Related papers: Bayesian Sphere-on-Sphere Regression with Optimal …
In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding…
Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local…
We present a unified treatment of the abstract problem of finding the best approximation between a cone and spheres in the image of affine transformations. Prominent instances of this problem are phase retrieval and source localization. The…
Stacking is a widely used model averaging technique that asymptotically yields optimal predictions among linear averages. We show that stacking is most effective when model predictive performance is heterogeneous in inputs, and we can…
The problem of packing equal spheres in a spherical container is a classic global optimization problem, which has attracted enormous studies in academia and found various applications in industry. This problem is computationally…
Recent studies have shown that ensemble approaches could not only improve accuracy and but also estimate model uncertainty in deep learning. However, it requires a large number of parameters according to the increase of ensemble models for…
Semantic segmentation aims to robustly predict coherent class labels for entire regions of an image. It is a scene understanding task that powers real-world applications (e.g., autonomous navigation). One important application, the use of…
Geographic Information Systems (GIS) and related technologies have generated substantial interest among statisticians with regard to scalable methodologies for analyzing large spatial datasets. A variety of scalable spatial process models…
Spatial modelling often uses Gaussian random fields to capture the stochastic nature of studied phenomena. However, this approach incurs significant computational burdens (O(n3)), primarily due to covariance matrix computations. In this…
In a variety of scientific applications we wish to characterize a physical system using measurements or observations. This often requires us to solve an inverse problem, which usually has non-unique solutions so uncertainty must be…
We study distribution-on-distribution regression problems in which a response distribution depends on multiple distributional predictors. Such settings arise naturally in applications where the outcome distribution is driven by several…
Local optimization presents a promising approach to expensive, high-dimensional black-box optimization by sidestepping the need to globally explore the search space. For objective functions whose gradient cannot be evaluated directly,…
This paper develops a class of Bayesian non- and semiparametric methods for estimating regression curves and surfaces. The main idea is to model the regression as locally linear, and then place suitable local priors on the local parameters.…
We introduce a convergent finite difference method for solving the optimal transportation problem on the sphere. The method applies to both the traditional squared geodesic cost (arising in mesh generation) and a logarithmic cost (arising…
A common method for delineating urban and suburban boundaries is to identify clusters of spatial units that are highly interconnected in a network of commuting flows, each cluster signaling a cohesive economic submarket. It is critical that…
The estimation of potential fields such as the gravitational or magnetic potential at the surface of a spherical planet from noisy observations taken at an altitude over an incomplete portion of the globe is a classic example of an…
In this work, we introduce an optimal transport framework for inferring power distributions over both spatial location and temporal frequency. Recently, it has been shown that optimal transport is a powerful tool for estimating spatial…
This paper presents Sparse Partitioning, a Bayesian method for identifying predictors that either individually or in combination with others affect a response variable. The method is designed for regression problems involving binary or…
Uncertainty-aware robot motion prediction is crucial for downstream traversability estimation and safe autonomous navigation in unstructured, off-road environments, where terrain is heterogeneous and perceptual uncertainty is high. Most…
The development of science has been transforming man's view towards nature for centuries. Observing structures and patterns in an effective approach to discover regularities from data is a key step toward theory-building. With increasingly…