Multi-Entity Dependence Learning with Rich Context via Conditional Variational Auto-encoder

Multi-Entity Dependence Learning (MEDL) explores conditional correlations among multiple entities. The availability of rich contextual information requires a nimble learning scheme that tightly integrates with deep neural networks and has the ability to capture correlation structures among exponentially many outcomes. We propose MEDL_CVAE, which encodes a conditional multivariate distribution as a generating process. As a result, the variational lower bound of the joint likelihood can be optimized via a conditional variational auto-encoder and trained end-to-end on GPUs. Our MEDL_CVAE was motivated by two real-world applications in computational sustainability: one studies the spatial correlation among multiple bird species using the eBird data and the other models multi-dimensional landscape composition and human footprint in the Amazon rainforest with satellite images. We show that MEDL_CVAE captures rich dependency structures, scales better than previous methods, and further improves on the joint likelihood taking advantage of very large datasets that are beyond the capacity of previous methods.Comment: The first two authors contribute equall

Statistical clustering of temporal networks through a dynamic stochastic block model

Statistical node clustering in discrete time dynamic networks is an emerging field that raises many challenges. Here, we explore statistical properties and frequentist inference in a model that combines a stochastic block model (SBM) for its static part with independent Markov chains for the evolution of the nodes groups through time. We model binary data as well as weighted dynamic random graphs (with discrete or continuous edges values). Our approach, motivated by the importance of controlling for label switching issues across the different time steps, focuses on detecting groups characterized by a stable within group connectivity behavior. We study identifiability of the model parameters, propose an inference procedure based on a variational expectation maximization algorithm as well as a model selection criterion to select for the number of groups. We carefully discuss our initialization strategy which plays an important role in the method and compare our procedure with existing ones on synthetic datasets. We also illustrate our approach on dynamic contact networks, one of encounters among high school students and two others on animal interactions. An implementation of the method is available as a R package called dynsbm

Sample Complexity Analysis for Learning Overcomplete Latent Variable Models through Tensor Methods

We provide guarantees for learning latent variable models emphasizing on the overcomplete regime, where the dimensionality of the latent space can exceed the observed dimensionality. In particular, we consider multiview mixtures, spherical Gaussian mixtures, ICA, and sparse coding models. We provide tight concentration bounds for empirical moments through novel covering arguments. We analyze parameter recovery through a simple tensor power update algorithm. In the semi-supervised setting, we exploit the label or prior information to get a rough estimate of the model parameters, and then refine it using the tensor method on unlabeled samples. We establish that learning is possible when the number of components scales as $k=o(d^{p/2})$, where $d$ is the observed dimension, and $p$ is the order of the observed moment employed in the tensor method. Our concentration bound analysis also leads to minimax sample complexity for semi-supervised learning of spherical Gaussian mixtures. In the unsupervised setting, we use a simple initialization algorithm based on SVD of the tensor slices, and provide guarantees under the stricter condition that $k\le \beta d$ (where constant $\beta$ can be larger than $1$), where the tensor method recovers the components under a polynomial running time (and exponential in $\beta$). Our analysis establishes that a wide range of overcomplete latent variable models can be learned efficiently with low computational and sample complexity through tensor decomposition methods.Comment: Title change