Finding optimal data for inpainting is a key problem in the context of partial differential equation-based image compression. We present a new model for optimising the data used for the reconstruction by the underlying homogeneous diffusion process. Our approach is based on an optimal control framework with a strictly convex cost functional containing an L1 term to enforce sparsity of the data ...

Deblending of simultaneous-source data is usually considered to be an underdetermined inverse problem, which can be solved by an iterative procedure, assuming additional constraints like sparsity and coherency. By exploiting the fact that seismic data are spatially band-limited, deblending of densely sampled sources can be carried out as a direct inversion process without imposing these constra...

Scripts representing common sense knowledge about stereotyped sequences of events have been shown to be a valuable resource for NLP applications. We present a hierarchical Bayesian model for unsupervised learning of script knowledge from crowdsourced descriptions of human activities. Events and constraints on event ordering are induced jointly in one unified framework. We use a statistical mode...

We consider dual coordinate ascent methods for minimizing a strictly convex (possibly nondifferentiable) function subject to linear constraints. Such methods are useful in large-scale applications (e.g., entropy maximization, quadratic programming, network flows), because they are simple, can exploit sparsity and in certain cases are highly parallelizable. We establish their global convergence ...

Segmentation of femurs in Anterior-Posterior x-ray images is very important for fracture detection, computer-aided surgery and surgical planning. Existing methods do not perform well in segmenting bones in x-ray images due to the presence of large amount of spurious edges. This paper presents an atlas-based approach for automatic segmentation of femurs in x-ray images. A robust global alignment...

We present posterior regularization, a probabilistic framework for structured, weakly supervised learning. Our framework efficiently incorporates indirect supervision via constraints on posterior distributions of probabilistic models with latent variables. Posterior regularization separates model complexity from the complexity of structural constraints it is desired to satisfy. By directly impo...

We propose an algorithm for the class of connected row convex constraints. In this algorithm, we introduce a novel variable elimination method to solve the constraints. This method is simple and able to make use of the sparsity of the problem instances. One of its key operations is the composition of two constraints. We have identified several nice properties of connected row convex constraints...

Recent work on Bayesian optimization has shown its effectiveness in global optimization of difficult black-box objective functions. Many real-world optimization problems of interest also have constraints which are unknown a priori. In this paper, we study Bayesian optimization for constrained problems in the general case that noise may be present in the constraint functions, and the objective a...

Single Index Models (SIMs) are simple yet flexible semiparametric models for machine learning, where the response variable is modeled as a monotonic function of a linear combination of features. Estimation in this context requires learning both the feature weights and the nonlinear function that relates features to observations. While methods have been described to learn SIMs in the low dimensi...