Stein V ariational Gradient Descent (SVGD) is a nonparametric particle-based deterministic sampling algorithm.

It's nowhere near early enough for those of us in the northern hemisphere to start struggling against winter's somnolent spell, so there's no need for excuses as you take to your bed with a pile of good books. And there's plenty to keep you occupied while you eschew the chilly outdoors. This month, we have climate hope from a well-placed environmental reporter, formerly of this parish, an honest memoir from a star scientist and a jaw-dropping account of the commodification of women's bodies. Given the Valentine's Day fun this month, we also have a book that may challenge what we thought we knew about finding love. It's always good to get all the help we can in that department - enjoy! "On clear moonlit nights we sometimes step outside and howl at the moon together. It is cathartic, primal and a really good laugh. I am not sure what our neighbours think about it, though."

America's fastest-growing state is selling the perfect lifestyle... and everyone's falling for it Devastating truth about Blind Side actor Quinton Aaron: More to this'than everyone is letting on', friends reveal... as co-star Sandra Bullock'monitors' situation Marco Rubio'cocoons like a mummy' in bizarre strategy to hide naps from Trump Explosive twist in'diva' inmate Bryan Kohberger's life in prison revealed in the FREE The Crime Desk newsletter Blake Lively's driver claims Justin Baldoni confessed to previously'forcing himself on women' during'disturbing' in-car conversation Maine's legendary'Lobster Lady' dies after working until she was 103 and waking up at 3am every day Sydney Sweeney shows off her bombshell curves in racy lingerie to promote her new SYRN line - as it's revealed Hollywood Sign bra stunt could leave her facing trespassing and vandalism charges The wild truth about my influencer sons, their psycho dad and how lawsuits nearly left them bankrupt - by Jake and Logan Paul's MOM Lawyer, 44, who died on flight to London after falling asleep on her mother's shoulder had undiagnosed cardiac condition, inquest hears Food Network star Valerie Bertinelli's heartbreaking struggles laid bare after confession about shock firing Gavin Newsom's ballyhooed'care first' $236 million mental health push helps ONLY 22 people in four years America's earthquake hotspot is more dangerous than feared as scientists make surprising discovery READ MORE: Prophecy from apocalyptic'messiah' warns of death so widespread'even birds won't escape' Scientists studying Northern California have uncovered previously hidden fault lines, raising alarms that seismic risk in the region may be underestimated. For decades, the Mendocino triple junction was believed to be where three tectonic plates meet: the San Andreas Fault ending in the north, the Cascadia Subduction Zone in the south, and the Mendocino Fault in the east. Because three major fault systems converge there, the area is one of the most active earthquake zones in the US and could produce a magnitude 8.0 quake. Now, researchers have discovered that the junction actually contains at least five tectonic plates or fragments deep below the surface, making the region far more complex than previously thought. That means there may be an unaccounted earthquake hazard in the area, and current models could be underestimating the true risk.

Under the assumption that data lie on a compact (unknown) manifold without boundary, we derive finite sample bounds for kernel smoothing and its (first and second) derivatives, and we establish asymptotic normality through Berry-Esseen type bounds. Special cases include kernel density estimation, kernel regression and the heat kernel signature. Connections to the graph Laplacian are also discussed.

Effective feature selection is essential for high-dimensional data analysis and machine learning. Unsupervised feature selection (UFS) aims to simultaneously cluster data and identify the most discriminative features. Most existing UFS methods linearly project features into a pseudo-label space for clustering, but they suffer from two critical limitations: (1) an oversimplified linear mapping that fails to capture complex feature relationships, and (2) an assumption of uniform cluster distributions, ignoring outliers prevalent in real-world data. To address these issues, we propose the Robust Autoencoder-based Unsupervised Feature Selection (RAEUFS) model, which leverages a deep autoencoder to learn nonlinear feature representations while inherently improving robustness to outliers. We further develop an efficient optimization algorithm for RAEUFS. Extensive experiments demonstrate that our method outperforms state-of-the-art UFS approaches in both clean and outlier-contaminated data settings.

In this work, inspired by machine learning techniques, we propose a new Bayesian model for Small Area Estimation (SAE), the Fay-Herriot model with Spectral Clustering (FH-SC). Unlike traditional approaches, clustering in FH-SC is based on spectral clustering algorithms that utilize external covariates, rather than geographical or administrative criteria. A major advantage of the FH-SC model is its flexibility in integrating existing SAE approaches, with or without clustering random effects. To enable benchmarking, we leverage the theoretical framework of posterior projections for constrained Bayesian inference and derive closed form expressions for the new Rao-Blackwell (RB) estimators of the posterior mean under the FH-SC model. Additionally, we introduce a novel measure of uncertainty for the benchmarked estimator, the Conditional Posterior Mean Square Error (CPMSE), which is generalizable to other Bayesian SAE estimators. We conduct model-based and data-based simulation studies to evaluate the frequentist properties of the CPMSE. The proposed methodology is motivated by a real case study involving the estimation of the proportion of households with internet access in the municipalities of Colombia. Finally, we also illustrate the advantages of FH-SC over existing Bayesian and frequentist approaches through our case study.

Understanding and distinguishing temporal patterns in time series data is essential for scientific discovery and decision-making. For example, in biomedical research, uncovering meaningful patterns in physiological signals can improve diagnosis, risk assessment, and patient outcomes. However, existing methods for time series pattern discovery face major challenges, including high computational complexity, limited interpretability, and difficulty in capturing meaningful temporal structures. To address these gaps, we introduce a novel learning framework that jointly trains two Transformer models using complementary time series representations: shapelet-based representations to capture localized temporal structures and traditional feature engineering to encode statistical properties. The learned shapelets serve as interpretable signatures that differentiate time series across classification labels. Additionally, we develop a visual analytics system -- SigTIme -- with coordinated views to facilitate exploration of time series signatures from multiple perspectives, aiding in useful insights generation. We quantitatively evaluate our learning framework on eight publicly available datasets and one proprietary clinical dataset. Additionally, we demonstrate the effectiveness of our system through two usage scenarios along with the domain experts: one involving public ECG data and the other focused on preterm labor analysis.

With the rapid development of Unmanned Aerial Vehicles (UAVs) and the increasing complexity of low-altitude security threats, traditional UAV identification methods struggle to extract reliable signal features and meet real-time requirements in complex environments. Recently, deep learning based Radio Frequency Fingerprint Identification (RFFI) approaches have greatly improved recognition accuracy. However, their large model sizes and high computational demands hinder deployment on resource-constrained edge devices. While model pruning offers a general solution for complexity reduction, existing weight, channel, and layer pruning techniques struggle to concurrently optimize compression rate, hardware acceleration, and recognition accuracy. To this end, in this paper, we introduce HSCP, a Hierarchical Spectral Clustering Pruning framework that combines layer pruning with channel pruning to achieve extreme compression, high performance, and efficient inference. In the first stage, HSCP employs spectral clustering guided by Centered Kernel Alignment (CKA) to identify and remove redundant layers. Subsequently, the same strategy is applied to the channel dimension to eliminate a finer redundancy. To ensure robustness, we further employ a noise-robust fine-tuning strategy. Experiments on the UAV-M100 benchmark demonstrate that HSCP outperforms existing channel and layer pruning methods. Specifically, HSCP achieves $86.39\%$ parameter reduction and $84.44\%$ FLOPs reduction on ResNet18 while improving accuracy by $1.49\%$ compared to the unpruned baseline, and maintains superior robustness even in low signal-to-noise ratio environments.

Recent image protection mechanisms such as Glaze and Nightshade introduce imperceptible, adversarially designed perturbations intended to disrupt downstream text-to-image generative models. While their empirical effectiveness has been demonstrated, the internal structure, detectability, and representational behavior of these perturbations remain poorly understood. In this study, we demonstrated a systematic explainable AI analysis of image protection perturbations using a unified framework that integrates white-box feature-space inspection and black-box signal-level probing. Through latent-space clustering, feature-channel activation analysis, occlusion-based spatial sensitivity mapping, and frequency-domain spectral characterization, we revealed that modern protection mechanisms operate as structured, low-entropy perturbations that remain tightly coupled to underlying image content across representational, spatial, and spectral domains in all evaluated cases. We showed that protected images preserve content-driven feature organization with protection-specific substructure rather than inducing global representational drift. Detectability is governed by interacting effects of perturbation entropy, spatial deployment, and frequency alignment as revealed through combined synthetic and spectral analyses, with sequential protection amplifying detectable structure rather than suppressing it. Frequency-domain analysis further demonstrated that Glaze and Nightshade redistribute energy along dominant image-aligned frequency axes rather than introducing spectrally diffuse noise. These results suggested that contemporary image protection operates through structured feature-level deformation rather than semantic dislocation, providing mechanistic insight into why protection signals remain visually subtle yet consistently detectable. This work advances the interpretability of adversarial image protection and informs the design of future defenses and detection strategies for generative AI systems.