Related papers: MAP Clustering under the Gaussian Mixture Model vi…

In this paper, we mainly study one class of convex mixed-integer nonlinear programming problems (MINLPs) with non-differentiable data. By dropping the differentiability assumption, we substitute gradients with subgradients obtained from KKT…

In this paper we provide a computation algorithm to get a global solution for the maximum rank correlation estimator using the mixed integer programming (MIP) approach. We construct a new constrained optimization problem by transforming all…

In mixture models, anisotropic noise within each cluster is widely present in real-world data. This work investigates both computationally efficient procedures and fundamental statistical limits for clustering in high-dimensional…

This paper introduces a novel algorithm for Mixed-Integer Nonlinear Programming (MINLP) problems with multilinear interpolations of look-up tables. These problems arise when objective or constraints contain black-box functions only known at…

This paper addresses the single-item single-stocking location stochastic lot sizing problem under the $(s, S) $ policy. We first present a mixed integer non-linear programming (MINLP) formulation for determining near-optimal $(s, S)$ policy…

We investigate the problem of recovering a partially observed high-rank matrix whose columns obey a nonlinear structure such as a union of subspaces, an algebraic variety or grouped in clusters. The recovery problem is formulated as the…

Mixture Markov Model (MMM) is a widely used tool to cluster sequences of events coming from a finite state-space. However the MMM likelihood being multi-modal, the challenge remains in its maximization. Although Expectation-Maximization…

Clusters of galaxies, being the largest collapsed structures in the universe, offer valuable insights into the nature of cosmic evolution. Precise calibration of the mass of clusters can be obtained by extracting their gravitational lensing…

We propose a mixed integer programming (MIP) model and iterative algorithms based on topological orders to solve optimization problems with acyclic constraints on a directed graph. The proposed MIP model has a significantly lower number of…

Mixed integer nonlinear programming (MINLP) problems are encountered in modeling a physical/industrial process consisting both nonlinearity and discrete selective parameters. There are variety of algorithms for solving MINLP problems most…

This paper proposes a joint decomposition method that combines La- grangian decomposition and generalized Benders decomposition, to efficiently solve multiscenario nonconvex mixed-integer nonlinear programming (MINLP) problems to global…

We describe a new optimization scheme for finding high-quality correlation clusterings in planar graphs that uses weighted perfect matching as a subroutine. Our method provides lower-bounds on the energy of the optimal correlation…

In the framework of Bayesian model-based clustering based on a finite mixture of Gaussian distributions, we present a joint approach to estimate the number of mixture components and identify cluster-relevant variables simultaneously as well…

Arising from many applications at the intersection of decision making and machine learning, Marginal Maximum A Posteriori (Marginal MAP) Problems unify the two main classes of inference, namely maximization (optimization) and marginal…

The Dirichlet process mixture (DPM) is a ubiquitous, flexible Bayesian nonparametric statistical model. However, full probabilistic inference in this model is analytically intractable, so that computationally intensive techniques such as…

Discrete black-box optimization problems are challenging for model-based optimization (MBO) algorithms, such as Bayesian optimization, due to the size of the search space and the need to satisfy combinatorial constraints. In particular,…

Non-Gaussian mixture models are gaining increasing attention for mixture model-based clustering particularly when dealing with data that exhibit features such as skewness and heavy tails. Here, such a mixture distribution is presented,…

We investigate the geometry of the maximal a posteriori (MAP) partition in the Bayesian Mixture Model where the component and the base distributions are chosen from conjugate exponential families. We prove that in this case the clusters are…

This paper considers the generalized maximal covering location problem (GMCLP) which establishes a fixed number of facilities to maximize the weighted sum of the covered customers, allowing customer weights to be positive or negative. Due…

Cluster analysis faces two problems in high dimensions: first, the `curse of dimensionality' that can lead to overfitting and poor generalization performance; and second, the sheer time taken for conventional algorithms to process large…