相关论文: Inference of a Dyadic Measure and its Simplicial G…

We present an improved method for symbolic regression that seeks to fit data to formulas that are Pareto-optimal, in the sense of having the best accuracy for a given complexity. It improves on the previous state-of-the-art by typically…

Many machine learning tools for regression are based on recursive partitioning of the covariate space into smaller regions, where the regression function can be estimated locally. Among these, regression trees and their ensembles have…

We propose a general statistical inference framework to capture the privacy threat incurred by a user that releases data to a passive but curious adversary, given utility constraints. We show that applying this general framework to the…

This paper relaxes the restrictive symmetry conditions adopted in [4], [5] and extends their universal feature selection framework to accommodate noisy observations as well as attribute structures that may exhibit directional preferences.…

Pixel-level feature attributions are an important tool in eXplainable AI for Computer Vision (XCV), providing visual insights into how image features influence model predictions. The Owen formula for hierarchical Shapley values has been…

Novelty detection methods aim at partitioning the test units into already observed and previously unseen patterns. However, two significant issues arise: there may be considerable interest in identifying specific structures within the…

Detecting symmetry from data is a fundamental problem in signal analysis, providing insight into underlying structure and constraints. When data emerge as trajectories of dynamical systems, symmetries encode structural properties of the…

Fine-grained anomaly detection has recently been dominated by segmentation based approaches. These approaches first classify each element of the sample (e.g., image patch) as normal or anomalous and then classify the entire sample as…

Constructing flexible probability models that respect constraints on key functionals -- such as the mean -- is a fundamental problem in nonparametric statistics. Existing approaches lack systematic tools for enforcing such constraints while…

Dimensionless numbers and scaling laws provide elegant insights into the characteristic properties of physical systems. Classical dimensional analysis and similitude theory fail to identify a set of unique dimensionless numbers for a…

Dyadic regression models are commonly analyzed under the conventional dyadic dependence paradigm, in which two observations may be dependent only if the corresponding dyads share a node. This paper studies inference when this paradigm…

Computing derivatives of noisy measurement data is ubiquitous in the physical, engineering, and biological sciences, and it is often a critical step in developing dynamic models or designing control. Unfortunately, the mathematical…

The advent of Scientific Machine Learning has heralded a transformative era in scientific discovery, driving progress across diverse domains. Central to this progress is uncovering scientific laws from experimental data through symbolic…

This paper presents a simple yet very effective data-driven approach to fuse both low-level and high-level local geometric features for 3D rigid data matching. It is a common practice to generate distinctive geometric descriptors by fusing…

We construct a "hyperparameter matrix" statistical method for performing the joint analyses of multiple correlated astronomical data sets, in which the weights of data sets are determined by their own statistical properties. This method is…

Differential privacy is the leading mathematical framework for privacy protection, providing a probabilistic guarantee that safeguards individuals' private information when publishing statistics from a dataset. This guarantee is achieved by…

Deep neural networks exhibit a simplicity bias, a well-documented tendency to favor simple functions over complex ones. In this work, we cast new light on this phenomenon through the lens of the Minimum Description Length principle,…

In this paper we introduce a biparametric family of transformations which can be seen as an extension of the so-called up and down transformations. This new class of transformations allows to us to introduce new informational functionals,…

Formal disclosure avoidance techniques are necessary to ensure that published data can not be used to identify information about individuals. The addition of statistical noise to unpublished data can be implemented to achieve differential…

Quantifying the similarity between mathematical expressions is a fundamental problem in computational mathematics, symbolic reasoning, and scientific discovery. While behavioral notions of similarity have previously been explored in the…