Related papers: A Kernel Score Perspective on Forecast Disagreemen…
We study the theoretical behavior of denoising score matching--the learning task associated to diffusion models--when the data distribution is supported on a low-dimensional manifold and the score is parameterized using a random feature…
Spectral clustering is a popular unsupervised learning technique which is able to partition unlabelled data into disjoint clusters of distinct shapes. However, the data under consideration are often experimental data, implying that the data…
Randomization, as a key technique in clinical trials, can eliminate sources of bias and produce comparable treatment groups. In randomized experiments, the treatment effect is a parameter of general interest. Researchers have explored the…
We consider the problem of predicting values of a random process or field satisfying a linear model $y(x)=\theta^\top f(x) + \varepsilon(x)$, where errors $\varepsilon(x)$ are correlated. This is a common problem in kriging, where the case…
Averaging provides an alternative to bandwidth selection for density kernel estimation. We propose a procedure to combine linearly several kernel estimators of a density obtained from different, possibly data-driven, bandwidths. The method…
The classic concept of "calibrated forecasts" and its more recent refinement, "calibeating," are defined with respect to the standard quadratic scoring rule. We extend these notions to the class of $\textit{proper}$ scoring rules (for which…
We study sets defined as the intersection of a rank-1 constraint with different choices of linear side constraints. We identify different conditions on the linear side constraints, under which the convex hull of the rank-1 set is polyhedral…
This paper introduces a novel decision-making framework that promotes consistency among decisions made by diverse models while utilizing external knowledge. Leveraging the Integer Linear Programming (ILP) framework, we map predictions from…
Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…
Kernel methods play a critical role in many machine learning algorithms. They are useful in manifold learning, classification, clustering and other data analysis tasks. Setting the kernel's scale parameter, also referred to as the kernel's…
Many theories have emerged which investigate how in- variance is generated in hierarchical networks through sim- ple schemes such as max and mean pooling. The restriction to max/mean pooling in theoretical and empirical studies has diverted…
In this paper, we will derive the first and 2nd order Wiener chaos decomposition for the multivariate linear statistics of the determinantal point processes associated with the spectral projection kernels on the unit spheres $S^d$. We will…
Pairwise learning or dyadic prediction concerns the prediction of properties for pairs of objects. It can be seen as an umbrella covering various machine learning problems such as matrix completion, collaborative filtering, multi-task…
AI weather prediction has advanced rapidly, yet no unified mathematical framework explains what determines forecast skill. Existing theory addresses specific architectural choices rather than the learning pipeline as a whole, while…
Spin asymmetries of semi-inclusive cross sections for the production of positively and negatively charged hadrons have been measured in deep-inelastic scattering of polarized positrons on polarized hydrogen and 3He targets, in the kinematic…
Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…
We develop scalable randomized kernel methods for jointly associating data from multiple sources and simultaneously predicting an outcome or classifying a unit into one of two or more classes. The proposed methods model nonlinear…
When multiple forecasts are available for a probability distribution, forecast combining enables a pragmatic synthesis of the information to extract the wisdom of the crowd. The linear opinion pool has been widely used, whereby the…
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…
Kernel-based modal statistical methods include mode estimation, regression, and clustering. Estimation accuracy of these methods depends on the kernel used as well as the bandwidth. We study effect of the selection of the kernel function to…