论文标题
项目响应理论的光谱方法
A Spectral Approach to Item Response Theory
论文作者
论文摘要
Rasch模型是\ emph {item响应理论}中最基本的模型之一，并且具有从教育测试到推荐系统的广泛应用。在带有$ n $用户和$ m $项目的宇宙中，Rasch型号假设用户$ l $的二进制响应$ x_ {li} \ in \ {0,1 \} $带有参数$θ^*_ l $对项目$ i $的参数$ i $β^*$β^*_ i $（例如，一个solvity assy a soligy a sosity a Movie a Movie a Movie a Movie a Movie a Movie Assips a paramite $θ^*_ l $ $ \ pr（x_ {li} = 1）= 1/（1 + \ exp { - （θ^*_ l -β^*_ i）}）$。在本文中，我们建议为此著名模型（即估计$β^*$）的\ emph {新项目估计}算法。我们算法的核心是计算在项目项目图上定义的马尔可夫链的固定分布。我们通过有限样本错误保证了我们的算法贡献，这是文献中的第一个，表明我们的算法是一致的，并且具有良好的最佳属性。我们讨论实践修改，以加速和鲁棒化从业者可以采用的算法。从小型教育测试数据集到大型推荐系统数据集的合成和现实数据集的实验表明，我们的算法具有可扩展，准确且具有文献中最常用方法的竞争性。
The Rasch model is one of the most fundamental models in \emph{item response theory} and has wide-ranging applications from education testing to recommendation systems. In a universe with $n$ users and $m$ items, the Rasch model assumes that the binary response $X_{li} \in \{0,1\}$ of a user $l$ with parameter $θ^*_l$ to an item $i$ with parameter $β^*_i$ (e.g., a user likes a movie, a student correctly solves a problem) is distributed as $\Pr(X_{li}=1) = 1/(1 + \exp{-(θ^*_l - β^*_i)})$. In this paper, we propose a \emph{new item estimation} algorithm for this celebrated model (i.e., to estimate $β^*$). The core of our algorithm is the computation of the stationary distribution of a Markov chain defined on an item-item graph. We complement our algorithmic contributions with finite-sample error guarantees, the first of their kind in the literature, showing that our algorithm is consistent and enjoys favorable optimality properties. We discuss practical modifications to accelerate and robustify the algorithm that practitioners can adopt. Experiments on synthetic and real-life datasets, ranging from small education testing datasets to large recommendation systems datasets show that our algorithm is scalable, accurate, and competitive with the most commonly used methods in the literature.
