Related papers: Subspace clustering in high-dimensions: Phase tran…

We consider tensor factorizations using a generative model and a Bayesian approach. We compute rigorously the mutual information, the Minimal Mean Squared Error (MMSE), and unveil information-theoretic phase transitions. In addition, we…

Sparse structure learning in high-dimensional Gaussian graphical models is an important problem in multivariate statistical signal processing; since the sparsity pattern naturally encodes the conditional independence relationship among…

We study estimation and clustering in Gaussian mixture models under variance misspecification. Observations are generated with true variance $\sigma^2$, while the component means are estimated using a likelihood with variance $\tau^2$,…

To model modern large-scale datasets, we need efficient algorithms to infer a set of $P$ unknown model parameters from $N$ noisy measurements. What are fundamental limits on the accuracy of parameter inference, given finite signal-to-noise…

State-of-the-art algorithms for sparse subspace clustering perform spectral clustering on a similarity matrix typically obtained by representing each data point as a sparse combination of other points using either basis pursuit (BP) or…

Iterative thresholding algorithms are well-suited for high-dimensional problems in sparse recovery and compressive sensing. The performance of this class of algorithms depends heavily on the tuning of certain threshold parameters. In…

Subspace clustering refers to the problem of clustering unlabeled high-dimensional data points into a union of low-dimensional linear subspaces, assumed unknown. In practice one may have access to dimensionality-reduced observations of the…

Sparse subspace clustering (SSC) is one of the current state-of-the-art methods for partitioning data points into the union of subspaces, with strong theoretical guarantees. However, it is not practical for large data sets as it requires…

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…

Heuristic tools from statistical physics have been used in the past to locate the phase transitions and compute the optimal learning and generalization errors in the teacher-student scenario in multi-layer neural networks. In this…

High-dimensional time series appear in many scientific setups, demanding a nuanced approach to model and analyze the underlying dependence structure. Theoretical advancements so far often rely on stringent assumptions regarding the sparsity…

In a recent paper, the authors proposed a new class of low-complexity iterative thresholding algorithms for reconstructing sparse signals from a small set of linear measurements \cite{DMM}. The new algorithms are broadly referred to as AMP,…

Recently, Approximate Message Passing (AMP) has been integrated with stochastic localization (diffusion model) by providing a computationally efficient estimator of the posterior mean. Existing (rigorous) analysis typically proves the…

Algebraic Subspace Clustering (ASC) is a simple and elegant method based on polynomial fitting and differentiation for clustering noiseless data drawn from an arbitrary union of subspaces. In practice, however, ASC is limited to…

We investigate a clustering problem with data from a mixture of Gaussians that share a common but unknown, and potentially ill-conditioned, covariance matrix. We start by considering Gaussian mixtures with two equally-sized components and…

As the data size in Machine Learning fields grows exponentially, it is inevitable to accelerate the computation by utilizing the ever-growing large number of available cores provided by high-performance computing hardware. However, existing…

Subspace clustering is the unsupervised grouping of points lying near a union of low-dimensional linear subspaces. Algorithms based directly on geometric properties of such data tend to either provide poor empirical performance, lack…

Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…

Compressed sensing posits that, within limits, one can undersample a sparse signal and yet reconstruct it accurately. Knowing the precise limits to such undersampling is important both for theory and practice. We present a formula that…

Subspace clustering is the problem of clustering data that lie close to a union of linear subspaces. In the abstract form of the problem, where no noise or other corruptions are present, the data are assumed to lie in general position…