Structure estimation for discrete graphical models: Generalized covariance matrices and their inverses

We investigate the relationship between the structure of a discrete graphical model and the support of the inverse of a generalized covariance matrix. We show that for certain graph structures, the support of the inverse covariance matrix of indicator variables on the vertices of a graph reflects the conditional independence structure of the graph. Our work extends results that have previously been established only in the context of multivariate Gaussian graphical models, thereby addressing an open question about the significance of the inverse covariance matrix of a non-Gaussian distribution. The proof exploits a combination of ideas from the geometry of exponential families, junction tree theory and convex analysis. These population-level results have various consequences for graph selection methods, both known and novel, including a novel method for structure estimation for missing or corrupted observations. We provide nonasymptotic guarantees for such methods and illustrate the sharpness of these predictions via simulations.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1162 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Learning Structured Inference Neural Networks with Label Relations

Images of scenes have various objects as well as abundant attributes, and diverse levels of visual categorization are possible. A natural image could be assigned with fine-grained labels that describe major components, coarse-grained labels that depict high level abstraction or a set of labels that reveal attributes. Such categorization at different concept layers can be modeled with label graphs encoding label information. In this paper, we exploit this rich information with a state-of-art deep learning framework, and propose a generic structured model that leverages diverse label relations to improve image classification performance. Our approach employs a novel stacked label prediction neural network, capturing both inter-level and intra-level label semantics. We evaluate our method on benchmark image datasets, and empirical results illustrate the efficacy of our model.Comment: Conference on Computer Vision and Pattern Recognition(CVPR) 201

Learning to Infer Graphics Programs from Hand-Drawn Images

We introduce a model that learns to convert simple hand drawings into graphics programs written in a subset of \LaTeX. The model combines techniques from deep learning and program synthesis. We learn a convolutional neural network that proposes plausible drawing primitives that explain an image. These drawing primitives are like a trace of the set of primitive commands issued by a graphics program. We learn a model that uses program synthesis techniques to recover a graphics program from that trace. These programs have constructs like variable bindings, iterative loops, or simple kinds of conditionals. With a graphics program in hand, we can correct errors made by the deep network, measure similarity between drawings by use of similar high-level geometric structures, and extrapolate drawings. Taken together these results are a step towards agents that induce useful, human-readable programs from perceptual input