Many dynamical systems exhibit latent states with intrinsic orderings such as "ally", "neutral" and "enemy" relationships in international relations. Such latent states are evidenced through entities' cooperative versus conflictual interactions which are similarly ordered. Models of such systems often involve state-to-action emission and state-to-state transition matrices. It is common practice to assume that the rows of these stochastic matrices are independently sampled from a Dirichlet distribution. However, this assumption discards ordinal information and treats states and actions falsely as order-invariant categoricals, which hinders interpretation and evaluation. To address this problem, we propose the Ordered Matrix Dirichlet (OMD): rows are sampled conditionally dependent such that probability mass is shifted to the right of the matrix as we move down rows. This results in a well-ordered mapping between latent states and observed action types. We evaluate the OMD in two settings: a Hidden Markov Model and a novel Bayesian Dynamic Poisson Tucker Model tailored to political event data. Models built on the OMD recover interpretable latent states and show superior forecasting performance in few-shot settings. We detail the wide applicability of the OMD to other domains where models with Dirichlet-sampled matrices are popular (e.g. topic modeling) and publish user-friendly code.
翻译:许多动态系统都表现出潜伏状态,其内在顺序如国际关系中的“完全”、“中性”和“敌人”关系等。这些潜伏状态通过实体的合作和冲突相互作用得到证明,而这些实体的相互作用也得到类似的命令。这些系统的模型往往涉及州对行动的排放和州对州之间的过渡矩阵。这种模型往往涉及州对行动的排放和州对州之间的过渡矩阵。这种假设是假设这些随机矩阵的行是独立地从dirichlet分布中抽取的。然而,这种假设抛弃了正统信息,并将国家和行动错误地作为阻碍解释和评价的定序内断。为了解决这个问题,我们建议采用有秩序的矩阵Drichlet(OMD):行的抽样取决于我们下行时的概率质量转移到矩阵右侧。这导致在潜在状态和观察到的行动类型之间有条不紊的绘图。我们用两种环境来评价OMD:隐藏的Markov模型和根据政治事件数据而定制的新的Bayesian动态Poisson Tuck模型。我们用OMD模型来建立模型,在OMD数据库的宽版版版版版用户模型上展示了高级预测性模型。