Related papers: Fast, memory efficient low-rank approximation of S…
Affine rank minimization algorithms typically rely on calculating the gradient of a data error followed by a singular value decomposition at every iteration. Because these two steps are expensive, heuristic approximations are often used to…
Structured low-rank approximation is the problem of minimizing a weighted Frobenius distance to a given matrix among all matrices of fixed rank in a linear space of matrices. We study exact solutions to this problem by way of computational…
The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest…
Recht, Fazel, and Parrilo provided an analogy between rank minimization and $\ell_0$-norm minimization. Subject to the rank-restricted isometry property, nuclear norm minimization is a guaranteed algorithm for rank minimization. The…
We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…
The burdensome training costs on large-scale graphs have aroused significant interest in graph condensation, which involves tuning Graph Neural Networks (GNNs) on a small condensed graph for use on the large-scale original graph. Existing…
Similarity matrix serves as a fundamental tool at the core of numerous downstream machine-learning tasks. However, missing data is inevitable and often results in an inaccurate similarity matrix. To address this issue, Similarity Matrix…
A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph into a large network. We propose two complementary MCMC algorithms for…
We consider in this paper the multivariate regression problem, when the target regression matrix $A$ is close to a low rank matrix. Our primary interest in on the practical case where the variance of the noise is unknown. Our main…
Word and sentence embeddings are useful feature representations in natural language processing. However, intrinsic evaluation for embeddings lags far behind, and there has been no significant update since the past decade. Word and sentence…
Let $A$ be an $m \times n$ matrix with rank $r$ and spectral decomposition $A = \sum_{i=1}^r \sigma_i u_i v_i^\top,$ where $\sigma_i$ are its singular values, ordered decreasingly, and $u_i, v_i$ are the corresponding left and right…
In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our…
A common problem in machine learning is to rank a set of n items based on pairwise comparisons. Here ranking refers to partitioning the items into sets of pre-specified sizes according to their scores, which includes identification of the…
We focus on the problem of query rewriting for sponsored search. We base rewrites on a historical click graph that records the ads that have been clicked on in response to past user queries. Given a query q, we first consider Simrank as a…
We propose a simple and optimal algorithm, BackMC, for local PageRank estimation in undirected graphs: given an arbitrary target node $t$ in an undirected graph $G$ comprising $n$ nodes and $m$ edges, BackMC accurately estimates the…
Short Read Alignment Mapping Metrics (SRAMM): is an efficient and versatile command line tool providing additional short read mapping metrics, filtering, and graphs. Short read aligners report MAPing Quality (MAPQ), but these methods…
Matrix factorization is a well-studied task in machine learning for compactly representing large, noisy data. In our approach, instead of using the traditional concept of matrix rank, we define a new notion of link-rank based on a…
Identifying semantically equivalent sentences is important for many cross-lingual and mono-lingual NLP tasks. Current approaches to semantic equivalence take a loose, sentence-level approach to "equivalence," despite previous evidence that…
The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization…
This paper introduces a new few-shot learning pipeline that casts relevance ranking for image retrieval as binary ranking relation classification. In comparison to image classification, ranking relation classification is sample efficient…