Jorge Loría

Lotta Mäkinen, Jorge Loría, Samuel Kaski

Meta-learning methods perform well on new within-distribution tasks but often fail when adapting to out-of-distribution target tasks, where transfer from source tasks can induce negative transfer. We propose a causally-aware Bayesian meta-learning method, by conditioning task-specific priors on precomputed latent causal task embeddings, enabling transfer based on mechanistic similarity rather than spurious correlations. Our approach explicitly considers realistic deployment settings where access to target-task data is limited, and adaptation relies on noisy (expert-provided) pairwise judgments of causal similarity between source and target tasks. We provide a theoretical analysis showing that conditioning on causal embeddings controls prior mismatch and mitigates negative transfer under task shift. Empirically, we demonstrate reductions in negative transfer and improved out-of-distribution adaptation in both controlled simulations and a large-scale real-world clinical prediction setting for cross-disease transfer, where causal embeddings align with underlying clinical mechanisms.

Carlos Fernández-Loría, Jorge Loría

Who should we prioritize for treatment when causal effects cannot be estimated? In practice, organizations often rely on predictive proxies: ads are targeted using purchase probabilities, and retention incentives are allocated using churn-risk scores. These models are not causal, but they are often used with the aim of ranking individuals by treatment effects, a task we call causal ordering. We develop a decision-focused framework to reason about this practice. We identify conditions under which proxies recover the correct effect ordering, which hold when a proxy reflects a dominant moderator of treatment effects. We show how these conditions emerge as a useful approximation in discrete choice settings, where the propensity to act without an intervention moderates persuasion. Moreover, we extend beyond this case, demonstrating that proxies capturing a non-dominant moderator can still outperform CATE estimates when they target signals that are easier to estimate precisely. Building on these insights, we introduce diagnostic tools to assess proxy usefulness in practice. Finally, we illustrate the framework in advertising, where a simple predictive proxy outperforms heterogeneous-effect estimation methods.

Zachris Björkman, Jorge Loría, Sophie Wharrie et al.

Bayesian causal discovery benefits from prior information elicited from domain experts, and in heterogeneous domains any prior knowledge would be badly needed. However, so far prior elicitation approaches have assumed a single causal graph and hence are not suited to heterogeneous domains. We propose a causal elicitation strategy for heterogeneous settings, based on Bayesian experimental design (BED) principles, and a variational mixture structure learning (VaMSL) method -- extending the earlier differentiable Bayesian structure learning (DiBS) method -- to iteratively infer mixtures of causal Bayesian networks (CBNs). We construct an informative graph prior incorporating elicited expert feedback in the inference of mixtures of CBNs. Our proposed method successfully produces a set of alternative causal models (mixture components or clusters), and achieves an improved structure learning performance on heterogeneous synthetic data when informed by a simulated expert. Finally, we demonstrate that our approach is capable of capturing complex distributions in a breast cancer database.

Carlos Fernández-Loría, Jorge Loría

Who should we prioritize for intervention when we cannot estimate intervention effects? In many applied domains (e.g., advertising, customer retention, and behavioral nudging) prioritization is guided by predictive models that estimate outcome probabilities rather than causal effects. This paper investigates when these predictions (scores) can effectively rank individuals by their intervention effects, particularly when direct effect estimation is infeasible or unreliable. We propose a conceptual framework based on amenability: an individual's latent proclivity to be influenced by an intervention. We then formalize conditions under which predictive scores serve as effective proxies for amenability. These conditions justify using non-causal scores for intervention prioritization, even when the scores do not directly estimate effects. We further show that, under plausible assumptions, predictive models can outperform causal effect estimators in ranking individuals by intervention effects. Empirical evidence from an advertising context supports our theoretical findings, demonstrating that predictive modeling can offer a more robust approach to targeting than effect estimation. Our framework suggests a shift in focus, from estimating effects to inferring who is amenable, as a practical and theoretically grounded strategy for prioritizing interventions in resource-constrained environments.

Jorge Loría, Anindya Bhadra

From the classical and influential works of Neal (1996), it is known that the infinite width scaling limit of a Bayesian neural network with one hidden layer is a Gaussian process, when the network weights have bounded prior variance. Neal's result has been extended to networks with multiple hidden layers and to convolutional neural networks, also with Gaussian process scaling limits. The tractable properties of Gaussian processes then allow straightforward posterior inference and uncertainty quantification, considerably simplifying the study of the limit process compared to a network of finite width. Neural network weights with unbounded variance, however, pose unique challenges. In this case, the classical central limit theorem breaks down and it is well known that the scaling limit is an $α$-stable process under suitable conditions. However, current literature is primarily limited to forward simulations under these processes and the problem of posterior inference under such a scaling limit remains largely unaddressed, unlike in the Gaussian process case. To this end, our contribution is an interpretable and computationally efficient procedure for posterior inference, using a conditionally Gaussian representation, that then allows full use of the Gaussian process machinery for tractable posterior inference and uncertainty quantification in the non-Gaussian regime.