Related papers: Matrix Completion via Factorizing Polynomials

Matrix completion aims to predict missing elements in a partially observed data matrix which in typical applications, such as collaborative filtering, is large and extremely sparsely observed. A standard solution is matrix factorization,…

Machine learning on graphs is an important and ubiquitous task with applications ranging from drug design to friendship recommendation in social networks. The primary challenge in this domain is finding a way to represent, or encode, graph…

Optimization of machine learning models is commonly performed through stochastic gradient updates on randomly ordered training examples. This practice means that sub-epochs comprise of independent random samples of the training data that…

Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample…

We are interested in building collaborative filtering models for recommendation systems where users interact with slates instead of individual items. These slates can be hierarchical in nature. The central idea of our approach is to learn…

This paper addresses the large-scale acquisition of end-to-end network performance. We made two distinct contributions: ordinal rating of network performance and inference by matrix completion. The former reduces measurement costs and…

Recommender system has been more and more popular and widely used in many applications recently. The increasing information available, not only in quantities but also in types, leads to a big challenge for recommender system that how to…

Fill-ins are new nonzero elements in the summation of the upper and lower triangular factors generated during LU factorization. For large sparse matrices, they will increase the memory usage and computational time, and be reduced through…

One of the prime problems of computer science and machine learning is to extract information efficiently from large-scale, heterogeneous data. Text data, with its syntax, semantics, and even hidden information content, possesses an…

Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization…

A standard model for Recommender Systems is the Matrix Completion setting: given partially known matrix of ratings given by users (rows) to items (columns), infer the unknown ratings. In the last decades, few attempts where done to handle…

Polynomial regression is widely used and can help to express nonlinear patterns. However, considering very high polynomial orders may lead to overfitting and poor extrapolation ability for unseen data. The paper presents a method for…

Link prediction infers potential links from observed networks, and is one of the essential problems in network analyses. In contrast to traditional graph representation modeling which only predicts two-way pairwise relations, we propose a…

Graph embedding has attracted increasing attention due to its critical application in social network analysis. Most existing algorithms for graph embedding only rely on the typology information and fail to use the copious information in…

In this paper, we study first-order methods on a large variety of low-rank matrix optimization problems, whose solutions only live in a low dimensional eigenspace. Traditional first-order methods depend on the eigenvalue decomposition at…

Matrix reordering in large sparse solvers seeks a permutation that minimizes factorization fill-in to reduce memory and computation. Because the minimum fill-in ordering problem is NP-complete and fill-in is implicit in the sparsity…

Randomization is a powerful tool that endows algorithms with remarkable properties. For instance, randomized algorithms excel in adversarial settings, often surpassing the worst-case performance of deterministic algorithms with large…

Learning a good representation of text is key to many recommendation applications. Examples include news recommendation where texts to be recommended are constantly published everyday. However, most existing recommendation techniques, such…

Learning rich and compact representations is an open topic in many fields such as object recognition or image retrieval. Deep neural networks have made a major breakthrough during the last few years for these tasks but their representations…

Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is…