Nikhil Rao

Goal-Directed Inductive Matrix Completion

Matrix completion (MC) with additional information has found wide applicability in several machine learning applications. Among algorithms for solving such problems, Inductive Matrix Completion(IMC) has drawn a considerable amount of attention, not only for its well established theoretical guarantees but also for its superior performance in various real-world applications. However, IMC based methods usually place very strong constraints on the quality of the features(side information) to ensure accurate recovery, which might not be met in practice. In this paper, we propose Goal-directed Inductive Matrix Completion(GIMC) to learn a nonlinear mapping of the features so that they satisfy the required properties. A key distinction between GIMC and IMC is that the feature mapping is learnt in a supervised manner, deviating from the traditional approach of unsupervised feature learning followed by model training. We establish the superiority of our method on several popular machine learning applications including multi-label learning, multi-class classification, and semi-supervised clustering.

Forward — Backward greedy algorithms for signal demixing

Signal demixing arises in many applications. Common among these are the separation of sparse and low rank components in image and video processing, sparse and group sparse models in multitask learning and spikes and sinusoids in source separation problems. For specific problems of interest, many methods exist to perform recovery, but an approach that generalizes to arbitrary notions of simplicity has not been forthcoming. We propose a framework for signal demixing when the components are defined to be simple in a fairly arbitrary manner. Our method remains computationally simple and can be used in a variety of practical applications.

PU matrix completion with graph information

Motivated by applications in recommendation systems and bioinformatics, we consider the problem of completing a low rank, partially observed binary matrix with graph information. We show that the corresponding problem can be set up in a positive and unlabeled data learning (referred to as PU learning in literature) framework. We make connections to convex optimization and show that existing greedy methods can be used to solve the problem. Experiments on simulated data as well as gene-disease associations data from bioinformatics show that using graphs, and adapting matrix completion in the PU learning setting, yield advantages over the standard binary matrix completion.