Proximal Methods for Hierarchical Sparse Coding

Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved using a recently introduced tree-structured sparse regularization norm, which has proven useful in several applications. This norm leads to regularized problems that are difficult to optimize, and we propose in this paper efficient algorithms for solving them. More precisely, we show that the proximal operator associated with this norm is computable exactly via a dual approach that can be viewed as the composition of elementary proximal operators. Our procedure has a complexity linear, or close to linear, in the number of atoms, and allows the use of accelerated gradient techniques to solve the tree-structured sparse approximation problem at the same computational cost as traditional ones using the L1-norm. Our method is efficient and scales gracefully to millions of variables, which we illustrate in two types of applications: first, we consider fixed hierarchical dictionaries of wavelets to denoise natural images. Then, we apply our optimization tools in the context of dictionary learning, where learned dictionary elements naturally organize in a prespecified arborescent structure, leading to a better performance in reconstruction of natural image patches. When applied to text documents, our method learns hierarchies of topics, thus providing a competitive alternative to probabilistic topic models

Abstract Meaning Representation for Multi-Document Summarization

Generating an abstract from a collection of documents is a desirable capability for many real-world applications. However, abstractive approaches to multi-document summarization have not been thoroughly investigated. This paper studies the feasibility of using Abstract Meaning Representation (AMR), a semantic representation of natural language grounded in linguistic theory, as a form of content representation. Our approach condenses source documents to a set of summary graphs following the AMR formalism. The summary graphs are then transformed to a set of summary sentences in a surface realization step. The framework is fully data-driven and flexible. Each component can be optimized independently using small-scale, in-domain training data. We perform experiments on benchmark summarization datasets and report promising results. We also describe opportunities and challenges for advancing this line of research.Comment: 13 page