Representing uncertainty in causal discovery is a crucial component for experimental design, and more broadly, for safe and reliable causal decision making. Bayesian Causal Discovery (BCD) offers a principled approach to encapsulating this uncertainty. Unlike non-Bayesian causal discovery, which relies on a single estimated causal graph and model parameters for assessment, evaluating BCD presents challenges due to the nature of its inferred quantity – the posterior distribution. As a result, the research community has proposed various metrics to assess the quality of the approximate posterior. However, there is, to date, no consensus on the most suitable metric(s) for evaluation. In this work, we reexamine this question by dissecting various metrics and understanding their limitations. Through extensive empirical evaluation, we find that many existing metrics fail to exhibit a strong correlation with the quality of approximation to the true posterior, especially in scenarios with low sample sizes where BCD is most desirable. We highlight the suitability (or lack thereof) of these metrics under two distinct factors: the identifiability of the underlying causal model and the quantity of available data. Both factors affect the entropy of the true posterior, indicating that the current metrics are less fitting in settings of higher entropy. Our findings underline the importance of a more nuanced evaluation of new methods by taking into account the nature of the true posterior, as well as guide and motivate the development of new evaluation procedures for this challenge.

We present Causal Amortized Active Structure Learning (CAASL), an active intervention design policy that can select interventions that are adaptive, real-time and that does not require access to the likelihood. This policy, an amortized network based on the transformer, is trained with reinforcement learning on a simulator of the design environment, and a reward function that measures how close the true causal graph is to a causal graph posterior inferred from the gathered data. On synthetic data and a single-cell gene expression simulator, we demonstrate empirically that the data acquired through our policy results in a better estimate of the underlying causal graph than alternative strategies. Our design policy successfully achieves amortized intervention design on the distribution of the training environment while also generalizing well to distribution shifts in test-time design environments. Further, our policy also demonstrates excellent zero-shot generalization to design environments with dimensionality higher than that during training, and to intervention types that it has not been trained on.

Leveraging human preferences for steering the behavior of Large Language Models (LLMs) has demonstrated notable success in recent years. Nonetheless, data selection and labeling are still a bottleneck for these systems, particularly at large scale. Hence, selecting the most informative points for acquiring human feedback may considerably reduce the cost of preference labeling and unleash the further development of LLMs. Bayesian Active Learning provides a principled framework for addressing this challenge and has demonstrated remarkable success in diverse settings. However, previous attempts to employ it for Preference Modeling did not meet such expectations. In this work, we identify that naive epistemic uncertainty estimation leads to the acquisition of redundant samples. We address this by proposing the Bayesian Active Learner for Preference Modeling (BAL-PM), a novel stochastic acquisition policy that not only targets points of high epistemic uncertainty according to the preference model but also seeks to maximize the entropy of the acquired prompt distribution in the feature space spanned by the employed LLM. Notably, our experiments demonstrate that BAL-PM requires 33\% to 68\% fewer preference labels in two popular human preference datasets and exceeds previous stochastic Bayesian acquisition policies.

We introduce a gradient-based approach for the problem of Bayesian optimal experimental design to learn causal models in a batch setting --- a critical component for causal discovery from finite data where interventions can be costly or risky. Existing methods rely on greedy approximations to construct a batch of experiments while using black-box methods to optimize over a *single target-state* pair to intervene with. In this work, we completely dispose of the black-box optimization techniques and greedy heuristics and instead propose a conceptually simple end-to-end gradient-based optimization procedure to acquire a set of optimal intervention target-value pairs. Such a procedure enables parameterization of the design space to efficiently optimize over a batch of *multi-target-state* interventions, a setting which has hitherto not been explored due to its complexity. We demonstrate that our proposed method outperforms baselines and existing acquisition strategies in both single-target and multi-target settings across a number of synthetic datasets.

Causal discovery from observational and interventional data is challenging due to limited data and non-identifiability which introduces uncertainties in estimating the underlying structural causal model (SCM). Incorporating these uncertainties and selecting optimal experiments (interventions) to perform can help to identify the true SCM faster. Existing methods in experimental design for causal discovery from limited data either rely on linear assumptions for the SCM or select only the intervention target. In this paper, we incorporate recent advances in Bayesian causal discovery into the Bayesian optimal experimental design framework, which allows for active causal discovery of nonlinear, large SCMs, while selecting both the target and the value to intervene with. We demonstrate the performance of the proposed method on synthetic graphs (Erdos-Rènyi, Scale Free) for both linear and nonlinear SCMs as well as on the \emph{in-silico} single-cell gene regulatory network dataset, DREAM.

Estimating personalized treatment effects from high-dimensional observational data is essential in situations where experimental designs are infeasible, unethical, or expensive. Existing approaches rely on fitting deep models on outcomes observed for treated and control populations. However, when measuring individual outcomes is costly, as is the case of a tumor biopsy, a sample-efficient strategy for acquiring each result is required. Deep Bayesian active learning provides a framework for efficient data acquisition by selecting points with high uncertainty. However, existing methods bias training data acquisition towards regions of non-overlapping support between the treated and control populations. These are not sample-efficient because the treatment effect is not identifiable in such regions. We introduce causal, Bayesian acquisition functions grounded in information theory that bias data acquisition towards regions with overlapping support to maximize sample efficiency for learning personalized treatment effects. We demonstrate the performance of the proposed acquisition strategies on synthetic and semi-synthetic datasets IHDP and CMNIST and their extensions, which aim to simulate common dataset biases and pathologies.

Out-of-training-distribution (OOD) scenarios are a common challenge of learning agents at deployment, typically leading to arbitrary deductions and poorly-informed decisions. In principle, detection of and adaptation to OOD scenes can mitigate their adverse effects. In this paper, we highlight the limitations of current approaches to novel driving scenes and propose an epistemic uncertainty-aware planning method, called \emph{robust imitative planning} (RIP). Our method can detect and recover from some distribution shifts, reducing the overconfident and catastrophic extrapolations in OOD scenes. If the model’s uncertainty is too great to suggest a safe course of action, the model can instead query the expert driver for feedback, enabling sample-efficient online adaptation, a variant of our method we term \emph{adaptive robust imitative planning} (AdaRIP). Our methods outperform current state-of-the-art approaches in the nuScenes \emph{prediction} challenge, but since no benchmark evaluating OOD detection and adaption currently exists to assess \emph{control}, we introduce an autonomous car novel-scene benchmark, \texttt{CARNOVEL}, to evaluate the robustness of driving agents to a suite of tasks with distribution shifts, where our methods outperform all the baselines.