Lars Lorch

Lars Lorch, Scott Sussex, Jonas Rothfuss et al.

Inferring causal structure poses a combinatorial search problem that typically involves evaluating structures with a score or independence test. The resulting search is costly, and designing suitable scores or tests that capture prior knowledge is difficult. In this work, we propose to amortize causal structure learning. Rather than searching over structures, we train a variational inference model to directly predict the causal structure from observational or interventional data. This allows our inference model to acquire domain-specific inductive biases for causal discovery solely from data generated by a simulator, bypassing both the hand-engineering of suitable score functions and the search over graphs. The architecture of our inference model emulates permutation invariances that are crucial for statistical efficiency in structure learning, which facilitates generalization to significantly larger problem instances than seen during training. On synthetic data and semisynthetic gene expression data, our models exhibit robust generalization capabilities when subject to substantial distribution shifts and significantly outperform existing algorithms, especially in the challenging genomics domain. Our code and models are publicly available at: https://github.com/larslorch/avici.

Christian Toth, Lars Lorch, Christian Knoll et al. · eth-zurich

Causal discovery and causal reasoning are classically treated as separate and consecutive tasks: one first infers the causal graph, and then uses it to estimate causal effects of interventions. However, such a two-stage approach is uneconomical, especially in terms of actively collected interventional data, since the causal query of interest may not require a fully-specified causal model. From a Bayesian perspective, it is also unnatural, since a causal query (e.g., the causal graph or some causal effect) can be viewed as a latent quantity subject to posterior inference -- other unobserved quantities that are not of direct interest (e.g., the full causal model) ought to be marginalized out in this process and contribute to our epistemic uncertainty. In this work, we propose Active Bayesian Causal Inference (ABCI), a fully-Bayesian active learning framework for integrated causal discovery and reasoning, which jointly infers a posterior over causal models and queries of interest. In our approach to ABCI, we focus on the class of causally-sufficient, nonlinear additive noise models, which we model using Gaussian processes. We sequentially design experiments that are maximally informative about our target causal query, collect the corresponding interventional data, and update our beliefs to choose the next experiment. Through simulations, we demonstrate that our approach is more data-efficient than several baselines that only focus on learning the full causal graph. This allows us to accurately learn downstream causal queries from fewer samples while providing well-calibrated uncertainty estimates for the quantities of interest.

Alexander Hägele, Jonas Rothfuss, Lars Lorch et al.

Inferring causal structures from experimentation is a central task in many domains. For example, in biology, recent advances allow us to obtain single-cell expression data under multiple interventions such as drugs or gene knockouts. However, the targets of the interventions are often uncertain or unknown and the number of observations limited. As a result, standard causal discovery methods can no longer be reliably used. To fill this gap, we propose a Bayesian framework (BaCaDI) for discovering and reasoning about the causal structure that underlies data generated under various unknown experimental or interventional conditions. BaCaDI is fully differentiable, which allows us to infer the complex joint posterior over the intervention targets and the causal structure via efficient gradient-based variational inference. In experiments on synthetic causal discovery tasks and simulated gene-expression data, BaCaDI outperforms related methods in identifying causal structures and intervention targets.

Lars Lorch, Andreas Krause, Bernhard Schölkopf

We develop a novel approach towards causal inference. Rather than structural equations over a causal graph, we learn stochastic differential equations (SDEs) whose stationary densities model a system's behavior under interventions. These stationary diffusion models do not require the formalism of causal graphs, let alone the common assumption of acyclicity. We show that in several cases, they generalize to unseen interventions on their variables, often better than classical approaches. Our inference method is based on a new theoretical result that expresses a stationarity condition on the diffusion's generator in a reproducing kernel Hilbert space. The resulting kernel deviation from stationarity (KDS) is an objective function of independent interest.

Weronika Ormaniec, Scott Sussex, Lars Lorch et al.

Synthetic datasets generated by structural causal models (SCMs) are commonly used for benchmarking causal structure learning algorithms. However, the variances and pairwise correlations in SCM data tend to increase along the causal ordering. Several popular algorithms exploit these artifacts, possibly leading to conclusions that do not generalize to real-world settings. Existing metrics like $\operatorname{Var}$-sortability and $\operatorname{R^2}$-sortability quantify these patterns, but they do not provide tools to remedy them. To address this, we propose internally-standardized structural causal models (iSCMs), a modification of SCMs that introduces a standardization operation at each variable during the generative process. By construction, iSCMs are not $\operatorname{Var}$-sortable. We also find empirical evidence that they are mostly not $\operatorname{R^2}$-sortable for commonly-used graph families. Moreover, contrary to the post-hoc standardization of data generated by standard SCMs, we prove that linear iSCMs are less identifiable from prior knowledge on the weights and do not collapse to deterministic relationships in large systems, which may make iSCMs a useful model in causal inference beyond the benchmarking problem studied here. Our code is publicly available at: https://github.com/werkaaa/iscm.

Lars Lorch, Heiner Kremer, William Trouleau et al.

Multiple lines of evidence strongly suggest that infection hotspots, where a single individual infects many others, play a key role in the transmission dynamics of COVID-19. However, most of the existing epidemiological models fail to capture this aspect by neither representing the sites visited by individuals explicitly nor characterizing disease transmission as a function of individual mobility patterns. In this work, we introduce a temporal point process modeling framework that specifically represents visits to the sites where individuals get in contact and infect each other. Under our model, the number of infections caused by an infectious individual naturally emerges to be overdispersed. Using an efficient sampling algorithm, we demonstrate how to estimate the transmission rate of infectious individuals at the sites they visit and in their households using Bayesian optimization and longitudinal case data. Simulations using fine-grained and publicly available demographic data and site locations from Bern, Switzerland showcase the flexibility of our framework. To facilitate research and analyses of other cities and regions, we release an open-source implementation of our framework.

Nora Schneider, Lars Lorch, Niki Kilbertus et al.

We consider the problem of predicting perturbation effects via causal models. In many applications, it is a priori unknown which mechanisms of a system are modified by an external perturbation, even though the features of the perturbation are available. For example, in genomics, some properties of a drug may be known, but not their causal effects on the regulatory pathways of cells. We propose a generative intervention model (GIM) that learns to map these perturbation features to distributions over atomic interventions in a jointly-estimated causal model. Contrary to prior approaches, this enables us to predict the distribution shifts of unseen perturbation features while gaining insights about their mechanistic effects in the underlying data-generating process. On synthetic data and scRNA-seq drug perturbation data, GIMs achieve robust out-of-distribution predictions on par with unstructured approaches, while effectively inferring the underlying perturbation mechanisms, often better than other causal inference methods.

Stratis Tsirtsis, Abir De, Lars Lorch et al.

Testing is recommended for all close contacts of confirmed COVID-19 patients. However, existing group testing methods are oblivious to the circumstances of contagion provided by contact tracing. Here, we build upon a well-known semi-adaptive pool testing method, Dorfman's method with imperfect tests, and derive a simple group testing method based on dynamic programming that is specifically designed to use the information provided by contact tracing. Experiments using a variety of reproduction numbers and dispersion levels, including those estimated in the context of the COVID-19 pandemic, show that the pools found using our method result in a significantly lower number of tests than those found using standard Dorfman's method, especially when the number of contacts of an infected individual is small. Moreover, our results show that our method can be more beneficial when the secondary infections are highly overdispersed.

Lars Lorch, Jonas Rothfuss, Bernhard Schölkopf et al.

Bayesian structure learning allows inferring Bayesian network structure from data while reasoning about the epistemic uncertainty -- a key element towards enabling active causal discovery and designing interventions in real world systems. In this work, we propose a general, fully differentiable framework for Bayesian structure learning (DiBS) that operates in the continuous space of a latent probabilistic graph representation. Contrary to existing work, DiBS is agnostic to the form of the local conditional distributions and allows for joint posterior inference of both the graph structure and the conditional distribution parameters. This makes our formulation directly applicable to posterior inference of complex Bayesian network models, e.g., with nonlinear dependencies encoded by neural networks. Using DiBS, we devise an efficient, general purpose variational inference method for approximating distributions over structural models. In evaluations on simulated and real-world data, our method significantly outperforms related approaches to joint posterior inference.

Wanqian Yang, Lars Lorch, Moritz A. Graule et al.

Domains where supervised models are deployed often come with task-specific constraints, such as prior expert knowledge on the ground-truth function, or desiderata like safety and fairness. We introduce a novel probabilistic framework for reasoning with such constraints and formulate a prior that enables us to effectively incorporate them into Bayesian neural networks (BNNs), including a variant that can be amortized over tasks. The resulting Output-Constrained BNN (OC-BNN) is fully consistent with the Bayesian framework for uncertainty quantification and is amenable to black-box inference. Unlike typical BNN inference in uninterpretable parameter space, OC-BNNs widen the range of functional knowledge that can be incorporated, especially for model users without expertise in machine learning. We demonstrate the efficacy of OC-BNNs on real-world datasets, spanning multiple domains such as healthcare, criminal justice, and credit scoring.

Wanqian Yang, Lars Lorch, Moritz A. Graule et al.

Bayesian neural network (BNN) priors are defined in parameter space, making it hard to encode prior knowledge expressed in function space. We formulate a prior that incorporates functional constraints about what the output can or cannot be in regions of the input space. Output-Constrained BNNs (OC-BNN) represent an interpretable approach of enforcing a range of constraints, fully consistent with the Bayesian framework and amenable to black-box inference. We demonstrate how OC-BNNs improve model robustness and prevent the prediction of infeasible outputs in two real-world applications of healthcare and robotics.

Lars Lorch, Abir De, Samir Bhatt et al.

We approach the development of models and control strategies of susceptible-infected-susceptible (SIS) epidemic processes from the perspective of marked temporal point processes and stochastic optimal control of stochastic differential equations (SDEs) with jumps. In contrast to previous work, this novel perspective is particularly well-suited to make use of fine-grained data about disease outbreaks and lets us overcome the shortcomings of current control strategies. Our control strategy resorts to treatment intensities to determine who to treat and when to do so to minimize the amount of infected individuals over time. Preliminary experiments with synthetic data show that our control strategy consistently outperforms several alternatives. Looking into the future, we believe our methodology provides a promising step towards the development of practical data-driven control strategies of epidemic processes.