Related papers: Likelihood Adjusted Semidefinite Programs for Clus…
We consider the problem of estimating the discrete clustering structures under the Sub-Gaussian Mixture Model. Our main results establish a hidden integrality property of a semidefinite programming (SDP) relaxation for this problem: while…
We consider semidefinite programming (SDP) for the binary stochastic block model with equal-sized communities. Prior work of Hajek, Wu, and Xu proposed an SDP (sym-SDP) for the symmetric case where the intra-community edge probabilities are…
Linear Predictive Clustering (LPC) partitions samples based on shared linear relationships between feature and target variables, with numerous applications including marketing, medicine, and education. Greedy optimization methods, commonly…
We study the statistical performance of semidefinite programming (SDP) relaxations for clustering under random graph models. Under the $\mathbb{Z}_{2}$ Synchronization model, Censored Block Model and Stochastic Block Model, we show that SDP…
We give the first approximation algorithm for mixed packing and covering semidefinite programs (SDPs) with polylogarithmic dependence on width. Mixed packing and covering SDPs constitute a fundamental algorithmic primitive with recent…
Any clustering algorithm must synchronously learn to model the clusters and allocate data to those clusters in the absence of labels. Mixture model-based methods model clusters with pre-defined statistical distributions and allocate data to…
The problem of community detection with two equal-sized communities is closely related to the minimum graph bisection problem over certain random graph models. In the stochastic block model distribution over networks with community…
In this paper, different strands of literature are combined in order to obtain algorithms for semi-parametric estimation of discrete choice models that include the modelling of unobserved heterogeneity by using mixing distributions for the…
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
Many statistical learning problems have recently been shown to be amenable to Semi-Definite Programming (SDP), with community detection and clustering in Gaussian mixture models as the most striking instances [javanmard et al., 2016]. Given…
Constrained approaches to maximum likelihood estimation in the context of finite mixtures of normals have been presented in the literature. A fully data-dependent constrained method for maximum likelihood estimation of clusterwise linear…
The goal of clustering is to group similar objects into meaningful partitions. This process is well understood when an explicit similarity measure between the objects is given. However, far less is known when this information is not readily…
We propose a semidefinite programming (SDP) algorithm for community detection in the stochastic block model, a popular model for networks with latent community structure. We prove that our algorithm achieves exact recovery of the latent…
We study two practically important cases of model based clustering using Gaussian Mixture Models: (1) when there is misspecification and (2) on high dimensional data, in the light of recent advances in Gradient Descent (GD) based…
In a mixture of linear regression model, the regression coefficients are treated as random vectors that may follow either a continuous or discrete distribution. We propose two Expectation-Maximization (EM) algorithms to estimate this prior…
Finite mixture modelling is a popular method in the field of clustering and is beneficial largely due to its soft cluster membership probabilities. A common method for fitting finite mixture models is to employ spectral clustering, which…
In this paper, we propose an efficient semidefinite programming (SDP) approach to worst-case linear discriminant analysis (WLDA). Compared with the traditional LDA, WLDA considers the dimensionality reduction problem from the worst-case…
Mixture models are a popular tool in model-based clustering. Such a model is often fitted by a procedure that maximizes the likelihood, such as the EM algorithm. At convergence, the maximum likelihood parameter estimates are typically…
The Expectation Maximization (EM) algorithm is widely used as an iterative modification to maximum likelihood estimation when the data is incomplete. We focus on a semi-supervised case to learn the model from labeled and unlabeled samples.…
We are concerned in clustering continuous data sets subject to non-ignorable missingness. We perform clustering with a specific semi-parametric mixture, under the assumption of conditional independence given the component. The mixture model…