相关论文: Generalized partitioned local depth

Robust estimation of location is a fundamental problem in statistics, particularly in scenarios where data contamination by outliers or model misspecification is a concern. In univariate settings, methods such as the sample median and…

Recent years have seen a surge of interest in the analysis of complex networks, facilitated by the availability of relational data and the increasingly powerful computational resources that can be employed for their analysis. Naturally, the…

Clustering is one of the most fundamental problems in data analysis and it has been studied extensively in the literature. Though many clustering algorithms have been proposed, clustering theories that justify the use of these clustering…

Clustering is a crucial task in various domains of knowledge, including medicine, epidemiology, genomics, environmental science, economics, and visual sciences, among others. Methodologies for inferring the number of clusters have often…

Despite its empirical success, deep learning still lacks a comprehensive theoretical understanding of model fitting and generalization. This paper proposes the probability distribution (PD) learning framework to analyze the optimization and…

This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…

In this paper we describe a machinery for homological calculations of representations of FI_G, and use it to develop a local cohomology theory over any commutative Noetherian ring. As an application, we show that the depth introduced by the…

The main goal of this paper is to provide a brief survey of recent results which connect together results from different areas of research. It is well known that numerical integration of functions with mixed smoothness is closely related to…

In Bayesian classification, it is important to establish a probabilistic model for each class for likelihood estimation. Most of the previous methods modeled the probability distribution in the whole sample space. However, real-world…

We study generalization in deep learning by appealing to complexity measures originally developed in approximation and information theory. While these concepts are challenged by the high-dimensional and data-defined nature of deep learning,…

The notion of local subgroupoids as generalition of a local equivalence relations was defined by the first author and R.Brown. Here we investigate some relations between transitive components and coherence properties of the local…

We present a flexible Bayesian semiparametric mixed model for longitudinal data analysis in the presence of potentially high-dimensional categorical covariates. Building on a novel hidden Markov tensor decomposition technique, our proposed…

We extend to Gaussian distributions a result providing smoothed analysis estimates for condition numbers given as relativized distances to illposedness. We also introduce a notion of local analysis meant to capture the behavior of these…

We develop a notion of projections between sets of probability measures using the geometric properties of the 2-Wasserstein space. It is designed for general multivariate probability measures, is computationally efficient to implement, and…

We propose a novel consensus notion, called "partial consensus", for distributed GM-PHD (Gaussian mixture probability hypothesis density) fusion based on a peer-to-peer (P2P) sensor network, in which only highly-weighted posterior Gaussian…

We show how complexity theory can be introduced in machine learning to help bring together apparently disparate areas of current research. We show that this new approach requires less training data and is more generalizable as it shows…

Community structure is largely regarded as an intrinsic property of complex real-world networks. However, recent studies reveal that networks comprise even more sophisticated modules than classical cohesive communities. More precisely,…

This work presents the concept of kernel mean embedding and kernel probabilistic programming in the context of stochastic systems. We propose formulations to represent, compare, and propagate uncertainties for fairly general stochastic…

This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…

We propose a new concept of generalized differentiation of set-valued maps that captures the first order information. This concept encompasses the standard notions of Frechet differentiability, strict differentiability, calmness and…