论文标题
来自配对比较的同时偏好和度量学习
Simultaneous Preference and Metric Learning from Paired Comparisons
论文作者
论文摘要
在推荐系统上下文中，一个流行的偏好模型是所谓的\ emph {point}模型。在此模型中，用户将用户与$ \ mathbf {u} $以及项目集合一起表示为$ \ mathbf {x_1}，\ ldots，\ mathbf {x_n} $在常见的低维空间中。向量$ \ mathbf {u} $表示用户的“理想点”，或者代表代表假设最喜欢的项目的特征的理想组合。该模型中的基本假设是，$ \ mathbf {u} $和一个项目$ \ mathbf {x_j} $之间的距离较小，表示对$ \ mathbf {x_j} $的偏好更强。在学习理想点模型的绝大多数现有工作中，已经假定基本距离是欧几里得人。但是，这消除了功能与用户基础偏好之间的交互的任何可能性。在本文中，我们考虑了学习距离度量是未知的马哈拉诺邦度量时，学习用户偏好的理想点表示的问题。具体来说，我们提出了一种新颖的方法，可以估算用户的理想点$ \ mathbf {u} $和MAHALANOBIS度量，从配对比较的“项目$ \ Mathbf {x_i} $相比，优先于项目$ \ Mathbf {x_jj} $。这可以看作是更通用的度量学习问题的特殊情况，在某些点的位置先验不明。我们对合成和实际数据集进行了广泛的实验，以表现出我们的算法的有效性。
A popular model of preference in the context of recommendation systems is the so-called \emph{ideal point} model. In this model, a user is represented as a vector $\mathbf{u}$ together with a collection of items $\mathbf{x_1}, \ldots, \mathbf{x_N}$ in a common low-dimensional space. The vector $\mathbf{u}$ represents the user's "ideal point," or the ideal combination of features that represents a hypothesized most preferred item. The underlying assumption in this model is that a smaller distance between $\mathbf{u}$ and an item $\mathbf{x_j}$ indicates a stronger preference for $\mathbf{x_j}$. In the vast majority of the existing work on learning ideal point models, the underlying distance has been assumed to be Euclidean. However, this eliminates any possibility of interactions between features and a user's underlying preferences. In this paper, we consider the problem of learning an ideal point representation of a user's preferences when the distance metric is an unknown Mahalanobis metric. Specifically, we present a novel approach to estimate the user's ideal point $\mathbf{u}$ and the Mahalanobis metric from paired comparisons of the form "item $\mathbf{x_i}$ is preferred to item $\mathbf{x_j}$." This can be viewed as a special case of a more general metric learning problem where the location of some points are unknown a priori. We conduct extensive experiments on synthetic and real-world datasets to exhibit the effectiveness of our algorithm.
