相关论文: Pair Correlation Factor and the Sample Complexity …

The predictions of the geometric collective model (GCM) for different sets of Hamiltonian parameter values are related by analytic scaling relations. For the quartic truncated form of the GCM -- which describes harmonic oscillator, rotor,…

We consider the problem of clustering with $K$-means and Gaussian mixture models with a constraint on the separation between the centers in the context of real-valued data. We first propose a dynamic programming approach to solving the…

This article presents an approach to Bayesian semiparametric inference for Gaussian multivariate response regression. We are motivated by various small and medium dimensional problems from the physical and social sciences. The statistical…

There has been substantial interest in estimating the value of a graph parameter, i.e., of a real-valued function defined on the set of finite graphs, by querying a randomly sampled substructure whose size is independent of the size of the…

The question of polynomial learnability of probability distributions, particularly Gaussian mixture distributions, has recently received significant attention in theoretical computer science and machine learning. However, despite major…

We study the problem of learning nonparametric distributions in a finite mixture, and establish tight bounds on the sample complexity for learning the component distributions in such models. Namely, we are given i.i.d. samples from a pdf…

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…

The Gaussian mixture model is widely used in unsupervised learning, owing to its simplicity and interpretability. However, a fundamental limitation of the classical Gaussian mixture model is that it forces each observation to belong to…

We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…

Deriving from the gradient vector of a generative model of local features, Fisher vector coding (FVC) has been identified as an effective coding method for image classification. Most, if not all, FVC implementations employ the Gaussian…

We discuss a clustering method for Gaussian mixture model based on the sparse principal component analysis (SPCA) method and compare it with the IF-PCA method. We also discuss the dependent case where the covariance matrix $\Sigma$ is not…

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…

We consider the problem of estimating the factors of a low-rank $n \times d$ matrix, when this is corrupted by additive Gaussian noise. A special example of our setting corresponds to clustering mixtures of Gaussians with equal (known)…

Coagulation and fragmentation (CF) is a fundamental process by which particles attach to each other to form clusters while existing clusters break up into smaller ones. It is a ubiquitous process that plays a key role in many physical and…

Modeling complex physical systems such as they arise in civil engineering applications requires finding a trade-off between physical fidelity and practicality. Consequently, deviations of simulation from measurements are ubiquitous even…

Graphical models are ubiquitous tools to describe the interdependence between variables measured simultaneously such as large-scale gene or protein expression data. Gaussian graphical models (GGMs) are well-established tools for…

Density modeling is notoriously difficult for high dimensional data. One approach to the problem is to search for a lower dimensional manifold which captures the main characteristics of the data. Recently, the Gaussian Process Latent…

We generalize the popular ensemble Kalman filter to an ensemble transform filter where the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous…

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…

Quantifying the complexity of systems consisting of many interacting parts has been an important challenge in the field of complex systems in both abstract and applied contexts. One approach, the complexity profile, is a measure of the…