Scientific hypotheses typically concern specific aspects of complex, imperfectly understood or entirely unknown mechanisms, such as the effect of gene expression levels on phenotypes or how microbial communities influence environmental health. Such queries are inherently causal (rather than purely associational), but in many settings, experiments can not be conducted directly on the target variables of interest, but are indirect. Therefore, they perturb the target variable, but do not remove potential confounding factors. If, additionally, the resulting experimental measurements are high-dimensional and the studied mechanisms nonlinear, the query of interest is generally not identified. We develop an adaptive strategy to design indirect experiments that optimally inform a targeted query about the ground truth mechanism in terms of sequentially narrowing the gap between an upper and lower bound on the query. While the general formulation consists of a bi-level optimization procedure, we derive an efficiently estimable analytical kernel-based estimator of the bounds for the causal effect, a query of key interest, and demonstrate the efficacy of our approach in confounded, multivariate, nonlinear synthetic settings.

Instrumental variable (IV) methods are used to estimate causal effects in settings with unobserved confounding, where we cannot directly experiment on the treatment variable. Instruments are variables which only affect the outcome indirectly via the treatment variable(s). Most IV applications focus on low-dimensional treatments and crucially require at least as many instruments as treatments. This assumption is restrictive: in the natural sciences we often seek to infer causal effects of high-dimensional treatments (e.g., the effect of gene expressions or microbiota on health and disease), but can only run few experiments with a limited number of instruments (e.g., drugs or antibiotics). In such under-specified problems, the full treatment effect is not identifiable in a single experiment even in the linear case. We show that one can still reliably recover the projection of the treatment effect onto the instrumented subspace and develop techniques to consistently combine such partial estimates from different sets of instruments. We then leverage our combined estimators in an algorithm that iteratively proposes the most informative instruments at each round of experimentation to maximize the overall information about the full causal effect.

Supervised learning, such as regression and classification, is an essential tool for analyzing modern high-throughput sequencing data, for example in microbiome research. However, due to the compositionality and sparsity, existing techniques are often inadequate. Either they rely on extensions of the linear log-contrast model (which adjust for compositionality but cannot account for complex signals or sparsity) or they are based on black-box machine learning methods (which may capture useful signals, but lack interpretability due to the compositionality). We propose KernelBiome, a kernel-based nonparametric regression and classification framework for compositional data. It is tailored to sparse compositional data and is able to incorporate prior knowledge, such as phylogenetic structure. KernelBiome captures complex signals, including in the zero-structure, while automatically adapting model complexity. We demonstrate on par or improved predictive performance compared with state-of-the-art machine learning methods on 33 publicly available microbiome datasets. Additionally, our framework provides two key advantages: (i) We propose two novel quantities to interpret contributions of individual components and prove that they consistently estimate average perturbation effects of the conditional mean, extending the interpretability of linear log-contrast coefficients to nonparametric models. (ii) We show that the connection between kernels and distances aids interpretability and provides a data-driven embedding that can augment further analysis. KernelBiome is available as an open-source Python package on PyPI and at https://github.com/shimenghuang/KernelBiome.