| Zusammenfassung: | Transforming a causal system from a given initial state to a desired target state is an important task permeating multiple fields including control theory, biology, and materials science. In causal models, such transformations can be achieved by performing a set of interventions. When the space of possible interventions is large, making an exhaustive search infeasible, experimental design strategies are needed. In this context, encoding the causal relationships between the variables, and thus the effect of interventions on the system, is critical in order to identify desirable interventions more efficiently. In this thesis, we develop an iterative causal method to identify optimal interventions, as measured by the discrepancy between the post-interventional mean of the distribution and a desired target mean. We formulate an active learning strategy that uses the samples obtained so far from different interventions to update the belief about the underlying causal model, as well as to identify the samples that are most informative about optimal interventions and thus should be acquired in the next batch. The approach employs a Bayesian update for the causal model and prioritizes informative interventions using a carefully designed, causally informed acquisition function. Moreover, the introduced acquisition function is evaluated in closed form, allowing for efficient optimization. The resulting algorithms are also theoretically grounded with information-theoretic bounds and provable consistency results. We illustrate the method on both synthetic data and real-world biological data, more precisely gene expression data from Perturb-CITE-seq experiments. In this case the goal is to identify optimal perturbations to induce a specific cell state transition; the proposed causal approach is observed to achieve better sample efficiency compared to several baselines. In both cases we observe that the causally informed acquisition function notably outperforms existing criteria allowing for optimal intervention design with significantly less experiments.
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