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We develop Clustered Random Forests, a random forests algorithm for clustered data, arising from independent groups that exhibit within-cluster dependence. The leaf-wise predictions for each decision tree making up clustered random forests…

Subspace segmentation assumes that data comes from the union of different subspaces and the purpose of segmentation is to partition the data into the corresponding subspace. Low-rank representation (LRR) is a classic spectral-type method…

We study the problem of clustering nodes in a dynamic graph, where the connections between nodes and nodes' cluster memberships may change over time, e.g., due to community migration. We first propose a dynamic stochastic block model that…

We develop and analyze a procedure for gradient-based optimization that we refer to as stochastically controlled stochastic gradient (SCSG). As a member of the SVRG family of algorithms, SCSG makes use of gradient estimates at two scales,…

Structural equation modeling (SEM) is a popular tool in the social and behavioural sciences, where it is being applied to ever more complex data types. The high-dimensional data produced by modern sensors, brain images, or (epi)genetic…

The cluster expansion model (CEM) provides a powerful computational framework for rapid estimation of configurational properties in disordered systems. However, the traditional CEM construction procedure is still plagued by two fundamental…

The latent block model is used to simultaneously rank the rows and columns of a matrix to reveal a block structure. The algorithms used for estimation are often time consuming. However, recent work shows that the log-likelihood ratios are…

We consider the problem of training machine learning models on distributed data in a decentralized way. For finite-sum problems, fast single-machine algorithms for large datasets rely on stochastic updates combined with variance reduction.…

This paper extends the blurring mean shift algorithm from vector-valued data to functional data, enabling effective clustering in infinite-dimensional settings without requiring specification of the number of clusters. To address the…

Graph clustering has many important applications in computing, but due to the increasing sizes of graphs, even traditionally fast clustering methods can be computationally expensive for real-world graphs of interest. Scalability problems…

As the size of modern data sets exceeds the disk and memory capacities of a single computer, machine learning practitioners have resorted to parallel and distributed computing. Given that optimization is one of the pillars of machine…

Cluster analysis plays an important role in decision making process for many knowledge-based systems. There exist a wide variety of different approaches for clustering applications including the heuristic techniques, probabilistic models,…

A model involving Gaussian processes (GPs) is introduced to simultaneously handle multi-task learning, clustering, and prediction for multiple functional data. This procedure acts as a model-based clustering method for functional data as…

Sparse matrix-matrix multiplication (SpGEMM) is a critical operation in numerous fields, including scientific computing, graph analytics, and deep learning. These applications exploit the sparsity of matrices to reduce storage and…

We derive bounds on the sample complexity of empirical risk minimization (ERM) in the context of minimizing non-convex risks that admit the strict saddle property. Recent progress in non-convex optimization has yielded efficient algorithms…

Hierarchical clustering is a fundamental task often used to discover meaningful structures in data, such as phylogenetic trees, taxonomies of concepts, subtypes of cancer, and cascades of particle decays in particle physics. Typically…

Although many successful ensemble clustering approaches have been developed in recent years, there are still two limitations to most of the existing approaches. First, they mostly overlook the issue of uncertain links, which may mislead the…

With the recent popularity of graphical clustering methods, there has been an increased focus on the information between samples. We show how learning cluster structure using edge features naturally and simultaneously determines the most…

We consider the problem of clustering data points in high dimensions, i.e. when the number of data points may be much smaller than the number of dimensions. Specifically, we consider a Gaussian mixture model (GMM) with non-spherical…

Clustering analysis identifies samples as groups based on either their mutual closeness or homogeneity. In order to detect clusters in arbitrary shapes, a novel and generic solution based on boundary erosion is proposed. The clusters are…