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 leads
in turn to a new Monte Carlo Expectation-Maximization algorithm with favorable
properties.

本文提出了 Gamma-Poisson 模型及其最大边际似然估计和 Monte Carlo Expectation-Maximization 算法等内容，并阐明这种方法的鲁棒性和自动减枝等优点。

Gamma-Poisson 矩阵分解的闭式边缘似然

Closed-form Marginal Likelihood in Gamma-Poisson Matrix Factorization

Collaborative filtering is an effective recommendation approach in which the
preference of a user on an item is predicted based on the preferences of other
users with similar interests. A big challenge in using collaborative filtering
methods is the data sparsity problem which often arises because each user
typically only rates very few items and hence the rating matrix is extremely
sparse. In this paper, we address this problem by considering multiple
collaborative filtering tasks in different domains simultaneously and
exploiting the relationships between domains. We refer to it as a multi-domain
collaborative filtering (MCF) problem. To solve the MCF problem, we propose a
probabilistic framework which uses probabilistic matrix factorization to model
the rating problem in each domain and allows the knowledge to be adaptively
transferred across different domains by automatically learning the correlation
between domains. We also introduce the link function for different domains to
correct their biases. Experiments conducted on several real-world applications
demonstrate the effectiveness of our methods when compared with some
representative methods.

本文介绍了多向领域协同过滤问题，通过概率矩阵分解模型不仅考虑了数据稀疏性问题，还能在不同领域自适应地传递知识，实验表明其在实际应用中的有效性。

多领域协同过滤

Multi-Domain Collaborative Filtering

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 with Gaussian
priors. We utilize results in state tracking, such as the Kalman filter, to
provide accurate recommendations in the presence of both process and
measurement noise. We show how system parameters can be learned via
expectation-maximization and provide comparisons to current published
techniques.

提出一种基于状态空间模型的矩阵分解方法，可解决处理用户随时间变化的推荐系统问题，利用卡尔曼滤波器等技术提供准确的推荐结果，通过期望最大化算法学习系统参数，并与当前发表的技术进行比较。

动态矩阵分解：一种状态空间方法

Dynamic Matrix Factorization: A State Space Approach

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 together
multiple PMF problems via Gaussian process priors. We replace scalar latent
features with functions that vary over the space of side information. The GP
priors on these functions require them to vary smoothly and share information.
We successfully use this new method to predict the scores of professional
basketball games, where side information about the venue and date of the game
are relevant for the outcome.

通过高斯过程先验相结合，用函数替代标量潜在特征，以实现信息的融合处理，从而成功地预测了与篮球比赛结果相关的比赛地点和日期等侧面信息。