First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The authors provide finite sample bounds on the excess risk of these classifiers. When taken to the limit these bounds reproduce the known consistency results for this class. However, they are superior in two ways: 1. They apply in the finite case 2. They apply to a broader set of metric spaces The presentation is very clear and the intuition is well described.

Consider an unweighted k-nearest neighbor graph on n points that have been sampled i.i.d.

Distance-based approaches to outlier detection are popular in data mining, as they do not require to model the underlying probability distribution, which is particularly challenging for high-dimensional data. We present an empirical comparison of various approaches to distance-based outlier detection across a large number of datasets. We report the surprising observation that a simple, sampling-based scheme outperforms state-of-the-art techniques in terms of both efficiency and effectiveness. To better understand this phenomenon, we provide a theoretical analysis why the sampling-based approach outperforms alternative methods based on k-nearest neighbor search.

All the existing multi-task local learning methods are defined on homogeneous neighborhood which consists of all data points from only one task. In this paper, different from existing methods, we propose local learning methods for multi-task classification and regression problems based on heterogeneous neighborhood which is defined on data points from all tasks. Specifically, we extend the k-nearest-neighbor classifier by formulating the decision function for each data point as a weighted voting among the neighbors from all tasks where the weights are task-specific. By defining a regularizer to enforce the task-specific weight matrix to approach a symmetric one, a regularized objective function is proposed and an efficient coordinate descent method is developed to solve it. For regression problems, we extend the kernel regression to multi-task setting in a similar way to the classification case. Experiments on some toy data and real-world datasets demonstrate the effectiveness of our proposed methods.

We formulate the problem of metric learning for k nearest neighbor classification as a large margin structured prediction problem, with a latent variable representing the choice of neighbors and the task loss directly corresponding to classification error. We describe an efficient algorithm for exact loss augmented inference,and a fast gradient descent algorithm for learning in this model. The objective drives the metric to establish neighborhood boundaries that benefit the true class labels for the training points. Our approach, reminiscent of gerrymandering (redrawing of political boundaries to provide advantage to certain parties), is more direct in its handling of optimizing classification accuracy than those previously proposed. In experiments on a variety of data sets our method is shown to achieve excellent results compared to current state of the art in metric learning.

We investigate the recovery dynamics of healthy cardiac activity after physical exertion using multimodal biosignals recorded with a polycardiograph. Multifractal features derived from the singularity spectrum capture the scale-invariant properties of cardiovascular regulation. Five supervised classification algorithms - Logistic Regression (LogReg), Suport Vector Machine with RBF kernel (SVM-RBF), k-Nearest Neighbors (kNN), Decision Tree (DT), and Random Forest (RF) - were evaluated to distinguish recovery states in a small, imbalanced dataset. Our results show that multifractal analysis, combined with multimodal sensing, yields reliable features for characterizing recovery and points toward nonlinear diagnostic methods for heart conditions.

Understanding how Large Language Models (LLMs) perform complex reasoning and their failure mechanisms is a challenge in interpretability research. To provide a measurable geometric analysis perspective, we define the concept of the Reasoning Manifold, a latent low-dimensional geometric structure formed by the internal representations corresponding to all correctly reasoned generations. This structure can be conceptualized as the embodiment of the effective thinking paths that the model has learned to successfully solve a given task. Based on this concept, we build REMA, a framework that explains the origins of failures by quantitatively comparing the spatial relationships of internal model representations corresponding to both erroneous and correct reasoning samples. Specifically, REMA first quantifies the geometric deviation of each erroneous representation by calculating its k-nearest neighbors distance to the approximated manifold formed by correct representations, thereby providing a unified failure signal. It then localizes the divergence points where these deviations first become significant by tracking this deviation metric across the model's layers and comparing it against a baseline of internal fluctuations from correct representations, thus identifying where the reasoning chain begins to go off-track. Our extensive experiments on diverse language and multimodal models and tasks demonstrate the low-dimensional nature of the reasoning manifold and the high separability between erroneous and correct reasoning representations. The results also validate the effectiveness of the REMA framework in analyzing the origins of reasoning failures. This research connects abstract reasoning failures to measurable geometric deviations in representations, providing new avenues for in-depth understanding and diagnosis of the internal computational processes of black-box models.

People with Multiple Sclerosis (MS) complain of problems with hand dexterity and cognitive fatigue. However, in many cases, impairments are subtle and difficult to detect. Functional near-infrared spectroscopy (fNIRS) is a non-invasive neuroimaging technique that measures brain hemodynamic responses during cognitive or motor tasks. We aimed to detect brain activity biomarkers that could explain subjective reports of cognitive fatigue while completing dexterous tasks and provide targets for future brain stimulation treatments. We recruited 15 people with MS who did not have a hand (Nine Hole Peg Test [NHPT]), mobility, or cognitive impairment, and 12 age- and sex-matched controls. Participants completed two types of hand dexterity tasks with their dominant hand, single task and dual task (NHPT while holding a ball between the fifth finger and hypothenar eminence of the same hand). We analyzed fNIRS data (oxygenated and deoxygenated hemoglobin levels) using a machine learning framework to classify MS patients from controls based on their brain activation patterns in bilateral prefrontal and sensorimotor cortices. The K-Nearest Neighbor classifier achieved an accuracy of 75.0% for single manual dexterity tasks and 66.7% for the more complex dual manual dexterity tasks. Using XAI, we found that the most important brain regions contributing to the machine learning model were the supramarginal/angular gyri and the precentral gyrus (sensory integration and motor regions) of the ipsilateral hemisphere, with suppressed activity and slower neurovascular response in the MS group. During both tasks, deoxygenated hemoglobin levels were better predictors than the conventional measure of oxygenated hemoglobin. This nonconventional method of fNIRS data analysis revealed novel brain activity biomarkers that can help develop personalized brain stimulation targets.