Many existing approaches to collaborative filtering can neither handle very large datasets nor easily deal with users who have very few ratings. In this paper we present the Probabilistic Matrix Factorization (PMF) model which scales linearly with the number of observations and, more importantly, performs well on the large, sparse, and very imbalanced Netflix dataset. We further extend the PMF model to include an adaptive prior on the model parameters and show how the model capacity can be controlled automatically. Finally, we introduce a constrained version of the PMF model that is based on the assumption that users who have rated similar sets of movies are likely to have similar preferences. The resulting model is able to generalize considerably better for users with very few ratings. When the predictions of multiple PMF models are linearly combined with the predictions of Restricted Boltzmann Machines models, we achieve an error rate of 0.8861, that is nearly 7% better than the score of Netflix's own system.

在本文中，我们介绍了一种用于学习非负矩阵分解（NMF）的概率模型，该模型通常用于预测数据中缺失值并在数据中找到隐藏模式，其中矩阵因子是与每个数据维度相关的潜在变量。通过在非负子空间上支持先验的先验，可以处理潜在因素的非阴性约束。采用基于Gibbs抽样的贝叶斯推理程序。我们在几个现实世界中的数据集上评估了该模型，包括Movielens 100K和Movielens 1M具有不同尺寸和尺寸的Movielens，并表明所提出的贝叶斯NMF GRRN模型可导致更好的预测，并避免与现有的贝叶斯NMF方法相比，避免过度适应。

最近，通过双段正则化的镜头，基于基于低矩阵完成的无监督学习的兴趣复兴，这显着改善了多学科机器学习任务的性能，例如推荐系统，基因型插图和图像插入。虽然双颗粒正则化贡献了成功的主要部分，但通常涉及计算昂贵的超参数调谐。为了避免这样的缺点并提高完成性能，我们提出了一种新颖的贝叶斯学习算法，该算法会自动学习与双重正规化相关的超参数，同时保证矩阵完成的低级别。值得注意的是，设计出一个小说的先验是为了促进矩阵的低级别并同时编码双电图信息，这比单圈对应物更具挑战性。然后探索所提出的先验和可能性函数之间的非平凡条件偶联性，以使有效算法在变化推理框架下得出。使用合成和现实世界数据集的广泛实验证明了针对各种数据分析任务的拟议学习算法的最先进性能。

Recommender systems provide users with personalized suggestions for products or services. These systems often rely on Collaborating Filtering (CF), where past transactions are analyzed in order to establish connections between users and products. The two more successful approaches to CF are latent factor models, which directly profile both users and products, and neighborhood models, which analyze similarities between products or users. In this work we introduce some innovations to both approaches. The factor and neighborhood models can now be smoothly merged, thereby building a more accurate combined model. Further accuracy improvements are achieved by extending the models to exploit both explicit and implicit feedback by the users. The methods are tested on the Netflix data. Results are better than those previously published on that dataset. In addition, we suggest a new evaluation metric, which highlights the differences among methods, based on their performance at a top-K recommendation task.

Item recommendation is the task of predicting a personalized ranking on a set of items (e.g. websites, movies, products). In this paper, we investigate the most common scenario with implicit feedback (e.g. clicks, purchases). There are many methods for item recommendation from implicit feedback like matrix factorization (MF) or adaptive knearest-neighbor (kNN). Even though these methods are designed for the item prediction task of personalized ranking, none of them is directly optimized for ranking. In this paper we present a generic optimization criterion BPR-Opt for personalized ranking that is the maximum posterior estimator derived from a Bayesian analysis of the problem. We also provide a generic learning algorithm for optimizing models with respect to BPR-Opt. The learning method is based on stochastic gradient descent with bootstrap sampling. We show how to apply our method to two state-of-the-art recommender models: matrix factorization and adaptive kNN. Our experiments indicate that for the task of personalized ranking our optimization method outperforms the standard learning techniques for MF and kNN. The results show the importance of optimizing models for the right criterion.

Factorization machines (FMs) are a powerful tool for regression and classification in the context of sparse observations, that has been successfully applied to collaborative filtering, especially when side information over users or items is available. Bayesian formulations of FMs have been proposed to provide confidence intervals over the predictions made by the model, however they usually involve Markov-chain Monte Carlo methods that require many samples to provide accurate predictions, resulting in slow training in the context of large-scale data. In this paper, we propose a variational formulation of factorization machines that allows us to derive a simple objective that can be easily optimized using standard mini-batch stochastic gradient descent, making it amenable to large-scale data. Our algorithm learns an approximate posterior distribution over the user and item parameters, which leads to confidence intervals over the predictions. We show, using several datasets, that it has comparable or better performance than existing methods in terms of prediction accuracy, and provide some applications in active learning strategies, e.g., preference elicitation techniques.

矩阵分解（MF）已广泛应用于建议系统中的协作过滤。它的贝叶斯变体可以得出用户和项目嵌入的后验分布，并且对稀疏评分更强大。但是，贝叶斯方法受到其后验参数的更新规则的限制，这是由于先验和可能性的结合。变量自动编码器（VAE）可以通过捕获后验参数和数据之间的复杂映射来解决此问题。但是，当前对合作过滤的VAE的研究仅根据明确的数据信息考虑映射，而隐含嵌入信息则被忽略了。在本文中，我们首先从两个观点（以用户为导向和面向项目的观点）得出了贝叶斯MF模型的贝叶斯MF模型的较低界限（ELBO）。根据肘部，我们提出了一个基于VAE的贝叶斯MF框架。它不仅利用数据，还利用嵌入信息来近似用户项目联合分布。正如肘部所建议的那样，近似是迭代的，用户和项目嵌入彼此的编码器的交叉反馈。更具体地说，在上一个迭代中采样的用户嵌入被馈送到项目端编码器中，以估计当前迭代处的项目嵌入的后验参数，反之亦然。该估计还可以关注交叉食品的嵌入式，以进一步利用有用的信息。然后，解码器通过当前重新采样的用户和项目嵌入方式通过矩阵分解重建数据。

Such systems are particularly useful for entertainment products such as movies, music, and TV shows. Many customers will view the same movie, and each customer is likely to view numerous different movies. Customers have proven willing to indicate their level of satisfaction with particular movies, so a huge volume of data is available about which movies appeal to which customers. Companies can analyze this data to recommend movies to particular customers. RecommendeR system stRategiesBroadly speaking, recommender systems are based on one of two strategies. The content filtering approach creates a profile for each user or product to characterize its nature. For example, a movie profile could include attributes regarding its genre, the participating actors, its box office popularity, and so forth. User profiles might include demographic information or answers provided on a suitable questionnaire. The profiles allow programs to associate users with matching products. Of course, content-based strategies require gathering external information that might not be available or easy to collect.A known successful realization of content filtering is the Music Genome Project, which is used for the Internet radio service Pandora.com. A trained music analyst scores M odern consumers are inundated with choices. Electronic retailers and content providers offer a huge selection of products, with unprecedented opportunities to meet a variety of special needs and tastes. Matching consumers with the most appropriate products is key to enhancing user satisfaction and loyalty. Therefore, more retailers have become interested in recommender systems, which analyze patterns of user interest in products to provide personalized recommendations that suit a user's taste. Because good personalized recommendations can add another dimension to the user experience, e-commerce leaders like Amazon.com and Netflix have made recommender systems a salient part of their websites.

我们引入了一个具有隐式规范正规化的概率模型，用于学习非负矩阵分解（NMF），该模型通常用于预测缺失值并在数据中找到隐藏模式，其中矩阵因子是与每个数据维度相关的潜在变量。潜在因素的非负限制是通过选择基于指数函数的指数密度或分布的支持的先验来处理的。采用基于Gibbs抽样的贝叶斯推理程序。我们在几个现实世界数据集上评估了该模型，包括癌症中药物敏感性的基因组学（GDSC $ ic_ {50} $）和具有不同尺寸和尺寸的基因体甲基化，并表明拟议的贝叶斯NMF GL $ _2^2^2 $ and and anGL $ _ \ infty $模型可以对不同的数据值进行强大的预测，并避免与竞争性贝叶斯NMF方法相比过度拟合。

大多数现有推荐系统仅基于评级数据，并且他们忽略了可能会增加建议质量的其他信息来源，例如文本评论或用户和项目特征。此外，这些系统的大多数仅适用于小型数据集（数千个观察）并且无法处理大型数据集（具有数百万观察结果）。我们提出了一种推荐人算法，该算法将评级建模技术（即潜在因子模型）与基于文本评论（即潜在Dirichlet分配）的主题建模方法组合，并且我们扩展了算法，使其允许添加额外的用户和项目 - 对系统的特定信息。我们使用具有不同大小的Amazon.com数据集来评估算法的性能，对应于23个产品类别。将建筑模型与四种其他型号进行比较后，我们发现将患有评级的文本评语相结合，导致更好的建议。此外，我们发现为模型添加额外的用户和项目功能会提高其预测精度，这对于中型和大数据集尤其如此。

Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse structures. Sparsity, in addition, is beneficial in terms of regularization and, thus, to avoid over-fitting. By exploiting Bayesian shrinkage priors, we devise a computationally convenient approach for high-dimensional matrix factorization. The dependence between row and column entities is modeled by inducing flexible sparse patterns within factors. The availability of external information is accounted for in such a way that structures are allowed while not imposed. Inspired by boosting algorithms, we pair the the proposed approach with a numerical strategy relying on a sequential inclusion and estimation of low-rank contributions, with data-driven stopping rule. Practical advantages of the proposed approach are demonstrated by means of a simulation study and the analysis of soccer heatmaps obtained from new generation tracking data.

This paper presents a machine learning approach to multidimensional item response theory (MIRT), a class of latent factor models that can be used to model and predict student performance from observed assessment data. Inspired by collaborative filtering, we define a general class of models that includes many MIRT models. We discuss the use of penalized joint maximum likelihood (JML) to estimate individual models and cross-validation to select the best performing model. This model evaluation process can be optimized using batching techniques, such that even sparse large-scale data can be analyzed efficiently. We illustrate our approach with simulated and real data, including an example from a massive open online course (MOOC). The high-dimensional model fit to this large and sparse dataset does not lend itself well to traditional methods of factor interpretation. By analogy to recommender-system applications, we propose an alternative "validation" of the factor model, using auxiliary information about the popularity of items consulted during an open-book exam in the course.

在本文中，我们提出了一种方法，用于预测社交媒体对等体之间的信任链接，其中一个是在多识别信任建模的人工智能面积。特别是，我们提出了一种数据驱动的多面信任信任建模，该信任建模包括许多不同的特征以进行全面分析。我们专注于展示类似用户的聚类如何实现关键新功能：支持更个性化的，从而为用户提供更准确的预测。在信任感知项目推荐任务中说明，我们在大yelp数据集的上下文中评估所提出的框架。然后，我们讨论如何提高社交媒体的可信关系的检测可以帮助在最近爆发的社交网络环境中支持在线用户的违法行为和谣言的传播。我们的结论是关于一个特别易受资助的用户基础，老年人的反思，以说明关于用户组的推理价值，期望通过通过数据分析获得的洞察力集成已知偏好的一些未来方向。

推荐系统，也称为推荐系统，是一种信息过滤系统，其尝试预测用户的额定值或偏好。本文根据类型，Pearson相关系数，基于KNN的基于KNN的基于KNN的滤波，使用TFIDF和SVD，基于TFIDF和SVD的协作滤波，基于TFIDF和SVD，基于TFIDF和SVD，基于TFIDF和SVD，基于SVD，基于TFIDF和SVD，基于SVD的协作的推荐系统技术来设计和实现完整的电影推荐系统原型。除此之外，我们还提供了一种新颖的想法，适用机器学习技术，基于流派构建电影的集群，然后观察定义了截线的惯性数量。已经描述了本工作中讨论的方法的约束，以及一个策略如何克服另一个策略的缺点。在集团镜头网站上的数据集电影镜片上完成了整个工作，其中包含100836个额定值和3683个TAG应用程序，跨越9742部电影。这些数据是由610年3月29日的610名用户在2018年3月29日和2018年9月24日创建。

多臂匪徒（MAB）提供了一种原则性的在线学习方法，以达到探索和剥削之间的平衡。由于表现出色和反馈学习低，没有学习在多种情况下采取行动，因此多臂匪徒在诸如推荐系统等应用程序中引起了广泛的关注。同样，在推荐系统中，协作过滤（CF）可以说是推荐系统中最早，最具影响力的方法。至关重要的是，新用户和不断变化的推荐项目池是推荐系统需要解决的挑战。对于协作过滤，经典方法是训练模型离线，然后执行在线测试，但是这种方法无法再处理用户偏好的动态变化，即所谓的冷启动。那么，如何在没有有效信息的情况下有效地向用户推荐项目？为了解决上述问题，已经提出了一个基于多臂强盗的协作过滤推荐系统，名为BanditMF。 BANDITMF旨在解决多军强盗算法和协作过滤中的两个挑战：（1）如何在有效信息稀缺的条件下解决冷启动问题以进行协作过滤，（2）强大社会关系域中的强盗算法问题是由独立估计与每个用户相关的未知参数并忽略用户之间的相关性引起的。

Large multilayer neural networks trained with backpropagation have recently achieved state-ofthe-art results in a wide range of problems. However, using backprop for neural net learning still has some disadvantages, e.g., having to tune a large number of hyperparameters to the data, lack of calibrated probabilistic predictions, and a tendency to overfit the training data. In principle, the Bayesian approach to learning neural networks does not have these problems. However, existing Bayesian techniques lack scalability to large dataset and network sizes. In this work we present a novel scalable method for learning Bayesian neural networks, called probabilistic backpropagation (PBP). Similar to classical backpropagation, PBP works by computing a forward propagation of probabilities through the network and then doing a backward computation of gradients. A series of experiments on ten real-world datasets show that PBP is significantly faster than other techniques, while offering competitive predictive abilities. Our experiments also show that PBP provides accurate estimates of the posterior variance on the network weights.

In this paper, we introduce Factorization Machines (FM) which are a new model class that combines the advantages of Support Vector Machines (SVM) with factorization models. Like SVMs, FMs are a general predictor working with any real valued feature vector. In contrast to SVMs, FMs model all interactions between variables using factorized parameters. Thus they are able to estimate interactions even in problems with huge sparsity (like recommender systems) where SVMs fail. We show that the model equation of FMs can be calculated in linear time and thus FMs can be optimized directly. So unlike nonlinear SVMs, a transformation in the dual form is not necessary and the model parameters can be estimated directly without the need of any support vector in the solution. We show the relationship to SVMs and the advantages of FMs for parameter estimation in sparse settings.On the other hand there are many different factorization models like matrix factorization, parallel factor analysis or specialized models like SVD++, PITF or FPMC. The drawback of these models is that they are not applicable for general prediction tasks but work only with special input data. Furthermore their model equations and optimization algorithms are derived individually for each task. We show that FMs can mimic these models just by specifying the input data (i.e. the feature vectors). This makes FMs easily applicable even for users without expert knowledge in factorization models.

在本文中，我们提出了一个新的低级矩阵分解模型，称为有界的单纯形成矩阵分解（BSSMF）。给定输入矩阵$ x $和一个分解等级$ r $，BSSMF寻找带有$ r $ lum $ $ columns的矩阵$ w $和a矩阵$ h $，带有$ r $行，以便$ x \ lot在$ w $的每一列中，都有边界，也就是说，它们属于给定的间隔，$ h $的列属于概率单纯词，即，$ h $是列随机。 BSSMF概括了非负矩阵分解（NMF）和单纯结构的矩阵分解（SSMF）。当输入矩阵$ x $的条目属于给定间隔时，BSSMF特别适合。例如，当$ x $的行代表图像时，或$ x $是一个额定矩阵，例如在Netflix和Movielens数据集中，其中$ x $的条目属于Interval $ [1,5] $。单纯结构的矩阵$ h $不仅导致易于理解的分解，从而提供了$ x $的列的软聚类，而且暗示着$ wh $的每个列的条目属于与$的列的相同间隔W $。在本文中，我们首先提出了BSSMF的快速算法，即使在$ x $中缺少数据的情况下。然后，我们为BSSMF提供可识别性条件，也就是说，我们提供了BSSMF承认独特分解的条件，直到微不足道的歧义。最后，我们说明了BSSMF对两个应用程序的有效性：在一组图像中提取特征，以及推荐系统的矩阵完成问题。

In recent years, deep neural networks have yielded immense success on speech recognition, computer vision and natural language processing. However, the exploration of deep neural networks on recommender systems has received relatively less scrutiny. In this work, we strive to develop techniques based on neural networks to tackle the key problem in recommendation -collaborative filtering -on the basis of implicit feedback.Although some recent work has employed deep learning for recommendation, they primarily used it to model auxiliary information, such as textual descriptions of items and acoustic features of musics. When it comes to model the key factor in collaborative filtering -the interaction between user and item features, they still resorted to matrix factorization and applied an inner product on the latent features of users and items.By replacing the inner product with a neural architecture that can learn an arbitrary function from data, we present a general framework named NCF, short for Neural networkbased Collaborative Filtering. NCF is generic and can express and generalize matrix factorization under its framework. To supercharge NCF modelling with non-linearities, we propose to leverage a multi-layer perceptron to learn the user-item interaction function. Extensive experiments on two real-world datasets show significant improvements of our proposed NCF framework over the state-of-the-art methods. Empirical evidence shows that using deeper layers of neural networks offers better recommendation performance.

由于本地潜在变量的数量与数据集缩放，因此难以使用分层模型中的变分推理。因此，分层模型中的推断仍然是大规模的挑战。使用与后部匹配的结构进行变形家庭是有帮助的，但由于局部分布的巨大数量，优化仍然缓慢。相反，本文建议摊销方法，其中共享参数同时表示所有本地分布。这种方法类似地是使用给定的联合分布（例如，全级高斯），但在数据集上是可行的，这些数量幅度较大。它也比使用结构化的变分布速度更快。