Related papers: Learning High-Dimensional Mixtures of Graphical Mo…
Recent research has established sufficient conditions for finite mixture models to be identifiable from grouped observations. These conditions allow the mixture components to be nonparametric and have substantial (or even total) overlap.…
Feature learning in the presence of a mixed type of variables, numerical and categorical types, is an important issue for related modeling problems. For simple neighborhood queries under mixed data space, standard practice is to consider…
Given a finite admixture model whose components and weights are unknown, let the number of identifiable components be a function of the amount of data sampled from a known distribution on the unit simplex. We use techniques from stochastic…
In this work, we propose a global model selection criterion to estimate the graph of conditional dependencies of a random vector based on a finite sample. By global criterion, we mean optimizing a function over the entire set of possible…
In this paper we propose a new method to learn the underlying acyclic mixed graph of a linear non-Gaussian structural equation model given observational data. We build on an algorithm proposed by Wang and Drton, and we show that one can…
We present an improved coupling technique for analyzing the mixing time of Markov chains. Using our technique, we simplify and extend previous results for sampling colorings and independent sets. Our approach uses properties of the…
Graph learning methods have recently been receiving increasing interest as means to infer structure in datasets. Most of the recent approaches focus on different relationships between a graph and data sample distributions, mostly in…
One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent…
Real-world optimization problems are generally not just black-box problems, but also involve mixed types of inputs in which discrete and continuous variables coexist. Such mixed-space optimization possesses the primary challenge of modeling…
Generation of graphs is a major challenge for real-world tasks that require understanding the complex nature of their non-Euclidean structures. Although diffusion models have achieved notable success in graph generation recently, they are…
Undirected graphical models are a key component in the analysis of complex observational data in a large variety of disciplines. In many of these applications one is interested in estimating the undirected graphical model underlying a…
Given a graph $G$, the hard-core model defines a probability distribution over its independent sets, assigning to each set of size $k$ a probability of $\frac{\lambda^k}{Z}$, where $\lambda>0$ is a parameter known as the \emph{fugacity} and…
Existing popular methods for semi-supervised learning with Graph Neural Networks (such as the Graph Convolutional Network) provably cannot learn a general class of neighborhood mixing relationships. To address this weakness, we propose a…
Numerous models for supervised and reinforcement learning benefit from combinations of discrete and continuous model components. End-to-end learnable discrete-continuous models are compositional, tend to generalize better, and are more…
This paper presents a nonlinear mixing model for joint hyperspectral image unmixing and nonlinearity detection. The proposed model assumes that the pixel reflectances are linear combinations of known pure spectral components corrupted by an…
Jointly identifying a mixture of discrete and continuous factors of variability without supervision is a key problem in unraveling complex phenomena. Variational inference has emerged as a promising method to learn interpretable mixture…
There has been a growing interest in statistical inference from data satisfying the so-called manifold hypothesis, assuming data points in the high-dimensional ambient space to lie in close vicinity of a submanifold of much lower dimension.…
Recently developed techniques have made it possible to quickly learn accurate probability density functions from data in low-dimensional continuous space. In particular, mixtures of Gaussians can be fitted to data very quickly using an…
Structure learning of Gaussian graphical models is an extensively studied problem in the classical multivariate setting where the sample size n is larger than the number of random variables p, as well as in the more challenging setting when…
We study the problem of learning a directed acyclic graph from data generated according to an additive, non-linear structural equation model with Gaussian noise. We express each non-linear function through a basis expansion, and derive a…