标题： 概率因子实验设计用于组合干预 显示英文标题

标题： Probabilistic Factorial Experimental Design for Combinatorial Interventions

摘要： 一种组合干预措施，由应用于单一单元的多种可能具有交互效应的治疗组成，在生物医学、工程等领域有重要的应用。 给定$p$种可能的治疗方案，执行所有可能的$2^p$种组合干预可能会非常繁琐，并且随着$p$的增加很快变得不可行。 在这里我们引入概率因子实验设计，这是从科学家如何进行实验室实验中形式化的。 在这个框架下，实验者为每种可能的治疗选择一个剂量，并将其应用于一组单元。 每个单元独立地接收从由剂量决定的乘积伯努利分布中抽取的随机治疗组合。 此外，实验者可以在多轮实验中进行此类实验，以主动的方式调整设计。 我们在一个干预模型中解决了最优实验设计问题，该模型对治疗之间施加了有界程度的交互作用。 在被动情况下，我们提供了接近最优设计的闭式解。 我们的结果证明，每种治疗的剂量为$\tfrac{1}{2}$在估计任何$k$-路交互模型时是最优的，相对于$1+O(\tfrac{\ln(n)}{n})$的因子而言，与$k$无关，并表明需要$O\big(kp^{3k}\ln(p)\big)$次观测才能准确估计该模型。 对于多轮设置，我们提供了一个接近最优的获取函数，可以进行数值优化。 我们还探讨了设计问题的几个扩展，并最终通过仿真验证了我们的发现。 显示英文摘要

摘要： A combinatorial intervention, consisting of multiple treatments applied to a single unit with potentially interactive effects, has substantial applications in fields such as biomedicine, engineering, and beyond. Given $p$ possible treatments, conducting all possible $2^p$ combinatorial interventions can be laborious and quickly becomes infeasible as $p$ increases. Here we introduce probabilistic factorial experimental design, formalized from how scientists perform lab experiments. In this framework, the experimenter selects a dosage for each possible treatment and applies it to a group of units. Each unit independently receives a random combination of treatments, sampled from a product Bernoulli distribution determined by the dosages. Additionally, the experimenter can carry out such experiments over multiple rounds, adapting the design in an active manner. We address the optimal experimental design problem within an intervention model that imposes bounded-degree interactions between treatments. In the passive setting, we provide a closed-form solution for the near-optimal design. Our results prove that a dosage of $\tfrac{1}{2}$ for each treatment is optimal up to a factor of $1+O(\tfrac{\ln(n)}{n})$ for estimating any $k$-way interaction model, regardless of $k$, and imply that $O\big(kp^{3k}\ln(p)\big)$ observations are required to accurately estimate this model. For the multi-round setting, we provide a near-optimal acquisition function that can be numerically optimized. We also explore several extensions of the design problem and finally validate our findings through simulations.