Graph Convolutional Networks (GCNs), aiming to obtain the representation of a node by aggregating its neighbors, have demonstrated great power in tackling various analytics tasks on graph (network) data. The remarkable performance of GCNs typically relies on the homophily assumption of networks, while such assumption cannot always be satisfied, since the heterophily or randomness are also widespread in real-world. This gives rise to one fundamental question: whether networks with different structural properties should adopt different propagation mechanisms? Surprisingly, we discover that there are actually segmentation rules for the propagation mechanism, i.e., 1-hop, 2-hop and k -nearest neighbor ( k NN) neighbors are more suitable as neighborhoods of network with complete homophily, complete heterophily and randomness, respectively. However, the real-world networks are complex, and may present diverse structural properties, e.g., the network dominated by homophily may contain a small amount of randomness.

This paper develops a prediction-based prescriptive model for optimal decision making that (i) predicts the outcome under each action using a robust nonlinear model, and (ii) adopts a randomized prescriptive policy determined by the predicted outcomes. The predictive model combines a new regularized regression technique, which was developed using Distributionally Robust Optimization (DRO) with an ambiguity set constructed from the Wasserstein metric, with the K-Nearest Neighbors (K-NN) regression, which helps to capture the nonlinearity embedded in the data. We show theoretical results that guarantee the out-of-sample performance of the predictive model, and prove the optimality of the randomized policy in terms of the expected true future outcome. We demonstrate the proposed methodology on a hypertension dataset, showing that our prescribed treatment leads to a larger reduction in the systolic blood pressure compared to a series of alternatives. A clinically meaningful threshold level used to activate the randomized policy is also derived under a sub-Gaussian assumption on the predicted outcome.

Multi-label classification (MLC) has wide practical importance, but the theoretical understanding of its statistical properties is still limited. As an attempt to fill this gap, we thoroughly study upper and lower regret bounds for two canonical MLC performance measures, Hamming loss and Precision@ \kappa . We consider two different statistical and algorithmic settings, a non-parametric setting tackled by plug-in classifiers \ a la k -nearest neighbors, and a parametric one tackled by empirical risk minimization operating on surrogate loss functions. For both, we analyze the interplay between a natural MLC variant of the low noise assumption, widely studied in binary classification, and the label sparsity, the latter being a natural property of large-scale MLC problems. We show that those conditions are crucial in improving the bounds, but the way they are tangled is not obvious, and also different across the two settings.

Mutual information provides a powerful, general-purpose metric for quantifying the amount of shared information between variables. Estimating normalized mutual information using a k-Nearest Neighbor (k-NN) based approach involves the calculation of the scaling-invariant k-NN radius. Calculation of the radius suffers from numerical overflow when the joint dimensionality of the data becomes high, typically in the range of several hundred dimensions. To address this issue, we propose a logarithmic transformation technique that improves the numerical stability of the radius calculation in high-dimensional spaces. By applying the proposed transformation during the calculation of the radius, numerical overflow is avoided, and precision is maintained. Proposed transformation is validated through both theoretical analysis and empirical evaluation, demonstrating its ability to stabilize the calculation without compromizing the precision of the results.

Making an adaptive prediction based on input is an important ability for general artificial intelligence. In this work, we step forward in this direction and propose a semi-parametric method, Meta-Neighborhoods, where predictions are made adaptively to the neighborhood of the input. We show that Meta-Neighborhoods is a generalization of k-nearest-neighbors. Due to the simpler manifold structure around a local neighborhood, Meta-Neighborhoods represent the predictive distribution p(y x) more accurately. To reduce memory and computation overheads, we propose induced neighborhoods that summarize the training data into a much smaller dictionary.

UMAP has supplanted t -SNE as state-of-the-art for visualizing high-dimensional datasets in many disciplines, but the reason for its success is not well understood. In this work, we investigate UMAP's sampling based optimization scheme in detail. We derive UMAP's true loss function in closed form and find that it differs from the published one in a dataset size dependent way. As a consequence, we show that UMAP does not aim to reproduce its theoretically motivated high-dimensional UMAP similarities. Instead, it tries to reproduce similarities that only encode the k nearest neighbor graph, thereby challenging the previous understanding of UMAP's effectiveness.

A novel approach to rank estimation, called geometric order learning (GOL), is proposed in this paper. First, we construct an embedding space, in which the direction and distance between objects represent order and metric relations between their ranks, by enforcing two geometric constraints: the order constraint compels objects to be sorted according to their ranks, while the metric constraint makes the distance between objects reflect their rank difference. Then, we perform the simple k nearest neighbor ( k -NN) search in the embedding space to estimate the rank of a test object. Moreover, to assess the quality of embedding spaces for rank estimation, we propose a metric called discriminative ratio for ranking (DRR). Extensive experiments on facial age estimation, historical color image (HCI) classification, and aesthetic score regression demonstrate that GOL constructs effective embedding spaces and thus yields excellent rank estimation performances.

RF-GAP has recently been introduced as an improved random forest proximity measure. In this paper, we present PF-GAP, an extension of RF-GAP proximities to proximity forests, an accurate and efficient time series classification model. We use the forest proximities in connection with Multi-Dimensional Scaling to obtain vector embeddings of univariate time series, comparing the embeddings to those obtained using various time series distance measures. We also use the forest proximities alongside Local Outlier Factors to investigate the connection between misclassified points and outliers, comparing with nearest neighbor classifiers which use time series distance measures. We show that the forest proximities may exhibit a stronger connection between misclassified points and outliers than nearest neighbor classifiers.

We propose a methodology to enhance local CO2 monitoring by integrating satellite data from the Orbiting Carbon Observatories (OCO-2 and OCO-3) with ground level observations from the Integrated Carbon Observation System (ICOS) and weather data from the ECMWF Reanalysis v5 (ERA5). Unlike traditional methods that downsample national data, our approach uses multimodal data fusion for high-resolution CO2 estimations. We employ weighted K-nearest neighbor (KNN) interpolation with machine learning models to predict ground level CO2 from satellite measurements, achieving a Root Mean Squared Error of 3.92 ppm. Our results show the effectiveness of integrating diverse data sources in capturing local emission patterns, highlighting the value of high-resolution atmospheric transport models. The developed model improves the granularity of CO2 monitoring, providing precise insights for targeted carbon mitigation strategies, and represents a novel application of neural networks and KNN in environmental monitoring, adaptable to various regions and temporal scales.

Studying the reliability of complex systems using machine learning techniques involves facing a series of technical and practical challenges, ranging from the intrinsic nature of the system and data to the difficulties in modeling and effectively deploying models in real-world scenarios. This study compares the effectiveness of classical statistical techniques and machine learning methods for improving complex system analysis in reliability assessments. We aim to demonstrate that classical statistical algorithms often yield more precise and interpretable results than black-box machine learning approaches in many practical applications. The evaluation is conducted using both real-world data and simulated scenarios. We report the results obtained from statistical modeling algorithms, as well as from machine learning methods including neural networks, K-nearest neighbors, and random forests.