Online Tensor Methods for Learning Latent Variable Models

We introduce an online tensor decomposition based approach for two latent variable modeling problems namely, (1) community detection, in which we learn the latent communities that the social actors in social networks belong to, and (2) topic modeling, in which we infer hidden topics of text articles. We consider decomposition of moment tensors using stochastic gradient descent. We conduct optimization of multilinear operations in SGD and avoid directly forming the tensors, to save computational and storage costs. We present optimized algorithm in two platforms. Our GPU-based implementation exploits the parallelism of SIMD architectures to allow for maximum speed-up by a careful optimization of storage and data transfer, whereas our CPU-based implementation uses efficient sparse matrix computations and is suitable for large sparse datasets. For the community detection problem, we demonstrate accuracy and computational efficiency on Facebook, Yelp and DBLP datasets, and for the topic modeling problem, we also demonstrate good performance on the New York Times dataset. We compare our results to the state-of-the-art algorithms such as the variational method, and report a gain of accuracy and a gain of several orders of magnitude in the execution time.Comment: JMLR 201

Learning Reputation in an Authorship Network

The problem of searching for experts in a given academic field is hugely important in both industry and academia. We study exactly this issue with respect to a database of authors and their publications. The idea is to use Latent Semantic Indexing (LSI) and Latent Dirichlet Allocation (LDA) to perform topic modelling in order to find authors who have worked in a query field. We then construct a coauthorship graph and motivate the use of influence maximisation and a variety of graph centrality measures to obtain a ranked list of experts. The ranked lists are further improved using a Markov Chain-based rank aggregation approach. The complete method is readily scalable to large datasets. To demonstrate the efficacy of the approach we report on an extensive set of computational simulations using the Arnetminer dataset. An improvement in mean average precision is demonstrated over the baseline case of simply using the order of authors found by the topic models

Learning the Structure of Auto-Encoding Recommenders

Autoencoder recommenders have recently shown state-of-the-art performance in the recommendation task due to their ability to model non-linear item relationships effectively. However, existing autoencoder recommenders use fully-connected neural network layers and do not employ structure learning. This can lead to inefficient training, especially when the data is sparse as commonly found in collaborative filtering. The aforementioned results in lower generalization ability and reduced performance. In this paper, we introduce structure learning for autoencoder recommenders by taking advantage of the inherent item groups present in the collaborative filtering domain. Due to the nature of items in general, we know that certain items are more related to each other than to other items. Based on this, we propose a method that first learns groups of related items and then uses this information to determine the connectivity structure of an auto-encoding neural network. This results in a network that is sparsely connected. This sparse structure can be viewed as a prior that guides the network training. Empirically we demonstrate that the proposed structure learning enables the autoencoder to converge to a local optimum with a much smaller spectral norm and generalization error bound than the fully-connected network. The resultant sparse network considerably outperforms the state-of-the-art methods like \textsc{Mult-vae/Mult-dae} on multiple benchmarked datasets even when the same number of parameters and flops are used. It also has a better cold-start performance.Comment: Proceedings of The Web Conference 202

A multi-scale framework for graph based machine learning problems

Graph data have become essential in representing and modeling relationships between entities and complex network structures in various domains such as social networks and recommender systems. As a main contributor of the recent Big Data trend, the massive scale of graphs in modern machine learning problems easily overwhelms existing methods and thus sophisticated scalable algorithms are needed for real-world applications. In this thesis, we develop a novel multi-scale framework based on the divide-and-conquer principle as an effective and scalable approach for machine learning tasks involving large sparse graphs. We first demonstrate how our multi-scale framework can be applied to the problem of computing the spectral decomposition of massive graphs, which is one of the most fundamental low-rank matrix approximations used in numerous machine learning tasks. While popular solvers suffer from slow convergence, especially when the desired rank is large, our method exploits the clustering structure of the graph and achieves superior performance compared to existing algorithms in terms of both accuracy and scalability. While the main goal of the divide-and-conquer approach is to efficiently compute solutions for the original problem, the proposed multi-scale framework further admits an attractive but less obvious feature that machine learning problems can benefit from. Particularly, we consider partial solutions of the subproblems computed in the process as localized models of the entire problem. By doing so, we can combine models at multiple scales from local to global and generate a holistic view of the underlying problem to achieve better performance than a single global view. We adapt such multi-scale view for the problems of link prediction in social networks and collaborative filtering in recommender systems with additional side information to obtain a model that can make accurate and robust predictions in a scalable manner.Computer Science

Online Matrix Completion Through Nuclear Norm Regularisation

It is the main goal of this paper to propose a novel method to perform matrix completion on-line. Motivated by a wide variety of applications, ranging from the design of recommender systems to sensor network localization through seismic data reconstruction, we consider the matrix completion problem when entries of the matrix of interest are observed gradually. Precisely, we place ourselves in the situation where the predictive rule should be refined incrementally, rather than recomputed from scratch each time the sample of observed entries increases. The extension of existing matrix completion methods to the sequential prediction context is indeed a major issue in the Big Data era, and yet little addressed in the literature. The algorithm promoted in this article builds upon the Soft Impute approach introduced in Mazumder et al. (2010). The major novelty essentially arises from the use of a randomised technique for both computing and updating the Singular Value Decomposition (SVD) involved in the algorithm. Though of disarming simplicity, the method proposed turns out to be very efficient, while requiring reduced computations. Several numerical experiments based on real datasets illustrating its performance are displayed, together with preliminary results giving it a theoretical basis.Comment: Corrected a typo in the affiliatio