We will incorporate this feedback.

In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS).

While many techniques for detecting these attacks have been proposed, they are easily bypassed when the adversary has full knowledge of the detection mechanism and adapts the attack strategy accordingly.

Given a sample (a set of i.i.d.

We study the problem of fair binary classification using the notion of Equal Opportunity.

Neural Information Processing Systems http://nips.cc/

Variable selection for high-dimensional, highly correlated data has long been a challenging problem, often yielding unstable and unreliable models. We propose a resample-aggregate framework that exploits diffusion models' ability to generate high-fidelity synthetic data. Specifically, we draw multiple pseudo-data sets from a diffusion model fitted to the original data, apply any off-the-shelf selector (e.g., lasso or SCAD), and store the resulting inclusion indicators and coefficients. Aggregating across replicas produces a stable subset of predictors with calibrated stability scores for variable selection. Theoretically, we show that the proposed method is selection consistent under mild assumptions. Because the generative model imports knowledge from large pre-trained weights, the procedure naturally benefits from transfer learning, boosting power when the observed sample is small or noisy. We also extend the framework of aggregating synthetic data to other model selection problems, including graphical model selection, and statistical inference that supports valid confidence intervals and hypothesis tests. Extensive simulations show consistent gains over the lasso, stability selection, and knockoff baselines, especially when predictors are strongly correlated, achieving higher true-positive rates and lower false-discovery proportions. By coupling diffusion-based data augmentation with principled aggregation, our method advances variable selection methodology and broadens the toolkit for interpretable, statistically rigorous analysis in complex scientific applications.

Loop closure detection is important for simultaneous localization and mapping (SLAM), which associates current observations with historical keyframes, achieving drift correction and global relocalization. However, a falsely detected loop can be fatal, and this is especially difficult in repetitive environments where appearance-based features fail due to the high similarity. Therefore, verification of a loop closure is a critical step in avoiding false positive detections. Existing works in loop closure verification predominantly focus on learning invariant appearance features, neglecting the prior knowledge of the robot's spatial-temporal motion cue, i.e., trajectory. In this letter, we propose ROVER, a loop closure verification method that leverages the historical trajectory as a prior constraint to reject false loops in challenging repetitive environments. For each loop candidate, it is first used to estimate the robot trajectory with pose-graph optimization. This trajectory is then submitted to a scoring scheme that assesses its compliance with the trajectory without the loop, which we refer to as the trajectory prior, to determine if the loop candidate should be accepted. Benchmark comparisons and real-world experiments demonstrate the effectiveness of the proposed method. Furthermore, we integrate ROVER into state-of-the-art SLAM systems to verify its robustness and efficiency. Our source code and self-collected dataset are available at https://github.com/jarvisyjw/ROVER.