Tensor factorization based models have shown great power in knowledge graph completion (KGC). However, their performance usually suffers from the overfitting problem seriously. This motivates various regularizers -- such as the squared Frobenius norm and tensor nuclear norm regularizers -- while the limited applicability significantly limits their practical usage. To address this challenge, we propose a novel regularizer -- namely, DUality-induced RegulArizer (DURA) -- which is not only effective in improving the performance of existing models but widely applicable to various methods. The major novelty of DURA is based on the observation that, for an existing tensor factorization based KGC model (primal), there is often another distance based KGC model (dual) closely associated with it. Experiments show that DURA yields consistent and significant improvements on benchmarks.
We introduce a probabilistic model with implicit norm regularization for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix factors are latent variables associated with each data dimension. The nonnegativity constraint for the latent factors is handled by choosing priors with support on the nonnegative subspace, e.g., exponential density or distribution based on exponential function. Bayesian inference procedure based on Gibbs sampling is employed. We evaluate the model on several real…
Istituto Italiano di Tecnologia（意大利技术研究院）；Johns Hopkins University（约翰斯·霍普金斯大学）
Regularization for matrix factorization (MF) and approximation problems has been carried out in many different ways. Due to its popularity in deep learning, dropout has been applied also for this class of problems. Despite its solid empirical performance, the theoretical properties of dropout as a regularizer remain quite elusive for this class of problems. In this paper, we present a theoretical analysis of dropout for MF, where Bernoulli random variables are used to drop columns of the factors. We demonstrate the equivalence between dropout and a fully deterministic model for MF in which the…
Rank minimization is of interest in machine learning applications such as recommender systems and robust principal component analysis. Minimizing the convex relaxation to the rank minimization problem, the nuclear norm, is an effective technique to solve the problem with strong performance guarantees. However, nonconvex relaxations have less estimation bias than the nuclear norm and can more accurately reduce the effect of noise on the measurements. We develop efficient algorithms based on iteratively reweighted nuclear norm schemes, while also utilizing the low rank factorization for semidefi…
Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity caused by the factorization model, there is a limited theoretical understanding of this formulation. In this paper, we establish a theoretical guarantee for the factorization formulation to correctly recover the underlying low-rank matrix. In particular, we show that under similar conditions to those in previous works, many standard optimization algorithms con…
New Jersey Institute of Technology（新泽西理工学院）；Central Michigan University（中密歇根大学）
Firms earning prediction plays a vital role in investment decisions, dividends expectation, and share price. It often involves multiple tensor-compatible datasets with non-linear multi-way relationships, spatiotemporal structures, and different levels of sparsity. Current non-linear tensor completion algorithms tend to learn noisy embedding and incur overfitting. This paper focuses on the embedding learning aspect of the tensor completion problem and proposes a new multi-layer neural network architecture for tensor factorization and completion (MLCTR). The network architecture entails multiple…
We derive analytical expression of matrix factorization/completion solution by variational Bayes method, under the assumption that observed matrix is originally the product of low-rank dense and sparse matrices with additive noise. We assume the prior of sparse matrix is Laplace distribution by taking matrix sparsity into consideration. Then we use several approximations for derivation of matrix factorization/completion solution. By our solution, we also numerically evaluate the performance of sparse matrix reconstruction in matrix factorization, and completion of missing matrix element in mat…
Tokyo Institute of Technology（东京工业大学）；Technicolor AI Lab（特艺集团人工智能实验室）
Several complex tasks that arise in organizations can be simplified by mapping them into a matrix completion problem. In this paper, we address a key challenge faced by our company: predicting the efficiency of artists in rendering visual effects (VFX) in film shots. We tackle this challenge by using a two-fold approach: first, we transform this task into a constrained matrix completion problem with entries bounded in the unit interval [0, 1]; second, we propose two novel matrix factorization models that leverage our knowledge of the VFX environment. Our first approach, expertise matrix factor…
This paper develops a new class of nonconvex regularizers for low-rank matrix recovery. Many regularizers are motivated as convex relaxations of the matrix rank function. Our new factor group-sparse regularizers are motivated as a relaxation of the number of nonzero columns in a factorization of the matrix. These nonconvex regularizers are sharper than the nuclear norm; indeed, we show they are related to Schatten-$p$ norms with arbitrarily small $0 < p \leq 1$. Moreover, these factor group-sparse regularizers can be written in a factored form that enables efficient and effective nonconvex opt…
We propose the convex factorization machine (CFM), which is a convex variant of the widely used Factorization Machines (FMs). Specifically, we employ a linear+quadratic model and regularize the linear term with the $\ell_2$-regularizer and the quadratic term with the trace norm regularizer. Then, we formulate the CFM optimization as a semidefinite programming problem and propose an efficient optimization procedure with Hazan's algorithm. A key advantage of CFM over existing FMs is that it can find a globally optimal solution, while FMs may get a poor locally optimal solution since the objectiv…
Tailed Low-Rank Matrix Factorization for Similarity Matrix Completion
Centre for Artificial Intelligence and Robotics, Hong Kong Institute of Science & Innovation, CAS（中国科学院香港创新研究院人工智能与机器人中心）；The Hong Kong Polytechnic University（香港理工大学）
Euclidean-Norm-Induced Schatten-p Quasi-Norm Regularization for Low-Rank Tensor Completion and Tensor Robust Principal Component Analysis
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Shenzhen Research Institute of Big Data（深圳大数据研究院）；University of Washington（华盛顿大学）；Cornell University（康奈尔大学）；Hefei University of Technology（合肥工业大学）；Stanford University（斯坦福大学）
The goal of tensor completion is to recover a tensor from a subset of its entries, often by exploiting its low-rank property. Among several useful definitions of tensor rank, the low-tubal-rank was shown to give a valuable characterization of the inherent low-rank structure of a tensor. While some low-tubal-rank tensor completion algorithms with favorable performance have been recently proposed, these algorithms utilize second-order statistics to measure the error residual, which may not work well when the observed entries contain large outliers. In this paper, we propose a new objective funct…
Department of Mathematics, UC Santa Barbara（加州大学圣巴巴拉分校数学系）；Department of ECE, UC Santa Barbara（加州大学圣巴巴拉分校电气工程与计算机科学系）
Streaming tensor factorization is a powerful tool for processing high-volume and multi-way temporal data in Internet networks, recommender systems and image/video data analysis. Existing streaming tensor factorization algorithms rely on least-squares data fitting and they do not possess a mechanism for tensor rank determination. This leaves them susceptible to outliers and vulnerable to over-fitting. This paper presents a Bayesian robust streaming tensor factorization model to identify sparse outliers, automatically determine the underlying tensor rank and accurately fit low-rank structure. We…
University of Edinburgh（爱丁堡大学）；Samsung AI Centre（三星人工智能中心）
Knowledge graphs are structured representations of real world facts. However, they typically contain only a small subset of all possible facts. Link prediction is a task of inferring missing facts based on existing ones. We propose TuckER, a relatively straightforward but powerful linear model based on Tucker decomposition of the binary tensor representation of knowledge graph triples. TuckER outperforms previous state-of-the-art models across standard link prediction datasets, acting as a strong baseline for more elaborate models. We show that TuckER is a fully expressive model, derive suffic…
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；IQVIA（艾昆纬）
Low-rank tensor factorization or completion is well-studied and applied in various online settings, such as online tensor factorization (where the temporal mode grows) and online tensor completion (where incomplete slices arrive gradually). However, in many real-world settings, tensors may have more complex evolving patterns: (i) one or more modes can grow; (ii) missing entries may be filled; (iii) existing tensor elements can change. Existing methods cannot support such complex scenarios. To fill the gap, this paper proposes a Generalized Online Canonical Polyadic (CP) Tensor factorization an…
IIIT - Delhi（德里印度理工学院）；Inria Saclay（法国国家信息与自动化研究所萨克雷分部）；Univ. Paris Saclay（巴黎萨克雷大学）
This work formulates antiviral repositioning as a matrix completion problem where the antiviral drugs are along the rows and the viruses along the columns. The input matrix is partially filled, with ones in positions where the antiviral has been known to be effective against a virus. The curated metadata for antivirals (chemical structure and pathways) and viruses (genomic structure and symptoms) is encoded into our matrix completion framework as graph Laplacian regularization. We then frame the resulting multiple graph regularized matrix completion problem as deep matrix factorization. This i…
Carnegie Mellon University（卡内基梅隆大学）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）
This work studies the strong duality of non-convex matrix factorization problems: we show that under certain dual conditions, these problems and its dual have the same optimum. This has been well understood for convex optimization, but little was known for non-convex problems. We propose a novel analytical framework and show that under certain dual conditions, the optimal solution of the matrix factorization program is the same as its bi-dual and thus the global optimality of the non-convex program can be achieved by solving its bi-dual which is convex. These dual conditions are satisfied by a…
We develop a new collaborative filtering (CF) method that combines both previously known users' preferences, i.e. standard CF, as well as product/user attributes, i.e. classical function approximation, to predict a given user's interest in a particular product. Our method is a generalized low rank matrix completion problem, where we learn a function whose inputs are pairs of vectors -- the standard low rank matrix completion problem being a special case where the inputs to the function are the row and column indices of the matrix. We solve this generalized matrix completion problem using tenso…
Northeastern University（东北大学）；Stevens Institute of Technology（斯蒂文斯理工学院）
Nonnegative matrix factorization (NMF) has been widely used to learn low-dimensional representations of data. However, NMF pays the same attention to all attributes of a data point, which inevitably leads to inaccurate representation. For example, in a human-face data set, if an image contains a hat on the head, the hat should be removed or the importance of its corresponding attributes should be decreased during matrix factorizing. This paper proposes a new type of NMF called entropy weighted NMF (EWNMF), which uses an optimizable weight for each attribute of each data point to emphasize thei…
If learning methods are to scale to the massive sizes of modern datasets, it is essential for the field of machine learning to embrace parallel and distributed computing. Inspired by the recent development of matrix factorization methods with rich theory but poor computational complexity and by the relative ease of mapping matrices onto distributed architectures, we introduce a scalable divide-and-conquer framework for noisy matrix factorization. We present a thorough theoretical analysis of this framework in which we characterize the statistical errors introduced by the "divide" step and cont…
Recommender systems are widely used to recommend the most appealing items to users. These recommendations can be generated by applying collaborative filtering methods. The low-rank matrix completion method is the state-of-the-art collaborative filtering method. In this work, we show that the skewed distribution of ratings in the user-item rating matrix of real-world datasets affects the accuracy of matrix-completion-based approaches. Also, we show that the number of ratings that an item or a user has positively correlates with the ability of low-rank matrix-completion-based approaches to predi…
Matrix completion is one of the key problems in signal processing and machine learning. In recent years, deep-learning-based models have achieved state-of-the-art results in matrix completion. Nevertheless, they suffer from two drawbacks: (i) they can not be extended easily to rows or columns unseen during training; and (ii) their results are often degraded in case discrete predictions are required. This paper addresses these two drawbacks by presenting a deep matrix factorization model and a generic method to allow joint training of the factorization model and the discretization operator. Exp…
University of Pittsburgh（匹兹堡大学）；UPMC Hillman Cancer Center（匹兹堡大学医学中心希尔曼癌症中心）；Rensselaer Polytechnic Institute（伦斯勒理工学院）
This paper considers a large class of problems where we seek to recover a low rank matrix and/or sparse vector from some set of measurements. While methods based on convex relaxations suffer from a (possibly large) estimator bias, and other nonconvex methods require the rank or sparsity to be known a priori, we use nonconvex regularizers to minimize the rank and $l_0$ norm without the estimator bias from the convex relaxation. We present a novel analysis of the alternating proximal gradient descent algorithm applied to such problems, and bound the error between the iterates and the ground trut…
Central China Normal University（华中师范大学）；The University of Hong Kong（香港大学）
In this paper, we study the sparse nonnegative tensor factorization and completion problem from partial and noisy observations for third-order tensors. Because of sparsity and nonnegativity, the underlying tensor is decomposed into the tensor-tensor product of one sparse nonnegative tensor and one nonnegative tensor. We propose to minimize the sum of the maximum likelihood estimation for the observations with nonnegativity constraints and the tensor $\ell_0$ norm for the sparse factor. We show that the error bounds of the estimator of the proposed model can be established under general noise o…
College of Computer Science and Technology, Chongqing University of Posts and Telecommunications（重庆邮电大学计算机科学与技术学院）；Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences（中国科学院重庆绿色智能技术研究院）；College of Computer and Information Science, Southwest University（西南大学计算机与信息科学学院）
Community is a fundamental and critical characteristic of an undirected social network, making community detection be a vital yet thorny issue in network representation learning. A symmetric and non-negative matrix factorization (SNMF) model is frequently adopted to address this issue owing to its great interpretability and scalability. However, it adopts a single latent factor matrix to represent an undirected network for precisely representing its symmetry, which leads to loss of representation learning ability due to the reduced latent space. Motivated by this discovery, this paper proposes…
Aix Marseille Univ（艾克斯-马赛大学）；Université de Toulon（土伦大学）；CNRS（法国国家科学研究中心）；LIS（信息与系统实验室）；Ecole Centrale de Marseille（马赛中央理工学院）
Attempts of studying implicit regularization associated to gradient descent (GD) have identified matrix completion as a suitable test-bed. Late findings suggest that this phenomenon cannot be phrased as a minimization-norm problem, implying that a paradigm shift is required and that dynamics has to be taken into account. In the present work we address the more general setup of tensor completion by leveraging two popularized tensor factorization, namely Tucker and TensorTrain (TT). We track relevant quantities such as tensor nuclear norm, effective rank, generalized singular values and we intro…
Google Brain（谷歌大脑）；Allen Institute for Artificial Intelligence (AI2)（艾伦人工智能研究所）
Given a knowledge base or KB containing (noisy) facts about common nouns or generics, such as "all trees produce oxygen" or "some animals live in forests", we consider the problem of inferring additional such facts at a precision similar to that of the starting KB. Such KBs capture general knowledge about the world, and are crucial for various applications such as question answering. Different from commonly studied named entity KBs such as Freebase, generics KBs involve quantification, have more complex underlying regularities, tend to be more incomplete, and violate the commonly used locally …
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 unifies various metrics which eases their processing in applications. The latter enables scalable and accurate inference with no requirement of structural information of the network nor geometric constraints. By combining both, the acquisition problem bears strong similarities to recommender systems. This paper investigates the applicability of various matrix fac…
Nowadays, the availability of large-scale data in disparate application domains urges the deployment of sophisticated tools for extracting valuable knowledge out of this huge bulk of information. In that vein, low-rank representations (LRRs) which seek low-dimensional embeddings of data have naturally appeared. In an effort to reduce computational complexity and improve estimation performance, LRR has been viewed via a matrix factorization (MF) perspective. Recently, low-rank MF (LRMF) approaches have been proposed for tackling the inherent weakness of MF i.e., the unawareness of the dimension…
University of Electronic Science and Technology of China（电子科技大学）
Tensor completion estimates missing components by exploiting the low-rank structure of multi-way data. The recently proposed methods based on tensor train (TT) and tensor ring (TR) show better performance in image recovery than classical ones. Compared with TT and TR, the projected entangled pair state (PEPS), which is also called tensor grid (TG), allows more interactions between different dimensions, and may lead to more compact representation. In this paper, we propose to perform image completion based on low-rank tensor grid. A two-stage density matrix renormalization group algorithm is us…
Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；NAVER LABS Europe（NAVER LABS 欧洲实验室）；University College London（伦敦大学学院）；Bloomsbury AI
In statistical relational learning, knowledge graph completion deals with automatically understanding the structure of large knowledge graphs---labeled directed graphs---and predicting missing relationships---labeled edges. State-of-the-art embedding models propose different trade-offs between modeling expressiveness, and time and space complexity. We reconcile both expressiveness and complexity through the use of complex-valued embeddings and explore the link between such complex-valued embeddings and unitary diagonalization. We corroborate our approach theoretically and show that all real sq…
Graphical model for factorization and completion of relatively high rank tensors by sparse sampling
D3 Center, Osaka University（大阪大学D3中心）；Department of Physics, Graduate School of Science, Osaka University（大阪大学理学研究生院物理学科）；Department of Systems Science, Graduate School of Informatics, Kyoto University（京都大学信息学研究生院系统科学学科）；RIKEN center for AIP（RIKEN AIP研究中心）
Latent Structural Categorical Matrix Completion with Application to Quasispecies Analysis
Engineering Systems and Design, Singapore University of Technology and Design（新加坡科技设计大学工程系统与设计系）；Institute of Statistics and Big Data, Renmin University of China（中国人民大学统计与大数据研究院）
Paradigm Inc（第四范式公司）；Hong Kong University of Science and Technology（香港科技大学）；Microsoft Research Asia（微软亚洲研究院）
Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical performance. However, the resulting optimization problem is much more challenging. Recent state-of-the-art requires an expensive full SVD in each iteration. In this paper, we show that for many commonly-used nonconvex low-rank regularizers, a cutoff can be derived to automatically threshold the singular values obtained from the proximal operator. This allows…
Rice University（莱斯大学）；Pennsylvania State University（宾夕法尼亚州立大学）
Knowledge graphs link entities through relations to provide a structured representation of real world facts. However, they are often incomplete, because they are based on only a small fraction of all plausible facts. The task of knowledge graph completion via link prediction aims to overcome this challenge by inferring missing facts represented as links between entities. Current approaches to link prediction leverage tensor factorization and/or deep learning. Factorization methods train and deploy rapidly thanks to their small number of parameters but have limited expressiveness due to their u…
The Ohio State University（俄亥俄州立大学）；The University of Hong Kong（香港大学）；Carnegie Mellon University（卡内基梅隆大学）
Low-rank matrix completion has achieved great success in many real-world data applications. A matrix factorization model that learns latent features is usually employed and, to improve prediction performance, the similarities between latent variables can be exploited by pairwise learning using the graph regularized matrix factorization (GRMF) method. However, existing GRMF approaches often use the squared loss to measure the pairwise differences, which may be overly influenced by dissimilar pairs and lead to inferior prediction. To fully empower pairwise learning for matrix completion, we prop…
Many fundamental low-rank optimization problems, such as matrix completion, phase synchronization/retrieval, power system state estimation, and robust PCA, can be formulated as the matrix sensing problem. Two main approaches for solving matrix sensing are based on semidefinite programming (SDP) and Burer-Monteiro (B-M) factorization. The SDP method suffers from high computational and space complexities, whereas the B-M method may return a spurious solution due to the non-convexity of the problem. The existing theoretical guarantees for the success of these methods have led to similar conservat…
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized methods, that reduce the complexity in one of the matrix dimension, but not in both of them. In this paper, we tackle very large matrices in both dimensions. We propose a new factoriza-tion method that scales gracefully to terabyte-scale datasets, that could not be processed by previous algorithms in a reasonable amount of time. We demonstrate the efficiency …
Istituto Italiano di Tecnologia（意大利技术研究院）；Johns Hopkins University（约翰斯·霍普金斯大学）
Dropout is a simple yet effective algorithm for regularizing neural networks by randomly dropping out units through Bernoulli multiplicative noise, and for some restricted problem classes, such as linear or logistic regression, several theoretical studies have demonstrated the equivalence between dropout and a fully deterministic optimization problem with data-dependent Tikhonov regularization. This work presents a theoretical analysis of dropout for matrix factorization, where Bernoulli random variables are used to drop a factor, thereby attempting to control the size of the factorization. Wh…
National University of Singapore（新加坡国立大学）；IRIT, Université de Toulouse, CNRS（图卢兹大学IRIT实验室、法国国家科学研究中心）
We consider an adversarially-trained version of the nonnegative matrix factorization, a popular latent dimensionality reduction technique. In our formulation, an attacker adds an arbitrary matrix of bounded norm to the given data matrix. We design efficient algorithms inspired by adversarial training to optimize for dictionary and coefficient matrices with enhanced generalization abilities. Extensive simulations on synthetic and benchmark datasets demonstrate the superior predictive performance on matrix completion tasks of our proposed method compared to state-of-the-art competitors, includin…
Princeton University（普林斯顿大学）；Institute for Advanced Study（高等研究院）；Tel Aviv University（特拉维夫大学）
Efforts to understand the generalization mystery in deep learning have led to the belief that gradient-based optimization induces a form of implicit regularization, a bias towards models of low "complexity." We study the implicit regularization of gradient descent over deep linear neural networks for matrix completion and sensing, a model referred to as deep matrix factorization. Our first finding, supported by theory and experiments, is that adding depth to a matrix factorization enhances an implicit tendency towards low-rank solutions, oftentimes leading to more accurate recovery. Secondly, …
Recent efforts to unravel the mystery of implicit regularization in deep learning have led to a theoretical focus on matrix factorization -- matrix completion via linear neural network. As a step further towards practical deep learning, we provide the first theoretical analysis of implicit regularization in tensor factorization -- tensor completion via certain type of non-linear neural network. We circumvent the notorious difficulty of tensor problems by adopting a dynamical systems perspective, and characterizing the evolution induced by gradient descent. The characterization suggests a form …
University of Cambridge（剑桥大学）；University of Toronto（多伦多大学）
Data often comes in the form of an array or matrix. Matrix factorization techniques attempt to recover missing or corrupted entries by assuming that the matrix can be written as the product of two low-rank matrices. In other words, matrix factorization approximates the entries of the matrix by a simple, fixed function---namely, the inner product---acting on the latent feature vectors for the corresponding row and column. Here we consider replacing the inner product by an arbitrary function that we learn from the data at the same time as we learn the latent feature vectors. In particular, we re…
We study the non-convex matrix factorization approach to matrix completion via Riemannian geometry. Based on an optimization formulation over a Grassmannian manifold, we characterize the landscape based on the notion of principal angles between subspaces. For the fully observed case, our results show that there is a region in which the cost is geodesically convex, and outside of which all critical points are strictly saddle. We empirically study the partially observed case based on our findings.
We propose a unified and systematic framework for performing online nonnegative matrix factorization in the presence of outliers. Our framework is particularly suited to large-scale data. We propose two solvers based on projected gradient descent and the alternating direction method of multipliers. We prove that the sequence of objective values converges almost surely by appealing to the quasi-martingale convergence theorem. We also show the sequence of learned dictionaries converges to the set of stationary points of the expected loss function almost surely. In addition, we extend our basic p…
CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem especially for CP rank. In addition, existing approaches do not take into account uncertainty information of latent factors, as well as missing entries. To address these issues, we formulate CP factorization using a hierarchical probabilistic model and employ a fully Bayesian trea…
We consider the general problem of utilizing both labeled and unlabeled data to improve data representation performance. A new semi-supervised learning framework is proposed by combing manifold regularization and data representation methods such as Non negative matrix factorization and sparse coding. We adopt unsupervised data representation methods as the learning machines because they do not depend on the labeled data, which can improve machine's generation ability as much as possible. The proposed framework forms the Laplacian regularizer through learning the affinity graph. We incorporate …
Many practical problems involve the recovery of a binary matrix from partial information, which makes the binary matrix completion (BMC) technique received increasing attention in machine learning. In particular, we consider a special case of BMC problem, in which only a subset of positive elements can be observed. In recent years, convex regularization based methods are the mainstream approaches for this task. However, the applications of nonconvex surrogates in standard matrix completion have demonstrated better empirical performance. Accordingly, we propose a novel BMC model with nonconvex …
Heterogeneous multi-typed, multimodal relational data is increasingly available in many domains and their exploratory analysis poses several challenges. We advance the state-of-the-art in neural unsupervised learning to analyze such data. We design the first neural method for collective matrix tri-factorization of arbitrary collections of matrices to perform spectral clustering of all constituent entities and learn cluster associations. Experiments on benchmark datasets demonstrate its efficacy over previous non-neural approaches. Leveraging signals from multi-way clustering and collective mat…
Baidu Research（百度研究院）；Paradigm Inc.（第四范式公司）；Tsinghua University（清华大学）；Hong Kong University of Science and Technology（香港科技大学）
Matrix learning is at the core of many machine learning problems. A number of real-world applications such as collaborative filtering and text mining can be formulated as a low-rank matrix completion problem, which recovers incomplete matrix using low-rank assumptions. To ensure that the matrix solution has a low rank, a recent trend is to use nonconvex regularizers that adaptively penalize singular values. They offer good recovery performance and have nice theoretical properties, but are computationally expensive due to repeated access to individual singular values. In this paper, based on th…
Valid causal inference in observational studies often requires controlling for confounders. However, in practice measurements of confounders may be noisy, and can lead to biased estimates of causal effects. We show that we can reduce the bias caused by measurement noise using a large number of noisy measurements of the underlying confounders. We propose the use of matrix factorization to infer the confounders from noisy covariates, a flexible and principled framework that adapts to missing values, accommodates a wide variety of data types, and can augment many causal inference methods. We boun…
