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Moreover,the proposed multi-class kernel learning algorithms have statistical guarantees and fast convergence rates. Experimental results on lots of benchmark datasets show that our proposed methods can significantly outperform the existing multi-class classification methods. The major contributions ofthispaper include: 1)Anewlocal Rademacher complexitybased bound withfastconvergence rate for multi-class classification is established. Existing works [16,27] for multi-class classifiers with Rademacher complexity does not take into account couplings among different classes.

We introduce a novel machine learning method called the Penalized Profile Support Vector Machine based on the Gabriel edited set for the computation of the probability of failure for a complex system as determined by a threshold condition on a computer model of system behavior. The method is designed to minimize the number of evaluations of the computer model while preserving the geometry of the decision boundary that determines the probability. It employs an adaptive sampling strategy designed to strategically allocate points near the boundary determining failure and builds a locally linear surrogate boundary that remains consistent with its geometry by strategic clustering of training points. We prove two convergence results and we compare the performance of the method against a number of state of the art classification methods on four test problems. We also apply the method to determine the probability of survival using the Lotka--Volterra model for competing species.

In this paper, we present a novel classification method called deep diffusion-invariant Wasserstein distributional classification (DeepWDC). DeepWDC represents input data and labels as probability measures to address severe perturbations in input data. It can output the optimal label measure in terms of diffusion invariance, where the label measure is stationary over time and becomes equivalent to a Gaussian measure. Furthermore, DeepWDC minimizes the 2-Wasserstein distance between the optimal label measure and Gaussian measure, which reduces the Wasserstein uncertainty. Experimental results demonstrate that DeepWDC can substantially enhance the accuracy of several baseline deterministic classification methods and outperforms state-of-the-art-methods on 2D and 3D data containing various types of perturbations (e.g., rotations, impulse noise, and down-scaling).

What sorts of structure might enable a learner to discover classes from unlabeled data? Traditional approaches rely on feature-space similarity and heroic assumptions on the data. In this paper, we introduce unsupervised learning under Latent Label Shift (LLS), where the label marginals $p_d(y)$ shift but the class conditionals $p(x|y)$ do not.

Our work is related to one-class classification which is aimed at "describing" the positive class by clustering-related methods, but one-class classification does not have the ability to tune hyper-parameters

Traditional human activity recognition uses either direct image analysis or data from wearable inertial measurement units (IMUs), but can be ineffective in challenging underwater environments. We introduce a novel hybrid approach that bridges this gap to monitor scuba diver safety. Our method leverages computer vision to generate high-fidelity motion data, effectively creating a ``pseudo-IMU'' from a stream of 3D human joint keypoints. This technique circumvents the critical problem of wireless signal attenuation in water, which plagues conventional diver-worn sensors communicating with an Autonomous Underwater Vehicle (AUV). We apply this system to the vital task of identifying anomalous scuba diver behavior that signals the onset of a medical emergency such as cardiac arrest -- a leading cause of scuba diving fatalities. By integrating our classifier onboard an AUV and conducting experiments with simulated distress scenarios, we demonstrate the utility and effectiveness of our method for advancing robotic monitoring and diver safety.

Here, we consider the jackknife+--i.e., Algorithm S1 describes the extension of Algorithm 1 discussed in Section 2.5, which ensures The validity of this algorithm is established by the following result. We begin by proving the lower bound on coverage. This will become apparent after we reduce our claim to the setting in the aforementioned paper. This is easy to verify. Let σ (1),...,σ ( n + m) be the permutation of the data points corresponding to Σ, so that (ΣA Σ S3.1 Implementation details We have applied the following black-box classification methods to estimate label probabilities: JK+ is omitted for computational reasons. The performances of the different methods on data generated from this model are compared in Figure S3.