Since many real-world data can be described from multiple views, multi-view learning has attracted considerable attention. Various methods have been proposed and successfully applied to multi-view learning, typically based on matrix factorization models. Recently, it is extended to the deep structure to exploit the hierarchical information of multi-view data, but the view-specific features and the label information are seldom considered. To address these concerns, we present a partially shared semi-supervised deep matrix factorization model (PSDMF). By integrating the partially shared deep decomposition structure, graph regularization and the semi-supervised regression model, PSDMF can learn a compact and discriminative representation through eliminating the effects of uncorrelated information. In addition, we develop an efficient iterative updating algorithm for PSDMF. Extensive experiments on five benchmark datasets demonstrate that PSDMF can achieve better performance than the state-of-the-art multi-view learning approaches. The MATLAB source code is available at https://github.com/libertyhhn/PartiallySharedDMF.
In this paper, we propose a new method for determining shared features of and measuring the distance between data sets or point clouds. Our approach uses the joint factorization of two data matrices $X_1,X_2$ into non-negative matrices $X_1 = AS_1, X_2 = AS_2$ to derive a similarity measure that determines how well the shared basis $A$ approximates $X_1, X_2$. We also propose a point cloud distance measure built upon this method and the learned factorization. Our method reveals structural differences in both image and text data. Potential applications include classification, detecting plagiari…
NTT Communication Science Laboratories（NTT通信科学实验室）
We propose a method that meta-learns a knowledge on matrix factorization from various matrices, and uses the knowledge for factorizing unseen matrices. The proposed method uses a neural network that takes a matrix as input, and generates prior distributions of factorized matrices of the given matrix. The neural network is meta-learned such that the expected imputation error is minimized when the factorized matrices are adapted to each matrix by a maximum a posteriori (MAP) estimation. We use a gradient descent method for the MAP estimation, which enables us to backpropagate the expected imputa…
Learning by integrating multiple heterogeneous data sources is a common requirement in many tasks. Collective Matrix Factorization (CMF) is a technique to learn shared latent representations from arbitrary collections of matrices. It can be used to simultaneously complete one or more matrices, for predicting the unknown entries. Classical CMF methods assume linearity in the interaction of latent factors which can be restrictive and fails to capture complex non-linear interactions. In this paper, we develop the first deep-learning based method, called dCMF, for unsupervised learning of multiple…
University of Electronic Science and Technology of China（电子科技大学）；Shanghai Jiao Tong University（上海交通大学）
Hyperspectral image (HSI) has some advantages over natural image for various applications due to the extra spectral information. During the acquisition, it is often contaminated by severe noises including Gaussian noise, impulse noise, deadlines, and stripes. The image quality degeneration would badly effect some applications. In this paper, we present a HSI restoration method named smooth and robust low rank tensor recovery. Specifically, we propose a structural tensor decomposition in accordance with the linear spectral mixture model of HSI. It decomposes a tensor into sums of outer matrix v…
School of Computer Science and Statistics, Trinity College（都柏林圣三一学院计算机科学与统计学院）
We propose a privacy-enhanced matrix factorization recommender that exploits the fact that users can often be grouped together by interest. This allows a form of "hiding in the crowd" privacy. We introduce a novel matrix factorization approach suited to making recommendations in a shared group (or nym) setting and the BLC algorithm for carrying out this matrix factorization in a privacy-enhanced manner. We demonstrate that the increased privacy does not come at the cost of reduced recommendation accuracy.
Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所 HIIT）；University of Helsinki（赫尔辛基大学）；Xerox Research Centre Europe（施乐欧洲研究中心）；Xerox Research Centre India（施乐印度研究中心）
CMF is a technique for simultaneously learning low-rank representations based on a collection of matrices with shared entities. A typical example is the joint modeling of user-item, item-property, and user-feature matrices in a recommender system. The key idea in CMF is that the embeddings are shared across the matrices, which enables transferring information between them. The existing solutions, however, break down when the individual matrices have low-rank structure not shared with others. In this work we present a novel CMF solution that allows each of the matrices to have a separate low-ra…
Matrix factorization (MF) and Autoencoder (AE) are among the most successful approaches of unsupervised learning. While MF based models have been extensively exploited in the graph modeling and link prediction literature, the AE family has not gained much attention. In this paper we investigate both MF and AE's application to the link prediction problem in sparse graphs. We show the connection between AE and MF from the perspective of multiview learning, and further propose MF+AE: a model training MF and AE jointly with shared parameters. We apply dropout to training both the MF and AE parts, …
Motivated by an application in computational biology, we consider low-rank matrix factorization with $\{0,1\}$-constraints on one of the factors and optionally convex constraints on the second one. In addition to the non-convexity shared with other matrix factorization schemes, our problem is further complicated by a combinatorial constraint set of size $2^{m \cdot r}$, where $m$ is the dimension of the data points and $r$ the rank of the factorization. Despite apparent intractability, we provide - in the line of recent work on non-negative matrix factorization by Arora et al. (2012) - an algo…
Several modern applications require the integration of multiple large data matrices that have shared rows and/or columns. For example, cancer studies that integrate multiple omics platforms across multiple types of cancer, pan-omics pan-cancer analysis, have extended our knowledge of molecular heterogenity beyond what was observed in single tumor and single platform studies. However, these studies have been limited by available statistical methodology. We propose a flexible approach to the simultaneous factorization and decomposition of variation across such bidimensionally linked matrices, BI…
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.
Recommender systems are emerging technologies that nowadays can be found in many applications such as Amazon, Netflix, and so on. These systems help users to find relevant information, recommendations, and their preferred items. Slightly improvement of the accuracy of these recommenders can highly affect the quality of recommendations. Matrix Factorization is a popular method in Recommendation Systems showing promising results in accuracy and complexity. In this paper we propose an extension of matrix factorization which adds general neighborhood information on the recommendation model. Users …
Multi-view clustering is an important yet challenging task in machine learning and data mining community. One popular strategy for multi-view clustering is matrix factorization which could explore useful feature representations at lower-dimensional space and therefore alleviate dimension curse. However, there are two major drawbacks in the existing work: i) most matrix factorization methods are limited to shadow depth, which leads to the inability to fully discover the rich hidden information of original data. Few deep matrix factorization methods provide a basis for the selection of the new r…
University of Maryland（马里兰大学）；IBM T.J. Watson Research Center（IBM托马斯·J·沃森研究中心）
The separability assumption (Donoho & Stodden, 2003; Arora et al., 2012) turns non-negative matrix factorization (NMF) into a tractable problem. Recently, a new class of provably-correct NMF algorithms have emerged under this assumption. In this paper, we reformulate the separable NMF problem as that of finding the extreme rays of the conical hull of a finite set of vectors. From this geometric perspective, we derive new separable NMF algorithms that are highly scalable and empirically noise robust, and have several other favorable properties in relation to existing methods. A parallel impleme…
Cross-Domain Collaborative Filtering (CDCF) provides a way to alleviate data sparsity and cold-start problems present in recommendation systems by exploiting the knowledge from related domains. Existing CDCF models are either based on matrix factorization or deep neural networks. Either of the techniques in isolation may result in suboptimal performance for the prediction task. Also, most of the existing models face challenges particularly in handling diversity between domains and learning complex non-linear relationships that exist amongst entities (users/items) within and across domains. In …
Supervised Deep Multimodal Matrix Factorization for Interpretable Brain Network Analysis
Dept. of Mathematics & Operational Research University of Mons（数学与运筹学系蒙斯大学）；Dept. of Computer Science & Engineering Lehigh University（计算机科学与工程系莱斯大学）；Dept. of Industrial & Systems Engineering Lehigh University（工业与系统工程系莱斯大学）
Despite the prominence of neural network approaches in the field of recommender systems, simple methods such as matrix factorization with quadratic loss are still used in industry for several reasons. These models can be trained with alternating least squares, which makes them easy to implement in a massively parallel manner, thus making it possible to utilize billions of events from real-world datasets. Large-scale recommender systems need to account for severe popularity skew in the distributions of users and items, so a lot of research is focused on implementing sparse, mixed dimension or s…
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…
Multi-view clustering (MVC) has been extensively studied to collect multiple source information in recent years. One typical type of MVC methods is based on matrix factorization to effectively perform dimension reduction and clustering. However, the existing approaches can be further improved with following considerations: i) The current one-layer matrix factorization framework cannot fully exploit the useful data representations. ii) Most algorithms only focus on the shared information while ignore the view-specific structure leading to suboptimal solutions. iii) The partition level informati…
University of Maryland, Baltimore County（马里兰大学巴尔的摩郡分校）；LANL（洛斯阿拉莫斯国家实验室）
Non-negative matrix factorization (NMF) with missing-value completion is a well-known effective Collaborative Filtering (CF) method used to provide personalized user recommendations. However, traditional CF relies on the privacy-invasive collection of users' explicit and implicit feedback to build a central recommender model. One-shot federated learning has recently emerged as a method to mitigate the privacy problem while addressing the traditional communication bottleneck of federated learning. In this paper, we present the first unsupervised one-shot federated CF implementation, named FedSP…
Southwest University（西南大学）；China University of Geosciences（中国地质大学）；George Mason University（乔治梅森大学）；Deakin University（迪肯大学）；Beijing University of Civil Engineering and Architecture（北京建筑大学）
Multi-view Multi-instance Multi-label Learning(M3L) deals with complex objects encompassing diverse instances, represented with different feature views, and annotated with multiple labels. Existing M3L solutions only partially explore the inter or intra relations between objects (or bags), instances, and labels, which can convey important contextual information for M3L. As such, they may have a compromised performance. In this paper, we propose a collaborative matrix factorization based solution called M3Lcmf. M3Lcmf first uses a heterogeneous network composed of nodes of bags, instances, and …
Nonnegative Matrix Factorization (NMF) is a widely used technique in many applications such as face recognition, motion segmentation, etc. It approximates the nonnegative data in an original high dimensional space with a linear representation in a low dimensional space by using the product of two nonnegative matrices. In many applications data are often partially corrupted with large additive noise. When the positions of noise are known, some existing variants of NMF can be applied by treating these corrupted entries as missing values. However, the positions are often unknown in many real worl…
Punjab University College of Information Technology (PUCIT), University of the Punjab（旁遮普大学旁遮普信息技术学院（PUCIT））
Transfer learning is a problem defined over two domains. These two domains share the same feature space and class label space, but have significantly different distributions. One domain has sufficient labels, named as source domain, and the other domain has few labels, named as target do- main. The problem is to learn a effective classifier for the target domain. In this paper, we propose a novel transfer learning method for this problem by learning a partially shared classifier for the target domain, and weighting the source domain data points. We learn some shared subspaces for both the data…
We propose a nonparametric model for time series with missing data based on low-rank matrix factorization. The model expresses each instance in a set of time series as a linear combination of a small number of shared basis functions. Constraining the functions and the corresponding coefficients to be nonnegative yields an interpretable low-dimensional representation of the data. A time-smoothing regularization term ensures that the model captures meaningful trends in the data, instead of overfitting short-term fluctuations. The low-dimensional representation makes it possible to detect outlier…
Near-optimal and Efficient First-Order Algorithm for Multi-Task Learning with Shared Linear Representation
State Key Lab of General AI, School of Intelligence Science and Technology, Peking University, China（人工智能国家重点实验室，智能科学与技术学院，北京大学，中国）；School of Mathematical Sciences, Peking University, China（数学科学学院，北京大学，中国）；Institute for Artificial Intelligence, Peking University, China（人工智能研究院，北京大学，中国）
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Microsoft Research（微软研究院）
Exploiting low-rank structure of the user-item rating matrix has been the crux of many recommendation engines. However, existing recommendation engines force raters with heterogeneous behavior profiles to map their intrinsic rating scales to a common rating scale (e.g. 1-5). This non-linear transformation of the rating scale shatters the low-rank structure of the rating matrix, therefore resulting in a poor fit and consequentially, poor recommendations. In this paper, we propose Clustered Monotone Transforms for Rating Factorization (CMTRF), a novel approach to perform regression up to unknown…
The vast majority of current machine learning algorithms are designed to predict single responses or a vector of responses, yet many types of response are more naturally organized as matrices or higher-order tensor objects where characteristics are shared across modes. We present a new machine learning algorithm BaTFLED (Bayesian Tensor Factorization Linked to External Data) that predicts values in a three-dimensional response tensor using input features for each of the dimensions. BaTFLED uses a probabilistic Bayesian framework to learn projection matrices mapping input features for each mode…
KU Leuven（鲁汶大学）；Leuven Brain Institute（鲁汶脑科学研究所）；Maastricht UMC+（马斯特里赫特大学医学中心+）；University Hospitals Leuven（鲁汶大学医院）；Delft University of Technology（代尔夫特理工大学）
EEG-correlated fMRI analysis is widely used to detect regional blood oxygen level dependent fluctuations that are significantly synchronized to interictal epileptic discharges, which can provide evidence for localizing the ictal onset zone. However, such an asymmetrical, mass-univariate approach cannot capture the inherent, higher order structure in the EEG data, nor multivariate relations in the fMRI data, and it is nontrivial to accurately handle varying neurovascular coupling over patients and brain regions. We aim to overcome these drawbacks in a data-driven manner by means of a novel stru…
Toyota Technological Institute at Chicago（芝加哥丰田理工学院）
We present experiments demonstrating that some other form of capacity control, different from network size, plays a central role in learning multilayer feed-forward networks. We argue, partially through analogy to matrix factorization, that this is an inductive bias that can help shed light on deep learning.
In this work, we examine the security of InstaHide, a scheme recently proposed by [Huang, Song, Li and Arora, ICML'20] for preserving the security of private datasets in the context of distributed learning. To generate a synthetic training example to be shared among the distributed learners, InstaHide takes a convex combination of private feature vectors and randomly flips the sign of each entry of the resulting vector with probability 1/2. A salient question is whether this scheme is secure in any provable sense, perhaps under a plausible hardness assumption and assuming the distributions gen…
University of Minnesota School of Public Health（明尼苏达大学公共卫生学院）；Division of Biostatistics（生物统计学系）
Advances in molecular "omics'" technologies have motivated new methodology for the integration of multiple sources of high-content biomedical data. However, most statistical methods for integrating multiple data matrices only consider data shared vertically (one cohort on multiple platforms) or horizontally (different cohorts on a single platform). This is limiting for data that take the form of bidimensionally linked matrices (e.g., multiple cohorts measured on multiple platforms), which are increasingly common in large-scale biomedical studies. In this paper, we propose BIDIFAC (Bidimensiona…
College of Computer Science, Zhejiang University（浙江大学计算机学院）
Matrix factorization is one of the most commonly used technologies in recommendation system. With the promotion of recommendation system in e-commerce shopping, online video and other aspects, distributed recommendation system has been widely promoted, and the privacy problem of multi-source data becomes more and more important. Based on Federated learning technology, this paper proposes a shared matrix factorization scheme called SharedMF. Firstly, a distributed recommendation system is built, and then secret sharing technology is used to protect the privacy of local data. Experimental result…
Training multi-agent systems (MAS) to achieve realistic equilibria gives us a useful tool to understand and model real-world systems. We consider a general sum partially observable Markov game where agents of different types share a single policy network, conditioned on agent-specific information. This paper aims at i) formally understanding equilibria reached by such agents, and ii) matching emergent phenomena of such equilibria to real-world targets. Parameter sharing with decentralized execution has been introduced as an efficient way to train multiple agents using a single policy network. …
High-order parametric models that include terms for feature interactions are applied to various data mining tasks, where ground truth depends on interactions of features. However, with sparse data, the high- dimensional parameters for feature interactions often face three issues: expensive computation, difficulty in parameter estimation and lack of structure. Previous work has proposed approaches which can partially re- solve the three issues. In particular, models with factorized parameters (e.g. Factorization Machines) and sparse learning algorithms (e.g. FTRL-Proximal) can tackle the first …
University of Illinois at Chicago（伊利诺伊大学芝加哥分校）；Cornell University（康奈尔大学）；Purdue University（普渡大学）；Tsinghua University（清华大学）
Real-world relations among entities can often be observed and determined by different perspectives/views. For example, the decision made by a user on whether to adopt an item relies on multiple aspects such as the contextual information of the decision, the item's attributes, the user's profile and the reviews given by other users. Different views may exhibit multi-way interactions among entities and provide complementary information. In this paper, we introduce a multi-tensor-based approach that can preserve the underlying structure of multi-view data in a generic predictive model. Specifical…
RIKEN Center for Advanced Intelligence Project（理化学研究所高级智能项目中心）；RIKEN（理化学研究所（RIKEN））
This paper introduces our solution to the 2018 Duolingo Shared Task on Second Language Acquisition Modeling (SLAM). We used deep factorization machines, a wide and deep learning model of pairwise relationships between users, items, skills, and other entities considered. Our solution (AUC 0.815) hopefully managed to beat the logistic regression baseline (AUC 0.774) but not the top performing model (AUC 0.861) and reveals interesting strategies to build upon item response theory models.
Regularization is essential when training large neural networks. As deep neural networks can be mathematically interpreted as universal function approximators, they are effective at memorizing sampling noise in the training data. This results in poor generalization to unseen data. Therefore, it is no surprise that a new regularization technique, Dropout, was partially responsible for the now-ubiquitous winning entry to ImageNet 2012 by the University of Toronto. Currently, Dropout (and related methods such as DropConnect) are the most effective means of regularizing large neural networks. Thes…
Peking University（北京大学）；Tencent AI Lab（腾讯人工智能实验室）；BAAI（北京智源人工智能研究院）
In cooperative multi-agent reinforcement learning (MARL), combining value decomposition with actor-critic enables agents to learn stochastic policies, which are more suitable for the partially observable environment. Given the goal of learning local policies that enable decentralized execution, agents are commonly assumed to be independent of each other, even in centralized training. However, such an assumption may prohibit agents from learning the optimal joint policy. To address this problem, we explicitly take the dependency among agents into centralized training. Although this leads to the…
University of Toronto（多伦多大学）；Center for Management of Technology & Entrepreneurship（技术管理与创业中心）；RBC Capital Markets（加拿大皇家银行资本市场）
Multi-Agent Reinforcement Learning (MARL) has demonstrated significant success in training decentralised policies in a centralised manner by making use of value factorization methods. However, addressing surprise across spurious states and approximation bias remain open problems for multi-agent settings. Towards this goal, we introduce the Energy-based MIXer (EMIX), an algorithm which minimizes surprise utilizing the energy across agents. Our contributions are threefold; (1) EMIX introduces a novel surprise minimization technique across multiple agents in the case of multi-agent partially-obse…
