Related papers: Analytical and statistical properties of local dep…

Normalizing flows model a complex target distribution in terms of a bijective transform operating on a simple base distribution. As such, they enable tractable computation of a number of important statistical quantities, particularly…

This paper investigates the computational and statistical limits in clustering matrix-valued observations. We propose a low-rank mixture model (LrMM), adapted from the classical Gaussian mixture model (GMM) to treat matrix-valued…

The most widely used internal measure for clustering evaluation is the silhouette coefficient, whose naive computation requires a quadratic number of distance calculations, which is clearly unfeasible for massive datasets. Surprisingly,…

In this paper a relative number density parameter, called the neighborhood function, is introduced so that the crowded nature of the neighborhood of individual sources can be described. With this parameter one can determine the probability…

There is significant recent interest to parallelize deep learning algorithms in order to handle the enormous growth in data and model sizes. While most advances focus on model parallelization and engaging multiple computing agents via using…

Local differential privacy (LDP) can provide each user with strong privacy guarantees under untrusted data curators while ensuring accurate statistics derived from privatized data. Due to its powerfulness, LDP has been widely adopted to…

Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. This paper introduces a…

The process of aggregation is ubiquitous in almost all deep nets models. It functions as an important mechanism for consolidating deep features into a more compact representation, whilst increasing robustness to overfitting and providing…

In this paper, we propose a new numerical method for the underdamped Langevin diffusion (ULD) and present a non-asymptotic analysis of its sampling error in the 2-Wasserstein distance when the $d$-dimensional target distribution…

Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…

Stochastic gradient descent (SGD) performed in an asynchronous manner plays a crucial role in training large-scale machine learning models. However, the generalization performance of asynchronous delayed SGD, which is an essential metric…

Graph clustering, which aims to divide a graph into several homogeneous groups, is a critical area of study with applications that span various fields such as social network analysis, bioinformatics, and image segmentation. This paper…

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…

In this paper, we propose a new covering technique localized for the trajectories of SGD. This localization provides an algorithm-specific complexity measured by the covering number, which can have dimension-independent cardinality in…

Diffusions and related random walk procedures are of central importance in many areas of machine learning, data analysis, and applied mathematics. Because they spread mass agnostically at each step in an iterative manner, they can sometimes…

We derive an efficient method to perform clustering of nodes in Gaussian graphical models directly from sample data. Nodes are clustered based on the similarity of their network neighborhoods, with edge weights defined by partial…

One of the most common methods to train machine learning algorithms today is the stochastic gradient descent (SGD). In a distributed setting, SGD-based algorithms have been shown to converge theoretically under specific circumstances. A…

Spectral clustering is widely used in practice due to its flexibility, computational efficiency, and well-understood theoretical performance guarantees. Recently, spectral clustering has been studied to find balanced clusters under…

Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…

Local graph clustering is an important machine learning task that aims to find a well-connected cluster near a set of seed nodes. Recent results have revealed that incorporating higher order information significantly enhances the results of…