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For supervised classification problems, this paper considers estimating the query's label probability through local regression using observed covariates. Well-known nonparametric kernel smoother and $k$-nearest neighbor ($k$-NN) estimator,…

Existing analysis of Local (Stochastic) Gradient Descent for heterogeneous objectives requires stepsizes $\eta \leq 1/K$ where $K$ is the communication interval, which ensures monotonic decrease of the objective. In contrast, we analyze…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

Geographical and Temporal Weighted Regression (GTWR) model is an important local technique for exploring spatial heterogeneity in data relationships, as well as temporal dependence due to its high fitting capacity when it comes to real…

We present a method for balancing between the Local and Global Structures (LGS) in graph embedding, via a tunable parameter. Some embedding methods aim to capture global structures, while others attempt to preserve local neighborhoods. Few…

The objective of this study is to investigate spatial structures of error in the assessment of continuous raster data. The use of conventional diagnostics of error often overlooks the possible spatial variation in error because such…

Spatial prediction is a fundamental task in geography. In recent years, with advances in geospatial artificial intelligence (GeoAI), numerous models have been developed to improve the accuracy of geographic variable predictions. Beyond…

Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization…

Adversarial Regression is a proposition to perform high dimensional non-linear regression with uncertainty estimation. We used Conditional Generative Adversarial Network to obtain an estimate of the full predictive distribution for a new…

This study proposes a mathematical programming-based algorithm for the integrated selection of variable subsets and bandwidth estimation in geographically weighted regression, a local regression method that allows the kernel bandwidth and…

In this paper, we aim to take one step forward to the scenario where an adaptive subspace detection framework is required to detect subspace signals in non-stationary environments. Despite the fact that this scenario is more realistic, the…

This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample…

Variational inference has experienced a recent surge in popularity owing to stochastic approaches, which have yielded practical tools for a wide range of model classes. A key benefit is that stochastic variational inference obviates the…

Multi-robot global localization (MR-GL) with unknown initial positions in a large scale environment is a challenging task. The key point is the data association between different robots' viewpoints. It also makes traditional…

Analysis of geospatial data has traditionally been model-based, with a mean model, customarily specified as a linear regression on the covariates, and a covariance model, encoding the spatial dependence. We relax the strong assumption of…

Applied macroeconomists often compute confidence intervals for impulse responses using local projections, i.e., direct linear regressions of future outcomes on current covariates. This paper proves that local projection inference robustly…

Although Generative Adversarial Networks have shown remarkable performance in image generation, there are some challenges in image realism and convergence speed. The results of some models display the imbalances of quality within a…

Goal Recognition (GR) is the problem of recognizing an agent's objectives based on observed actions. Recent data-driven approaches for GR alleviate the need for costly, manually crafted domain models. However, these approaches can only…

A well-known combinatorial algorithm can decide generic rigidity in the plane by determining if the graph is of Pollaczek-Geiringer-Laman type. Methods from matroid theory have been used to prove other interesting results, again under the…

This paper develops a new automatic and location-adaptive procedure for estimating regression in a Functional Single-Index Model (FSIM). This procedure is based on $k$-Nearest Neighbours ($k$NN) ideas. The asymptotic study includes results…