The recovery of causal effects in structural models with missing data often relies on $m$-graphs, which assume that missingness mechanisms do not directly influence substantive variables. Yet, in many real-world settings, missing data can alter decision-making processes, as the absence of key information may affect downstream actions and states. To overcome this limitation, we introduce $lm$-SCMs and $lm$-graphs, which extend $m$-graphs by integrating a label set that represents relevant context-specific independencies (CSI), accounting for mechanism shifts induced by missingness. We define two causal effects within these systems: the Full Average Treatment Effect (FATE), which reflects the effect in a hypothetical scenario had no data been missing, and the Natural Average Treatment Effect (NATE), which captures the effect under the unaltered CSIs in the system. We propose recovery criteria for these queries and present doubly-robust estimators for a graphical model inspired by a real-world application. Simulations highlight key differences between these estimands and estimation methods. Findings from the application case suggest a small effect of ADHD treatment upon test achievement among Norwegian children, with a slight effect shift due to missing pre-tests scores.

Deep learning methods, including deep multiple instance learning methods, have been criticized for their limited ability to incorporate domain knowledge. A reason that knowledge incorporation is challenging in deep learning is that the models usually lack a mapping between their model components and the entities of the domain, making it a non-trivial task to incorporate probabilistic prior information. In this work, we show that such a mapping between domain entities and model components can be defined for a multiple instance learning setting and propose a framework DeeMILIP that encompasses multiple strategies to exploit this mapping for prior knowledge incorporation. We motivate and formalize these strategies from a probabilistic perspective. Experiments on an immune-based diagnostics case show that our proposed strategies allow to learn generalizable models even in settings with weak signals, limited dataset size, and limited compute.

We introduce Locally Interpretable Tree Boosting (LitBoost), a tree boosting model tailored to applications where the data comes from several heterogeneous yet known groups with a limited number of observations per group. LitBoost constraints the complexity of a Gradient Boosted Trees model in a way that allows us to express the final model as a set of local Generalized Additive Models, yielding significant interpretability benefits while still maintaining some of the predictive power of a Gradient Boosted Trees model. We use house price prediction as a motivating example and demonstrate the performance of LitBoost on a data set of N=14382 observations from 15 different city districts in Oslo (Norway). We also test the robustness of LitBoost in an extensive simulation study on a synthetic data set.

We present a novel Bayesian method for the challenging task of estimating causal effects from passively observed data when the underlying causal DAG structure is unknown. To rigorously capture the inherent uncertainty associated with the estimate, our method builds a Bayesian posterior distribution of the linear causal effect, by integrating Bayesian linear regression and averaging over DAGs. For computing the exact posterior for all cause-effect variable pairs, we give an algorithm that runs in time O(3d d) for d variables, being feasible up to 20 variables. We also give a variant that computes the posterior probabilities of all pairwise ancestor relations within the same time complexity, significantly improving the fastest previous algorithm. In simulations, our Bayesian method outperforms previous methods in estimation accuracy, especially for small sample sizes. We further show that our method for effect estimation is well-adapted for detecting strong causal effects markedly deviating from zero, while our variant for computing posteriors of ancestor relations is the method of choice for detecting the mere existence of a causal relation. Finally, we apply our method on observational flow cytometry data, detecting several causal relations that concur with previous findings from experimental data.

We give methods for Bayesian inference of directed acyclic graphs, DAGs, and the induced causal effects from passively observed complete data. Our methods build on a recent Markov chain Monte Carlo scheme for learning Bayesian networks, which enables efficient approximate sampling from the graph posterior, provided that each node is assigned a small number K of candidate parents. We present algorithmic techniques to significantly reduce the space and time requirements, which make the use of substantially larger values of K feasible. Furthermore, we investigate the problem of selecting the candidate parents per node so as to maximize the covered posterior mass. Finally, we combine our sampling method with a novel Bayesian approach for estimating causal effects in linear Gaussian DAG models. Numerical experiments demonstrate the performance of our methods in detecting ancestor–descendant relations, and in causal effect estimation our Bayesian method is shown to outperform previous approaches.

We investigate the problem of learning the structure of a Markov network from data. It is shown that the structure of such networks can be described in terms of constraints which enables the use of existing solver technology with optimization capabilities to compute optimal networks starting from initial scores computed from the data. To achieve efficient encodings, we develop a novel characterization of Markov network structure using a balancing condition on the separators between cliques forming the network. The resulting translations into propositional satisfiability and its extensions such as maximum satisfiability, satisfiability modulo theories, and answer set programming, enable us to prove the optimality of networks which have been previously found by stochastic search.