Related papers: Binary perceptron: efficient algorithms can find s…

Motivated by the fact that distances between data points in many real-world clustering instances are often based on heuristic measures, Bilu and Linial~\cite{BL} proposed analyzing objective based clustering problems under the assumption…

Biclustering has proved to be a powerful data analysis technique due to its wide success in various application domains. However, the existing literature presents efficient solutions only for enumerating maximal biclusters with constant…

We consider the symmetric binary perceptron model, a simple model of neural networks that has gathered significant attention in the statistical physics, information theory and probability theory communities, with recent connections made to…

In this paper, we consider sparse networks consisting of a finite number of non-overlapping communities, i.e. disjoint clusters, so that there is higher density within clusters than across clusters. Both the intra- and inter-cluster edge…

Limited precision of synaptic weights is a key aspect of both biological and hardware implementation of neural networks. To assign low-precise weights during learning is a non-trivial task, but may benefit from representing to-be-learned…

The detection of weak and rare effects in large amounts of data arises in a number of modern data analysis problems. Known results show that in this situation the potential of statistical inference is severely limited by the large-scale…

The problem of clustering noisy and incompletely observed high-dimensional data points into a union of low-dimensional subspaces and a set of outliers is considered. The number of subspaces, their dimensions, and their orientations are…

The problem of super-resolution is concerned with the reconstruction of temporally/spatially localized events (or spikes) from samples of their convolution with a low-pass filter. Distinct from prior works which exploit sparsity in…

We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the…

We give an efficient algorithm for robustly clustering of a mixture of two arbitrary Gaussians, a central open problem in the theory of computationally efficient robust estimation, assuming only that the the means of the component Gaussians…

We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel…

In the past few years powerful generalizations to the Euclidean k-means problem have been made, such as Bregman clustering [7], co-clustering (i.e., simultaneous clustering of rows and columns of an input matrix) [9,18], and tensor…

We consider the problem of grouping items into clusters based on few random pairwise comparisons between the items. We introduce three closely related algorithms for this task: a belief propagation algorithm approximating the Bayes optimal…

For a large number of random constraint satisfaction problems, such as random k-SAT and random graph and hypergraph coloring, there are very good estimates of the largest constraint density for which solutions exist. Yet, all known…

In the context of clustering, we consider a generative model in a Euclidean ambient space with clusters of different shapes, dimensions, sizes and densities. In an asymptotic setting where the number of points becomes large, we obtain…

The last decades have seen a surge of interests in distributed computing thanks to advances in clustered computing and big data technology. Existing distributed algorithms typically assume {\it all the data are already in one place}, and…

A novel nonparametric clustering algorithm is proposed using the interpoint distances between the members of the data to reveal the inherent clustering structure existing in the given set of data, where we apply the classical nonparametric…

Coresets are efficient representations of data sets such that models trained on the coreset are provably competitive with models trained on the original data set. As such, they have been successfully used to scale up clustering models such…

Binary perceptron is a fundamental model of supervised learning for the non-convex optimization, which is a root of the popular deep learning. Binary perceptron is able to achieve a classification of random high-dimensional data by…

We consider a multi-stage distributed detection scenario, where $n$ sensors and a fusion center (FC) are deployed to accomplish a binary hypothesis test. At each time stage, local sensors generate binary messages, assumed to be spatially…