Despite the success of existing tensor factorization methods, most of them conduct a multilinear decomposition, and rarely exploit powerful modeling frameworks, like deep neural networks, to capture a variety of complicated interactions in data. More important, for highly expressive, deep factorization, we lack an effective approach to handle streaming data, which are ubiquitous in real-world applications. To address these issues, we propose SPIDER, a Streaming ProbabilistIc Deep tEnsoR factorization method. We first use Bayesian neural networks (NNs) to construct a deep tensor factorization model. We assign a spike-and-slab prior over the NN weights to encourage sparsity and prevent overfitting. We then use Taylor expansions and moment matching to approximate the posterior of the NN output and calculate the running model evidence, based on which we develop an efficient streaming posterior inference algorithm in the assumed-density-filtering and expectation propagation framework. Our algorithm provides responsive incremental updates for the posterior of the latent factors and NN weights upon receiving new tensor entries, and meanwhile select and inhibit redundant/useless weights. We show the advantages of our approach in four real-world applications.
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…
Columbia University（哥伦比亚大学）；Colorado State University（科罗拉多州立大学）；Stony Brook University（石溪大学）；Brookhaven National Laboratory（布鲁克海文国家实验室）
We validate the use of matrix factorization for the automatic identification of relevant components from atomic pair distribution function (PDF) data. We also present a newly developed software infrastructure for analyzing the PDF data arriving in streaming manner. We then apply two matrix factorization techniques, Principal Component Analysis (PCA) and Non-negative Matrix Factorization (NMF), to study simulated and experiment datasets in the context of in situ experiment.
Probabilistic Temporal Tensor Factorization (PTTF) is an effective algorithm to model the temporal tensor data. It leverages a time constraint to capture the evolving properties of tensor data. Nowadays the exploding dataset demands a large scale PTTF analysis, and a parallel solution is critical to accommodate the trend. Whereas, the parallelization of PTTF still remains unexplored. In this paper, we propose a simple yet efficient Parallel Probabilistic Temporal Tensor Factorization, referred to as P$^2$T$^2$F, to provide a scalable PTTF solution. P$^2$T$^2$F is fundamentally disparate from e…
Factorizing tensors has recently become an important optimization module in a number of machine learning pipelines, especially in latent variable models. We show how to do this efficiently in the streaming setting. Given a set of $n$ vectors, each in $\mathbb{R}^d$, we present algorithms to select a sublinear number of these vectors as coreset, while guaranteeing that the CP decomposition of the $p$-moment tensor of the coreset approximates the corresponding decomposition of the $p$-moment tensor computed from the full data. We introduce two novel algorithmic techniques: online filtering and k…
National Chiao Tung Univ.（国立交通大学）；Inst. of Information Science, Academia Sinica, Taiwan（中央研究院资讯科学研究所）；The Pennsylvania State Univ.（宾夕法尼亚州立大学）
In contrast to traditional online videos, live multi-streaming supports real-time social interactions between multiple streamers and viewers, such as donations. However, donation and multi-streaming channel recommendations are challenging due to complicated streamer and viewer relations, asymmetric communications, and the tradeoff between personal interests and group interactions. In this paper, we introduce Multi-Stream Party (MSP) and formulate a new multi-streaming recommendation problem, called Donation and MSP Recommendation (DAMRec). We propose Multi-stream Party Recommender System (MARS…
This paper presents a sequential randomized lowrank matrix factorization approach for incrementally predicting values of an unknown function at test points using the Gaussian Processes framework. It is well-known that in the Gaussian processes framework, the computational bottlenecks are the inversion of the (regularized) kernel matrix and the computation of the hyper-parameters defining the kernel. The main contributions of this paper are two-fold. First, we formalize an approach to compute the inverse of the kernel matrix using randomized matrix factorization algorithms in a streaming scenar…
Probabilistic approach to Boolean matrix factorization can provide solutions robustagainst noise and missing values with linear computational complexity. However,the assumption about latent factors can be problematic in real world applications.This study proposed a new probabilistic algorithm free of assumptions of latentfactors, while retaining the advantages of previous algorithms. Real data experimentshowed that our algorithm was favourably compared with current state-of-the-artprobabilistic algorithms.
LTCI, Institut Polytechnique de Paris, Télécom Paris（巴黎理工学院LTCI、巴黎电信学院）；Smart Impulse（Smart Impulse公司）
We present a new probabilistic model to address semi-nonnegative matrix factorization (SNMF), called Skellam-SNMF. It is a hierarchical generative model consisting of prior components, Skellam-distributed hidden variables and observed data. Two inference algorithms are derived: Expectation-Maximization (EM) algorithm for maximum \emph{a posteriori} estimation and Variational Bayes EM (VBEM) for full Bayesian inference, including the estimation of parameters prior distribution. From this Skellam-based model, we also introduce a new divergence $\mathcal{D}$ between a real-valued target data $x$ …
Probabilistic matrix factorization (PMF) is a powerful method for modeling data associated with pairwise relationships, finding use in collaborative filtering, computational biology, and document analysis, among other areas. In many domains, there is additional information that can assist in prediction. For example, when modeling movie ratings, we might know when the rating occurred, where the user lives, or what actors appear in the movie. It is difficult, however, to incorporate this side information into the PMF model. We propose a framework for incorporating side information by coupling to…
Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所 HIIT）；Aalto University（阿尔托大学）；Tampere University（坦佩雷大学）；Kyoto University（京都大学）
In matrix factorization, available graph side-information may not be well suited for the matrix completion problem, having edges that disagree with the latent-feature relations learnt from the incomplete data matrix. We show that removing these $\textit{contested}$ edges improves prediction accuracy and scalability. We identify the contested edges through a highly-efficient graphical lasso approximation. The identification and removal of contested edges adds no computational complexity to state-of-the-art graph-regularized matrix factorization, remaining linear with respect to the number of no…
University of Toronto（多伦多大学）；University of Edinburgh（爱丁堡大学）
Probabilistic matrix factorization (PMF) is a powerful method for modeling data associ- ated with pairwise relationships, Finding use in collaborative Filtering, computational bi- ology, and document analysis, among other areas. In many domains, there are additional covariates that can assist in prediction. For example, when modeling movie ratings, we might know when the rating occurred, where the user lives, or what actors appear in the movie. It is difficult, however, to incorporate this side information into the PMF model. We propose a framework for incorporating side information by couplin…
Item response theory (IRT) is a non-linear generative probabilistic paradigm for using exams to identify, quantify, and compare latent traits of individuals, relative to their peers, within a population of interest. In pre-existing multidimensional IRT methods, one requires a factorization of the test items. For this task, linear exploratory factor analysis is used, making IRT a posthoc model. We propose skipping the initial factor analysis by using a sparsity-promoting horseshoe prior to perform factorization directly within the IRT model so that all training occurs in a single self-consisten…
Aalborg University（奥尔堡大学）；University of Almería（阿尔梅里亚大学）；HUGIN EXPERT A/S
The AMIDST Toolbox is a software for scalable probabilistic machine learning with a spe- cial focus on (massive) streaming data. The toolbox supports a flexible modeling language based on probabilistic graphical models with latent variables and temporal dependencies. The specified models can be learnt from large data sets using parallel or distributed implementa- tions of Bayesian learning algorithms for either streaming or batch data. These algorithms are based on a flexible variational message passing scheme, which supports discrete and continu- ous variables from a wide range of probability…
The Alan Turing Institute（阿兰·图灵研究所）；University of Warwick（华威大学）
We introduce the probabilistic sequential matrix factorization (PSMF) method for factorizing time-varying and non-stationary datasets consisting of high-dimensional time-series. In particular, we consider nonlinear Gaussian state-space models where sequential approximate inference results in the factorization of a data matrix into a dictionary and time-varying coefficients with potentially nonlinear Markovian dependencies. The assumed Markovian structure on the coefficients enables us to encode temporal dependencies into a low-dimensional feature space. The proposed inference method is solely …
Matrix factorization (MF) has become a common approach to collaborative filtering, due to ease of implementation and scalability to large data sets. Two existing drawbacks of the basic model is that it does not incorporate side information on either users or items, and assumes a common variance for all users. We extend the work of constrained probabilistic matrix factorization by deriving the Gibbs updates for the side feature vectors for items (Salakhutdinov and Minh, 2008). We show that this Bayesian treatment to the constrained PMF model outperforms simple MAP estimation. We also consider e…
This paper aims at the problem of link pattern prediction in collections of objects connected by multiple relation types, where each type may play a distinct role. While common link analysis models are limited to single-type link prediction, we attempt here to capture the correlations among different relation types and reveal the impact of various relation types on performance quality. For that, we define the overall relations between object pairs as a \textit{link pattern} which consists in interaction pattern and connection structure in the network, and then use tensor formalization to joint…
We consider the probabilistic analogue to neural network matrix factorization (Dziugaite & Roy, 2015), which we construct with Bayesian neural networks and fit with variational inference. We find that a linear model fit with variational inference can attain equivalent predictive performance to the regular neural network variants on the Movielens data sets. We discuss the implications of this result, which include some suggestions on the pros and cons of using the neural network construction, as well as the variational approach to inference. Such a probabilistic approach is required, however, w…
In order to achieve state-of-the-art performance, modern machine learning techniques require careful data pre-processing and hyperparameter tuning. Moreover, given the ever increasing number of machine learning models being developed, model selection is becoming increasingly important. Automating the selection and tuning of machine learning pipelines consisting of data pre-processing methods and machine learning models, has long been one of the goals of the machine learning community. In this paper, we tackle this meta-learning task by combining ideas from collaborative filtering and Bayesian …
Inria Saclay（法国国家信息与自动化研究所萨克莱分所）；Univ. Paris Saclay（巴黎萨克雷大学）；IIIT - Delhi（德里英迪拉·甘地信息技术学院）
Co-administration of two or more drugs simultaneously can result in adverse drug reactions. Identifying drug-drug interactions (DDIs) is necessary, especially for drug development and for repurposing old drugs. DDI prediction can be viewed as a matrix completion task, for which matrix factorization (MF) appears as a suitable solution. This paper presents a novel Graph Regularized Probabilistic Matrix Factorization (GRPMF) method, which incorporates expert knowledge through a novel graph-based regularization strategy within an MF framework. An efficient and sounded optimization algorithm is pro…
Probabilistic matrix factorization (PMF) plays a crucial role in recommendation systems. It requires a large amount of user data (such as user shopping records and movie ratings) to predict personal preferences, and thereby provides users high-quality recommendation services, which expose the risk of leakage of user privacy. Differential privacy, as a provable privacy protection framework, has been applied widely to recommendation systems. It is common that different individuals have different levels of privacy requirements on items. However, traditional differential privacy can only provide a…
University of Minnesota, Twin Cities（明尼苏达大学双城分校）；Max Planck Institute for Biogeochemistry（马克斯·普朗克生物地球化学研究所）
Plant traits are a key to understanding and predicting the adaptation of ecosystems to environmental changes, which motivates the TRY project aiming at constructing a global database for plant traits and becoming a standard resource for the ecological community. Despite its unprecedented coverage, a large percentage of missing data substantially constrains joint trait analysis. Meanwhile, the trait data is characterized by the hierarchical phylogenetic structure of the plant kingdom. While factorization based matrix completion techniques have been widely used to address the missing data proble…
Polytechnique Montreal（蒙特利尔综合理工学院）；McGill University（麦吉尔大学）；Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT)（校际企业网络、物流与交通研究中心（CIRRELT））
Large-scale and multidimensional spatiotemporal data sets are becoming ubiquitous in many real-world applications such as monitoring urban traffic and air quality. Making predictions on these time series has become a critical challenge due to not only the large-scale and high-dimensional nature but also the considerable amount of missing data. In this paper, we propose a Bayesian temporal factorization (BTF) framework for modeling multidimensional time series -- in particular spatiotemporal data -- in the presence of missing values. By integrating low-rank matrix/tensor factorization and vecto…
University of Southampton（南安普顿大学）；Imperial College, London（伦敦帝国理工学院）
A key challenge in crowdsourcing is inferring the ground truth from noisy and unreliable data. To do so, existing approaches rely on collecting redundant information from the crowd, and aggregating it with some probabilistic method. However, oftentimes such methods are computationally inefficient, are restricted to some specific settings, or lack theoretical guarantees. In this paper, we revisit the problem of binary classification from crowdsourced data. Specifically we propose Streaming Bayesian Inference for Crowdsourcing (SBIC), a new algorithm that does not suffer from any of these limita…
IRIT, Université de Toulouse, CNRS（图卢兹大学IRIT研究所、法国国家科学研究中心）
We present novel understandings of the Gamma-Poisson (GaP) model, a probabilistic matrix factorization model for count data. We show that GaP can be rewritten free of the score/activation matrix. This gives us new insights about the estimation of the topic/dictionary matrix by maximum marginal likelihood estimation. In particular, this explains the robustness of this estimator to over-specified values of the factorization rank, especially its ability to automatically prune irrelevant dictionary columns, as empirically observed in previous work. The marginalization of the activation matrix lead…
Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心（MCQST））；Dahlem Center for Complex Quantum Systems, Freie Universität Berlin（柏林自由大学达勒姆复杂量子系统中心）；Freie Universität Berlin（柏林自由大学）
Tensor-network techniques have enjoyed outstanding success in physics, and have recently attracted attention in machine learning, both as a tool for the formulation of new learning algorithms and for enhancing the mathematical understanding of existing methods. Inspired by these developments, and the natural correspondence between tensor networks and probabilistic graphical models, we provide a rigorous analysis of the expressive power of various tensor-network factorizations of discrete multivariate probability distributions. These factorizations include non-negative tensor-trains/MPS, which …
Non-negative matrix factorization (NMF) has become a well-established class of methods for the analysis of non-negative data. In particular, a lot of effort has been devoted to probabilistic NMF, namely estimation or inference tasks in probabilistic models describing the data, based for example on Poisson or exponential likelihoods. When dealing with time series data, several works have proposed to model the evolution of the activation coefficients as a non-negative Markov chain, most of the time in relation with the Gamma distribution, giving rise to so-called temporal NMF models. In this pap…
Online nonnegative matrix factorization (ONMF) is a matrix factorization technique in the online setting where data are acquired in a streaming fashion and the matrix factors are updated each time. This enables factor analysis to be performed concurrently with the arrival of new data samples. In this article, we demonstrate how one can use online nonnegative matrix factorization algorithms to learn joint dictionary atoms from an ensemble of correlated data sets. We propose a temporal dictionary learning scheme for time-series data sets, based on ONMF algorithms. We demonstrate our dictionary l…
Graduate School of Informatics, Kyoto University（京都大学信息学研究生院）；Center for Advanced Intelligence Project, RIKEN（理化学研究所高级智能项目中心）
This paper presents a statistical method of single-channel speech enhancement that uses a variational autoencoder (VAE) as a prior distribution on clean speech. A standard approach to speech enhancement is to train a deep neural network (DNN) to take noisy speech as input and output clean speech. Although this supervised approach requires a very large amount of pair data for training, it is not robust against unknown environments. Another approach is to use non-negative matrix factorization (NMF) based on basis spectra trained on clean speech in advance and those adapted to noise on the fly. T…
China University of Petroleum（中国石油大学）；Minjiang University（闽江学院）；Dalian University of Technology（大连理工大学）；Federation University Australia（澳大利亚联邦大学）
The rapid growth of edge data generated by mobile devices and applications deployed at the edge of the network has exacerbated the problem of information overload. As an effective way to alleviate information overload, recommender system can improve the quality of various services by adding application data generated by users on edge devices, such as visual and textual information, on the basis of sparse rating data. The visual information in the movie trailer is a significant part of the movie recommender system. However, due to the complexity of visual information extraction, data sparsity c…
Matrix Factorization is one of the most successful recommender system techniques over the past decade. However, the classic probabilistic theory framework for matrix factorization is modeled using normal distributions. To find better probabilistic models, algorithms such as RankMat, ZeroMat and DotMat have been invented in recent years. In this paper, we model the user rating behavior in recommender system as a Poisson process, and design an algorithm that relies on no input data to solve the recommendation problem and the cold start issue at the same time. We prove the superiority of our algo…
Many modern data analysis problems involve inferences from streaming data. However, streaming data is not easily amenable to the standard probabilistic modeling approaches, which assume that we condition on finite data. We develop population variational Bayes, a new approach for using Bayesian modeling to analyze streams of data. It approximates a new type of distribution, the population posterior, which combines the notion of a population distribution of the data with Bayesian inference in a probabilistic model. We study our method with latent Dirichlet allocation and Dirichlet process mixtur…
IRIT, Université de Toulouse, CNRS（图卢兹大学 IRIT 研究所、法国国家科学研究中心）；ISAE-SUPAERO, Université de Toulouse（图卢兹大学 ISAE-SUPAERO 高等航空与航天学院）
We introduce a new non-negative matrix factorization (NMF) method for ordinal data, called OrdNMF. Ordinal data are categorical data which exhibit a natural ordering between the categories. In particular, they can be found in recommender systems, either with explicit data (such as ratings) or implicit data (such as quantized play counts). OrdNMF is a probabilistic latent factor model that generalizes Bernoulli-Poisson factorization (BePoF) and Poisson factorization (PF) applied to binarized data. Contrary to these methods, OrdNMF circumvents binarization and can exploit a more informative repr…
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…
Sparse pseudo-point approximations for Gaussian process (GP) models provide a suite of methods that support deployment of GPs in the large data regime and enable analytic intractabilities to be sidestepped. However, the field lacks a principled method to handle streaming data in which both the posterior distribution over function values and the hyperparameter estimates are updated in an online fashion. The small number of existing approaches either use suboptimal hand-crafted heuristics for hyperparameter learning, or suffer from catastrophic forgetting or slow updating when new data arrive. T…
In statistical learning for real-world large-scale data problems, one must often resort to "streaming" algorithms which operate sequentially on small batches of data. In this work, we present an analysis of the information-theoretic limits of mini-batch inference in the context of generalized linear models and low-rank matrix factorization. In a controlled Bayes-optimal setting, we characterize the optimal performance and phase transitions as a function of mini-batch size. We base part of our results on a detailed analysis of a mini-batch version of the approximate message-passing algorithm (M…
Mining massive spatio-temporal data can help a variety of real-world applications such as city capacity planning, event management, and social network analysis. The tensor representation can be used to capture the correlation between space and time and simultaneously exploit the latent structure of the spatial and temporal patterns in an unsupervised fashion. However, the increasing volume of spatio-temporal data has made it prohibitively expensive to store and analyze using tensor factorization. In this paper, we propose SkeTenSmooth, a novel tensor factorization framework that uses adaptive …
Scalable methods for nonnegative matrix factorizations of near-separable tall-and-skinny matrices
Stanford University（斯坦福大学）；Purdue University（普渡大学）；Purdue University Institute for Computational and Bindley Biosciences Center（普渡大学计算与Bindley生物科学中心）；Computer Science Mathematical Engineering（计算机科学数学工程）
Sharif University of Technology（谢里夫理工大学）；Georgia Institute of Technology（佐治亚理工学院）
Poisson factorization is a probabilistic model of users and items for recommendation systems, where the so-called implicit consumer data is modeled by a factorized Poisson distribution. There are many variants of Poisson factorization methods who show state-of-the-art performance on real-world recommendation tasks. However, most of them do not explicitly take into account the temporal behavior and the recurrent activities of users which is essential to recommend the right item to the right user at the right time. In this paper, we introduce Recurrent Poisson Factorization (RPF) framework that …
In this paper, we introduce a probabilistic model 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. Bayesian inference procedure based on Gibbs sampling is employed. We evaluate the model on several real-world datasets including MovieLens 100K and MovieLens 1M with different sizes and dimension…
Criteo AI Lab（Criteo人工智能实验室）；IRIT（图卢兹计算机科学研究所）；Université de Toulouse（图卢兹大学）；CNRS（法国国家科学研究中心）
Binary data matrices can represent many types of data such as social networks, votes, or gene expression. In some cases, the analysis of binary matrices can be tackled with nonnegative matrix factorization (NMF), where the observed data matrix is approximated by the product of two smaller nonnegative matrices. In this context, probabilistic NMF assumes a generative model where the data is usually Bernoulli-distributed. Often, a link function is used to map the factorization to the $[0,1]$ range, ensuring a valid Bernoulli mean parameter. However, link functions have the potential disadvantage …
Matrix factorization from a small number of observed entries has recently garnered much attention as the key ingredient of successful recommendation systems. One unresolved problem in this area is how to adapt current methods to handle changing user preferences over time. Recent proposals to address this issue are heuristic in nature and do not fully exploit the time-dependent structure of the problem. As a principled and general temporal formulation, we propose a dynamical state space model of matrix factorization. Our proposal builds upon probabilistic matrix factorization, a Bayesian model …
Nonnegative matrix factorization (NMF) with group sparsity constraints is formulated as a probabilistic graphical model and, assuming some observed data have been generated by the model, a feasible variational Bayesian algorithm is derived for learning model parameters. When used in a supervised learning scenario, NMF is most often utilized as an unsupervised feature extractor followed by classification in the obtained feature subspace. Having mapped the class labels to a more general concept of groups which underlie sparsity of the coefficients, what the proposed group sparse NMF model allows…
Constrained non-negative matrix factorization enabling real-time insights of $\textit{in situ}$ and high-throughput experiments
National Synchrotron Light Source II, Brookhaven National Laboratory（布鲁克海文国家实验室国家同步辐射光源II）；Center for Computational Biology, Flatiron Institute（弗拉蒂隆研究所计算生物学中心）
Spectral inference provides fast algorithms and provable optimality for latent topic analysis. But for real data these algorithms require additional ad-hoc heuristics, and even then often produce unusable results. We explain this poor performance by casting the problem of topic inference in the framework of Joint Stochastic Matrix Factorization (JSMF) and showing that previous methods violate the theoretical conditions necessary for a good solution to exist. We then propose a novel rectification method that learns high quality topics and their interactions even on small, noisy data. This metho…
Technische Universität Berlin（柏林工业大学）；Twitter（推特）；Stanford University（斯坦福大学）
We present Factorbird, a prototype of a parameter server approach for factorizing large matrices with Stochastic Gradient Descent-based algorithms. We designed Factorbird to meet the following desiderata: (a) scalability to tall and wide matrices with dozens of billions of non-zeros, (b) extensibility to different kinds of models and loss functions as long as they can be optimized using Stochastic Gradient Descent (SGD), and (c) adaptability to both batch and streaming scenarios. Factorbird uses a parameter server in order to scale to models that exceed the memory of an individual machine, and…
Probabilistic models analyze data by relying on a set of assumptions. Data that exhibit deviations from these assumptions can undermine inference and prediction quality. Robust models offer protection against mismatch between a model's assumptions and reality. We propose a way to systematically detect and mitigate mismatch of a large class of probabilistic models. The idea is to raise the likelihood of each observation to a weight and then to infer both the latent variables and the weights from data. Inferring the weights allows a model to identify observations that match its assumptions and d…
Motivated by the need of the linking records across various databases, we propose a novel graphical model based classifier that uses a mixture of Poisson distributions with latent variables. The idea is to derive insight into each pair of hypothesis records that match by inferring its underlying latent rate of error using Bayesian Modeling techniques. The novel approach of using gamma priors for learning the latent variables along with supervised labels is unique and allows for active learning. The naive assumption is made deliberately as to the independence of the fields to propose a generali…
University of Minnesota（明尼苏达大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
Grid security and open markets are two major smart grid goals. Transparency of market data facilitates a competitive and efficient energy environment, yet it may also reveal critical physical system information. Recovering the grid topology based solely on publicly available market data is explored here. Real-time energy prices are calculated as the Lagrange multipliers of network-constrained economic dispatch; that is, via a linear program (LP) typically solved every 5 minutes. Granted the grid Laplacian is a parameter of this LP, one could infer such a topology-revealing matrix upon observin…
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）
Subspace clustering (SC) aims to cluster data lying in a union of low-dimensional subspaces. Usually, SC learns an affinity matrix and then performs spectral clustering. Both steps suffer from high time and space complexity, which leads to difficulty in clustering large datasets. This paper presents a method called k-Factorization Subspace Clustering (k-FSC) for large-scale subspace clustering. K-FSC directly factorizes the data into k groups via pursuing structured sparsity in the matrix factorization model. Thus, k-FSC avoids learning affinity matrix and performing eigenvalue decomposition, …
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…
What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?
School of Informatics, University of Edinburgh（爱丁堡大学信息学院）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Eindhoven University of Technology（埃因霍温理工大学）；Graz University of Technology（格拉茨工业大学）；University of Bari Aldo Moro（巴里大学 Aldo Moro）
We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning, sparse component analysis, and non-negative matrix factorization. Our algorithm streams matrix columns while subsampling them to iteratively learn the matrix factors. At each iteration, the row dimension of a new sample is reduced by subsampling, resulting in lower time complexity compared to a simple streaming algorithm. Our method comes with convergence guara…
We introduce a novel way to incorporate prior information into (semi-) supervised non-negative matrix factorization, which we call differentiable dictionary search. It enables general, highly flexible and principled modelling of mixtures where non-linear sources are linearly mixed. We study its behavior on an audio decomposition task, and conduct an extensive, highly controlled study of its modelling capabilities.
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…
