The sample efficiency of Bayesian optimization algorithms depends on carefully crafted acquisition functions (AFs) guiding the sequential collection of function evaluations. The best-performing AFs can vary significantly across optimization problems, often requiring ad-hoc and problem-specific choices. This work tackles the challenge of designing novel AFs that perform well across a variety of experimental settings. Based on FunSearch, a recent work using Large Language Models (LLMs) for discovery in mathematical sciences, we propose FunBO, an LLM-based method that can be used to learn new AFs written in computer code by leveraging access to a number of evaluations for a limited set of objective functions. We provide the analytic expression of all discovered AFs and evaluate them on various global optimization benchmarks and hyperparameter optimization tasks. We show how FunBO identifies AFs that generalize well both in and out of the training distribution of functions, thus outperforming established general-purpose AFs and achieving competitive performance against AFs that are customized to specific function types and are learned via transfer-learning algorithms.

As the complexity of AI systems and their interactions with the world increases, generating explanations for their behaviour is important for safely deploying AI. For agents, the most natural abstractions for predicting behaviour attribute beliefs, intentions and goals to the system. If an agent behaves as if it has a certain goal or belief, then we can make reasonable predictions about how it will behave in novel situations, including those where comprehensive safety evaluations are untenable. How well can we infer an agent’s beliefs from their behaviour, and how reliably can these inferred beliefs predict the agent’s behaviour in novel situations? We provide a precise answer to this question under the assumption that the agent’s behaviour is guided by a world model. Our contribution is the derivation of novel bounds on the agent's behaviour in new (unseen) deployment environments, which represent a theoretical limit for predicting intentional agents from behavioural data alone. We discuss the implications of these results for several research areas including fairness and safety.

Structural learning is arguably one of the most challenging and pervasive tasks found throughout the data sciences. There exists a growing literature that studies structural learning in non-parametric settings where conditional independence constraints are taken to define the equivalence class. In the presence of unobserved confounders, it is understood that non-conditional independence constraints are imposed over the observational distribution, including certain equalities and inequalities between functionals of the joint distribution. In this paper, we develop structural learning methods that leverage additional constraints beyond conditional independences. Specifically, we first introduce a score for arbitrary graphs combining Watanabe's asymptotic expansion of the marginal likelihood and new bounds over the cardinality of the exogenous variables. Second, we show that the new score has desirable properties in terms of expressiveness and computability. In terms of expressiveness, we prove that the score captures distinct constraints imprinted in the data, including Verma's and inequalities'. In terms of computability, we show properties of score equivalence and decomposability, which allows, in principle, to break the problem of structural learning in smaller and more manageable pieces. Third, we implement this score using an MCMC sampling algorithm and test its properties in several simulation scenarios.

As many practical fields transition to provide personalized decisions, data is increasingly relevant to support the evaluation of candidate plans and policies (e.g., guidelines for the treatment of disease, government directives, etc.). In the machine learning literature, significant efforts have been put into developing machinery to predict the effectiveness of policies efficiently. The challenge is that, in practice, the effectiveness of a candidate policy is not always identifiable, i.e., not uniquely estimable from the combination of the available data and assumptions about the domain at hand (e.g., encoded in a causal graph). In this paper, we develop graphical characterizations and estimation tools to bound the effect of policies given a causal graph and observational data collected in non-identifiable settings. Specifically, our contributions are two-fold: (1) we derive analytical bounds for general probabilistic and conditional policies that are tighter than existing results, (2) we develop an estimation framework to estimate bounds from finite samples, applicable in higher-dimensional spaces and continuously-valued data. We further show that the resulting estimators have favourable statistical properties such as fast convergence and robustness to model misspecification.

A fundamental task in AI is providing performance guarantees for predictions made in unseen domains. In practice, there can be substantial uncertainty about the distribution of new data, and corresponding variability in the performance of existing predictors. Building on the theory of partial identification and transportability, this paper introduces new results for bounding the value of a functional of the target distribution, such as the generalization error of a classifiers, given data from source domains and assumptions about the data generating mechanisms, encoded in causal diagrams. Our contribution is to provide the first general estimation technique for transportability problems, adapting existing parameterization schemes such Neural Causal Models to encode the structural constraints necessary for cross-population inference. We demonstrate the expressiveness and consistency of this procedure and further propose a gradient-based optimization scheme for making scalable inferences in practice. Our results are corroborated with experiments.

Artificial intelligence systems are trained combining various observational and experimental datasets from different source sites, and are increasingly used to reason about the effectiveness of candidate policies. One common assumption in this context is that the data in source and target sites (where the candidate policy is due to be deployed) come from the same distribution. This assumption is often violated in practice, causing challenges for generalization, transportability, or external validity. Despite recent advances for determining the identifiability of the effectiveness of policies in a target domain, there are still challenges for the accurate estimation of effects from finite samples. In this paper, we develop novel graphical criteria and estimators for evaluating the effectiveness of policies (e.g., conditional, stochastic) by combining data from multiple experimental studies. Asymptotic error analysis of our estimators provides fast convergence guarantee. We empirically verified the robustness of estimators through simulations.

Failures of fairness or robustness in machine learning predictive settings can be due to undesired dependencies between covariates, outcomes and auxiliary factors of variation. A common strategy to mitigate these failures is data balancing, which attempts to remove those undesired dependencies. In this work, we define conditions on the training distribution for data balancing to lead to fair or robust models. Our results display that in many cases, the balanced distribution does not correspond to selectively removing the undesired dependencies in a causal graph of the task, leading to multiple failure modes and even interference with other mitigation techniques such as regularization. Overall, our results highlight the importance of taking the causal graph into account before performing data balancing.

Predicting the effect of unseen interventions is a fundamental research question across the data sciences. It is well established that in general such questions cannot be answered definitively from observational data. This realization has fuelled a growing literature introducing various identifying assumptions, for example in the form of a causal diagram among relevant variables. In practice, this paradigm is still too rigid for many practical applications as it is generally not possible to confidently delineate the true causal diagram. In this paper, we consider the derivation of bounds on causal effects given only observational data. We propose to take as input a less informative structure known as a Partial Ancestral Graph, which represents a Markov equivalence class of causal diagrams and is learnable from data. In this more “data-driven” setting, we provide a systematic algorithm to derive bounds on causal effects that exploit the invariant properties of the equivalence class, and that can be computed analytically. We demonstrate our method with synthetic and real data examples.

This article deals with the discovery of causal relations from a combination of observational data and qualitative assumptions about the nature of causality in the presence of unmeasured confounding. We focus on applications where unobserved variables are known to have a widespread effect on many of the observed ones, which makes the problem particularly difficult for constraint-based methods, because most pairs of variables are conditionally dependent given any other subset, rendering the causal effect unidentifiable. In this article, we show that under the principle of independent mechanisms, unobserved confounding in this setting leaves a statistical footprint in the observed data distribution that allows for disentangling spurious and causal effects. Using this insight, we demonstrate that a sparse linear Gaussian directed acyclic graph (DAG) among observed variables may be recovered approximately and propose a simple adjusted score-based causal discovery algorithm that may be implemented with general-purpose solvers and scales to high-dimensional problems. We find, in addition, that despite the conditions we pose to guarantee causal recovery, performance in practice is robust to large deviations in model assumptions, and extensions to nonlinear structural models are possible.

A unifying theme in the design of intelligent agents is to efficiently optimize a policy based on what prior knowledge of the problem is available and what actions can be taken to learn more about it. Bandits are a canonical instance of this task that has been intensely studied in the literature. Most methods, however, typically rely solely on an agent's experimentation in a single environment (or multiple closely related environments). In this paper, we relax this assumption and consider the design of bandit algorithms from a combination of batch data and qualitative assumptions about the relatedness across different environments, represented in the form of causal models. In particular, we show that it is possible to exploit invariances across environments, wherever they may occur in the underlying causal model, to consistently improve learning. The resulting bandit algorithm has a sub-linear regret bound with an explicit dependency on a term that captures how informative related environments are for the task at hand; and may have substantially lower regret than experimentation-only bandit instances.

We propose functional causal Bayesian optimization (fCBO), a method for finding interventions that optimize a target variable in a known causal graph. fCBO extends the CBO family of methods to enable functional interventions, which set a variable to be a deterministic function of other variables in the graph. fCBO models the unknown objectives with Gaussian processes whose inputs are defined in a reproducing kernel Hilbert space, thus allowing to compute distances among vector-valued functions. In turn, this enables to sequentially select functions to explore by maximizing an expected improvement acquisition functional while keeping the typical computational tractability of standard BO settings. We introduce graphical criteria that establish when considering functional interventions allows attaining better target effects, and conditions under which selected interventions are also optimal for conditional target effects. We demonstrate the benefits of the method in a synthetic and in a real-world causal graph.

Estimating counterfactual outcomes over time has the potential to unlock personalized healthcare by assisting decision-makers to answer "what-if" questions. Existing causal inference approaches typically consider regular, discrete-time intervals between observations and treatment decisions and hence are unable to naturally model irregularly sampled data, which is the common setting in practice. To handle arbitrary observation patterns, we interpret the data as samples from an underlying continuous-time process and propose to model its latent trajectory explicitly using the mathematics of controlled differential equations. This leads to a new approach, the Treatment Effect Neural Controlled Differential Equation (TE-CDE), that allows the potential outcomes to be evaluated at any time point. In addition, adversarial training is used to adjust for time-dependent confounding which is critical in longitudinal settings and is an added challenge not encountered in conventional time series. To assess solutions to this problem, we propose a controllable simulation environment based on a model of tumor growth for a range of scenarios with irregular sampling reflective of a variety of clinical scenarios. TE-CDE consistently outperforms existing approaches in all scenarios with irregular sampling.

Counterfactual estimation using synthetic controls is one of the most successful recent methodological developments in causal inference. Despite its popularity, the current description only considers time series aligned across units and synthetic controls expressed as linear combinations of observed control units. We propose a continuous-time alternative that models the latent counterfactual path explicitly using the formalism of controlled differential equations. This model is directly applicable to the general setting of irregularly-aligned multivariate time series and may be optimized in rich function spaces – thereby improving on some limitations of existing approaches.

Missing data is an important problem in machine learning practice. Starting from the premise that imputation methods should preserve the causal structure of the data, we develop a regularization scheme that encourages any baseline imputation method to be causally consistent with the underlying data generating mechanism. Our proposal is a causally-aware imputation algorithm (MIRACLE). MIRACLE iteratively refines the imputation of a baseline by simultaneously modeling the missingness generating mechanism, encouraging imputation to be consistent with the causal structure of the data. We conduct extensive experiments on synthetic and a variety of publicly available datasets to show that MIRACLE is able to consistently improve imputation over a variety of benchmark methods across all three missingness scenarios: at random, completely at random, and not at random.

We present a general framework for kernel hypothesis testing on distributions of sets of individual examples. Sets may represent many common data sources such as groups of observations in time series, collections of words in text or a batch of images of a given phenomenon. This observation pattern, however, differs from the common assumptions required for hypothesis testing: each set differs in size, may have differing levels of noise, and also may incorporate nuisance variability, irrelevant for the analysis of the phenomenon of interest; all features that bias test decisions if not accounted for. In this paper, we propose to interpret sets as independent samples from a collection of latent probability distributions, and introduce kernel two-sample and independence tests in this latent space of distributions. We prove the consistency of these tests and observe them to outperform in a wide range of synthetic and real data experiments, where previously heuristics were needed for feature extraction and testing.

Hypothesis testing can help decision-making by quantifying distributional differences between two populations from observational data. However, these tests may inherit biases embedded in the data collection mechanism (some instances often being systematically more likely included in our sample) and consistently reproduce biased decisions. We propose a two-sample test that adjusts for selection bias by accounting for differences in marginal distributions of confounding variables. Our test statistic is a weighted distance between samples embedded in a reproducing kernel Hilbert space, whose balancing weights provably correct for bias. We establish the asymptotic distributions under null and alternative hypotheses, and prove the consistency of empirical approximations to the underlying population quantity. We conclude with performance evaluations on artificial data and experiments on treatment effect studies from economics.

Comorbid diseases co-occur and progress via complex temporal patterns that vary among individuals. In electronic medical records, we only observe onsets of diseases, but not their triggering comorbidities — i.e., the mechanisms underlying temporal relations between diseases need to be inferred. Learning such temporal patterns from event data is crucial for understanding disease pathology and predicting prognoses. To this end, we develop deep diffusion processes (DDP) to model ’dynamic comorbidity networks’, i.e., the temporal relationships between comorbid disease onsets expressed through a dynamic graph. A DDP comprises events modelled as a multi-dimensional point process, with an intensity function parameterized by the edges of a dynamic weighted graph. The graph structure is modulated by a neural network that maps patient history to edge weights, enabling rich temporal representations for disease trajectories. The DDP parameters decouple into clinically meaningful components, which enables serving the dual purpose of accurate risk prediction and intelligible representation of disease pathology. We illustrate these features in experiments using cancer registry data.

The choice of making an intervention depends on its potential benefit or harm in comparison to alternatives. Estimating the likely outcome of alternatives from observational data is a challenging problem as all outcomes are never observed, and selection bias precludes the direct comparison of differently intervened groups. Despite their empirical success, we show that algorithms that learn domain-invariant representations of inputs (on which to make predictions) are often inappropriate, and develop generalization bounds that demonstrate the dependence on domain overlap and highlight the need for invertible latent maps. Based on these results, we develop a deep kernel regression algorithm and posterior regularization framework that substantially outperforms the state-of-the-art on a variety of benchmarks data sets.

Using electronic medical records to learn personalized risk trajectories poses significant challenges because often very few samples are available in a patient’s history, and, when available, their information content is highly diverse. In this article, we consider how to integrate sparsely sampled longitudinal data, missing measurements informative of the underlying health status, and static information to estimate (dynamically, as new information becomes available) personalized survival distributions. We achieve this by developing a nonparametric probabilistic model that generates survival trajectories, and corresponding uncertainty estimates, from an ensemble of Bayesian trees in which time is incorporated explicitly to learn variable interactions over time, without needing to specify the longitudinal process beforehand. As such, the changing influence on survival of variables over time is inferred from the data directly, which we analyze with post-processing statistics derived from our model.

Survival models derived from health care data are an important support to inform critical screening and therapeutic decisions. Most models however, do not generalize to populations outside the marginal and conditional distribution assumptions for which they were derived. This presents a significant barrier to the deployment of machine learning techniques into wider clinical practice as most medical studies are data scarce, especially for the analysis of time-to-event outcomes. In this work we propose a survival prediction model that is able to improve predictions on a small data domain of interest - such as a local hospital - by leveraging related data from other domains - such as data from other hospitals. We construct an ensemble of weak survival predictors which iteratively adapt the marginal distributions of the source and target data such that similar source patients contribute to the fit and ultimately improve predictions on target patients of interest. This represents the first boosting-based transfer learning algorithm in the survival analysis literature. We demonstrate the performance and utility of our algorithm on synthetic and real healthcare data collected at various locations.

We consider the hypothesis testing problem of detecting conditional dependence, with a focus on high-dimensional feature spaces. Our contribution is a new test statistic based on samples from a generative adversarial network designed to approximate directly a conditional distribution that encodes the null hypothesis, in a manner that maximizes power (the rate of true negatives). We show that such an approach requires only that density approximation be viable in order to ensure that we control type I error (the rate of false positives); in particular, no assumptions need to be made on the form of the distributions or feature dependencies. Using synthetic simulations with high-dimensional data we demonstrate significant gains in power over competing methods. In addition, we illustrate the use of our test to discover causal markers of disease in genetic data.

We study the problem of personalizing survival estimates of patients in heterogeneous populations for clinical decision support. The desiderata are to improve predictions by making them personalized to the patient-at-hand, to better understand diseases and their risk factors, and to provide interpretable model outputs to clinicians. To enable accurate survival prognosis in heterogeneous populations we propose a novel probabilistic survival model which flexibly captures individual traits through a hierarchical latent variable formulation. Survival paths are estimated by jointly sampling the location and shape of the individual survival distribution resulting in patient-specific curves with quantifiable uncertainty estimates. An understanding of model predictions is paramount in medical practice where decisions have major social consequences. We develop a personalized interpreter that can be used to test the effect of covariates on each individual patient, in contrast to traditional methods that focus on population average effects. We extensively validated the proposed approach in various clinical settings, with a special focus on cardiovascular disease.

Many chronic diseases possess a shared biology. Therapies designed for patients at risk of multiple diseases need to account for the shared impact they may have on related diseases to ensure maximum overall well-being. Learning from data in this setting differs from classical survival analysis methods since the incidence of an event of interest may be obscured by other related competing events. We develop a semi-parametric Bayesian regression model for survival analysis with competing risks, which can be used for jointly assessing a patient’s risk of multiple (competing) adverse outcomes. We construct a Hierarchical Bayesian Mixture (HBM) model to describe survival paths in which a patient’s covariates influence both the estimation of the type of adverse event and the subsequent survival trajectory through Multivariate Random Forests. In addition variable importance measures, which are essential for clinical interpretability are induced naturally by our model. We aim with this setting to provide accurate individual estimates but also interpretable conclusions for use as a clinical decision support tool. We compare our method with various state-of-the-art benchmarks on both synthetic and clinical data.

The co-occurrence of multiple diseases among the general population is an important problem as those patients have more risk of complications and represent a large share of health care expenditure. Learning to predict time-to-event probabilities for these patients is a challenging problem because the risks of events are correlated (there are competing risks) with often only few patients experiencing individual events of interest, and of those only a fraction are actually observed in the data. We introduce in this paper a survival model with the flexibility to leverage a common representation of related events that is designed to correct for the strong imbalance in observed outcomes. The procedure is sequential: outcome-specific survival distributions form the components of nonparametric multivariate estimators which we combine into an ensemble in such a way as to ensure accurate predictions on all outcome types simultaneously. Our algorithm is general and represents the first boosting-like method for time-to-event data with multiple outcomes. We demonstrate the performance of our algorithm on synthetic and real data.