly optimal sample size requirements using the proposed methodology. Extensive numerical simulations and real data examples are also presented to further illustrate its practical merits.