Related papers: Analytical and statistical properties of local dep…
Motivated by modern applications in which one constructs graphical models based on a very large number of features, this paper introduces a new class of cluster-based graphical models, in which variable clustering is applied as an initial…
Clustering is a commonplace problem in many areas of data science, with applications in biology and bioinformatics, understanding chemical structure, image segmentation, building recommender systems, and many more fields. While there are…
After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…
GROUSE (Grassmannian Rank-One Update Subspace Estimation) is an iterative algorithm for identifying a linear subspace of R^n from data consisting of partial observations of random vectors from that subspace. This paper examines local…
Clustering is a fundamental problem in statistics and machine learning. Lloyd's algorithm, proposed in 1957, is still possibly the most widely used clustering algorithm in practice due to its simplicity and empirical performance. However,…
When using stochastic gradient descent to solve large-scale machine learning problems, a common practice of data processing is to shuffle the training data, partition the data across multiple machines if needed, and then perform several…
We present new results for LambdaCC and MotifCC, two recently introduced variants of the well-studied correlation clustering problem. Both variants are motivated by applications to network analysis and community detection, and have…
We consider the optimization of a smooth and strongly convex objective using constant step-size stochastic gradient descent (SGD) and study its properties through the prism of Markov chains. We show that, for unbiased gradient estimates…
In this study, we focus on a generalized nonparametric scalar-on-function regression model for heterogeneously distributed and strongly mixing data. We provide almost complete convergence rates for the local linear estimator of the…
Stochastic gradient descent (SGD) with mini-batching is a standard tool in large-scale optimization, yet its theoretical properties under heavy-tailed gradient noise remain largely unexplored. In this paper we study SGD with increasing…
One of the most widely used techniques for data clustering is agglomerative clustering. Such algorithms have been long used across many different fields ranging from computational biology to social sciences to computer vision in part…
Popular clustering algorithms based on usual distance functions (e.g., Euclidean distance) often suffer in high dimension, low sample size (HDLSS) situations, where concentration of pairwise distances has adverse effects on their…
We propose a stochastic approximation (SA) based method with randomization of samples for policy evaluation using the least squares temporal difference (LSTD) algorithm. Our proposed scheme is equivalent to running regular temporal…
We propose a novel perspective on varied-density clustering for high-dimensional data by framing it as a label propagation process in neighborhood graphs that adapt to local density variations. Our method formally connects density-based…
Distributed Gaussian process (DGP) is a popular approach to scale GP to big data which divides the training data into some subsets, performs local inference for each partition, and aggregates the results to acquire global prediction. To…
Stochastic Gradient Langevin Dynamics (SGLD) is a sampling scheme for Bayesian modeling adapted to large datasets and models. SGLD relies on the injection of Gaussian Noise at each step of a Stochastic Gradient Descent (SGD) update. In this…
Instance-level alignment is widely exploited for person re-identification, e.g. spatial alignment, latent semantic alignment and triplet alignment. This paper probes another feature alignment modality, namely cluster-level feature alignment…
In distributed training of machine learning models, gradient descent with local iterative steps, commonly known as Local (Stochastic) Gradient Descent (Local-(S)GD) or Federated averaging (FedAvg), is a very popular method to mitigate…
The main aim of this paper is to provide an analysis of gradient descent (GD) algorithms with gradient errors that do not necessarily vanish, asymptotically. In particular, sufficient conditions are presented for both stability (almost sure…
Stochastic gradient Langevin dynamics (SGLD) has gained the attention of optimization researchers due to its global optimization properties. This paper proves an improved convergence property to local minimizers of nonconvex objective…