Mehran Kazemi, Bahare Fatemi, Hritik Bansal, John Palowitch, Chrysovalantis Anastasiou, Sanket Vaibhav Mehta, Lalit K Jain, Virginia Aglietti, Disha Jindal, Peter Chen, Nishanth Dikkala, Gladys Tyen, Xin Liu, Uri Shalit, Silvia Chiappa, Kate Olszewska, Yi Tay, Vinh Q. Tran, Quoc V Le, Orhan Firat. Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2025.

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 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.

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.

We propose constrained causal Bayesian optimization (cCBO), an approach for finding interventions in a known causal graph that optimize a target variable under some constraints. cCBO first reduces the search space by exploiting the graph structure and, if available, an observational dataset; and then solves the restricted optimization problem by modelling target and constraint quantities using Gaussian processes and by sequentially selecting interventions via a constrained expected improvement acquisition function. We propose different surrogate models that enable to integrate observational and interventional data while capturing correlation among effects with increasing levels of sophistication. We evaluate cCBO on artificial and real-world causal graphs showing successful trade off between fast convergence and percentage of feasible interventions.

We explore algorithms to select actions in the causal bandit setting where the learner can choose to intervene on a set of random variables related by a causal graph, and the learner sequentially chooses interventions and observes a sample from the interventional distribution. The learner’s goal is to quickly find the intervention, among all interventions on observable variables, that maximizes the expectation of an outcome variable. We depart from previous literature by assuming no knowledge of the causal graph except that latent confounders between the outcome and its ancestors are not present. We first show that the unknown graph problem can be exponentially hard in the parents of the outcome. To remedy this, we adopt an additional additive assumption on the outcome which allows us to solve the problem by casting it as an additive combinatorial linear bandit problem with full-bandit feedback. We propose a novel action-elimination algorithm for this setting, show how to apply this algorithm to the causal bandit problem, provide sample complexity bounds, and empirically validate our findings on a suite of randomly generated causal models, effectively showing that one does not need to explicitly learn the parents of the outcome to identify the best intervention.

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.

In addition to reproducing discriminatory relationships in the training data, machine learning (ML) systems can also introduce or amplify discriminatory effects. We refer to this as introduced unfairness, and investigate the conditions under which it may arise. To this end, we propose introduced total variation as a measure of introduced unfairness, and establish graphical conditions under which it may be incentivised to occur. These criteria imply that adding the sensitive attribute as a feature removes the incentive for introduced variation under well-behaved loss functions. Additionally, taking a causal perspective, introduced path-specific effects shed light on the issue of when specific paths should be considered fair.

Diagnosing and mitigating changes in model fairness under distribution shift is an important component of the safe deployment of machine learning in healthcare settings. Importantly, the success of any mitigation strategy strongly depends on the \textit{structure} of the shift. Despite this, there has been little discussion of how to empirically assess the structure of a distribution shift that one is encountering in practice. In this work, we adopt a causal framing to motivate conditional independence tests as a key tool for characterizing distribution shifts. Using our approach in two medical applications, we show that this knowledge can help diagnose failures of fairness transfer, including cases where real-world shifts are more complex than is often assumed in the literature. Based on these results, we discuss potential remedies at each step of the machine learning pipeline.

This paper considers the problem of selecting a formula for identifying a causal quantity of interest among a set of available formulas. We assume an online setting in which the investigator may alter the data collection mechanism in a data-dependent way with the aim of identifying the formula with lowest asymptotic variance in as few samples as possible. We formalize this setting by using the best-arm-identification bandit framework where the standard goal of learning the arm with the lowest loss is replaced with the goal of learning the arm that will produce the best estimate. We introduce new tools for constructing finite-sample confidence bounds on estimates of the asymptotic variance that account for the estimation of potentially complex nuisance functions, and adapt the best-arm-identification algorithms of LUCB and Successive Elimination to use these bounds. We validate our method by providing upper bounds on the sample complexity and an empirical study on artificially generated data.

We propose a general approach to fairness based on transporting distributions corresponding to different sensitive attributes to a common distribution. We use optimal transport theory to derive target distributions and methods that allow us to achieve fairness with minimal changes to the unfair model. Our approach is applicable to both classification and regression problems, can enforce different notions of fairness, and enable us to achieve a Pareto-optimal trade-off between accuracy and fairness. We demonstrate that it outperforms previous approaches in several benchmark fairness datasets.

We consider the problem of learning fair decision systems from data in which a sensitive attribute might affect the decision along both fair and unfair pathways. We introduce a counterfactual approach to disregard effects along unfair pathways that does not incur in the same loss of individual-specific information as previous approaches. Our method corrects observations adversely affected by the sensitive attribute, and uses these to form a decision. We leverage recent developments in deep learning and approximate inference to develop a VAE-type method that is widely applicable to complex nonlinear models.

Machine learning is used extensively in recommender systems deployed in products. The decisions made by these systems can influence user beliefs and preferences which in turn affect the feedback the learning system receives - thus creating a feedback loop. This phenomenon can give rise to the so-called "echo chambers" or "filter bubbles" that have user and societal implications. In this paper, we provide a novel theoretical analysis that examines both the role of user dynamics and the behavior of recommender systems, disentangling the echo chamber from the filter bubble effect. In addition, we offer practical solutions to slow down system degeneracy. Our study contributes toward understanding and developing solutions to commonly cited issues in the complex temporal scenario, an area that is still largely unexplored.

Many time-series such as human movement data consist of a sequence of basic actions, e.g., forehands and backhands in tennis. Automatically extracting and characterizing such actions is an important problem for a variety of different applications. In this paper, we present a probabilistic segmentation approach in which an observed time-series is modeled as a concatenation of segments corresponding to different basic actions. Each segment is generated through a noisy transformation of one of a few hidden trajectories representing different types of movement, with possible time re-scaling. We analyze three different approximation methods for dealing with model intractability, and demonstrate how the proposed approach can successfully segment table tennis movements recorded using a robot arm as haptic input device.

Many real-world applications with graph data require the solution of a given regression task as well as the identification of the subgraphs which are relevant for the task. In these cases graphs are commonly represented as high dimensional binary vectors of indicators of subgraphs. However, since the dimensionality of such indicator vectors can be high even for small datasets, traditional regression algorithms become intractable and past approaches used to preselect a feasible subset of subgraphs. A different approach was recently proposed by a Lasso-type method where the objective function optimization with a large number of variables is reformulated as a dual mathematical programming problem with a small number of variables but a large number of constraints. The dual problem is then solved by column generation, where the subgraphs corresponding to the most violated constraints are found by weighted subgraph mining. This paper proposes an extension of this method to a Bayesian approach in which the regression parameters are considered as random variables and integrated out from the model likelihood, thus providing a posterior distribution on the target variable as opposed to a point estimate. We focus on a linear regression model with a Gaussian prior distribution on the parameters. We evaluate our approach on several molecular graph datasets and analyze whether the uncertainty in the target estimate given by the target posterior distribution variance can be used to improve model performance and therefore provides useful additional information.

Time-series segmentation in the fully unsupervised scenario in which the number of segment-types is a priori unknown is a fundamental problem in many applications. We propose a Bayesian approach to a segmentation model based on the switching linear Gaussian state-space model that enforces a sparse parametrization, such as to use only a small number of a priori available different dynamics to explain the data. This enables us to estimate the number of segment-types within the model, in contrast to previousnon-Bayesian approaches where training and comparing several separate models was required. As the resulting model is computationally intractable, we introduce a variational approximation where a reformulation of the problem enables the use of efficient inference algorithms.

Motor primitives or motion templates have become an important concept for both modeling human motor control as well as generating robot behaviors using imitation learning. Recent impressive results range from humanoid robot movement generation to timing models of human motions. The automatic generation of skill libraries containing multiple motion templates is an important step in robot learning. Such a skill learning system needs to cluster similar movements together and represent each resulting motion template as a generative model which is subsequently used for the execution of the behavior by a robot system. In this paper, we show how human trajectories captured as multidimensional time-series can be clustered using Bayesian mixtures of linear Gaussian state-space models based on the similarity of their dynamics. The appropriate number of templates is automatically determined by enforcing a parsimonious parametrization. As the resulting model is intractable, we introduce a novel approximation method based on variational Bayes, which is especially designed to enable the use of efficient inference algorithms. On recorded human Balero movements, this method is not only capable of finding reasonable motion templates but also yields a generative model which works well in the execution of this complex task on a simulated anthropomorphic SARCOS arm.

We discuss a method to extract independent dynamical systems underlying a single or multiple channels of observation. In particular, we search for one-dimensional subsignals to aid the interpretability of the decomposition. The method uses an approximate Bayesian analysis to determine automatically the number and appropriate complexity of the underlying dynamics, with a preference for the simplest solution. We apply this method to unfiltered EEG signals to discover low-complexity sources with preferential spectral properties, demonstrating improved interpretability of the extracted sources over related methods

Linear Gaussian State-Space Models are widely used and a Bayesian treatment of parameters is therefore of considerable interest. The approximate Variational Bayesian method applied to these models is an attractive approach, used successfully in applications ranging from acoustics to bioinformatics. The most challenging aspect of implementing the method is in performing inference on the hidden state sequence of the model. We show how to convert the inference problem so that standard Kalman Filtering/Smoothing recursions from the literature may be applied. This is in contrast to previously published approaches based on Belief Propagation. Our framework both simplifies and unifies the inference problem, so that future applications may be more easily developed. We demonstrate the elegance of the approach on Bayesian temporal ICA, with an application to finding independent dynamical processes underlying noisy EEG signals. 1 Linear Gaussian State-Space Models Linear Gaussian State-Space Models (LGSSMs)1 are fundamental in time-series analysis [1, 2, 3]. In these models the observations v1:T 2 are generated from an underlying dynamical system on h1:T according to: v v vt = B ht + t , t N (0V , V ), h h ht = Aht-1 + t , t N (0H , H ) , where N (, ) denotes a Gaussian with mean and covariance , and 0X denotes an X dimensional zero vector. The observation vt has dimension V and the hidden state ht has dimension H . Probabilistically, the LGSSM is defined by: p(v1:T , h1:T |) = p(v1 |h1 )p(h1 ) tT p(vt |ht )p(ht |ht-1 ), =2 with p(vt |ht ) = N (B ht , V ), p(ht |ht-1 ) = N (Aht-1 , H ), p(h1 ) = N (, ) and where = {A, B , H , V , , } denotes the model parameters. Because of the widespread use of these models, a Bayesian treatment of parameters is of considerable interest [4, 5, 6, 7, 8]. An exact implementation of the Bayesian LGSSM is formally intractable [8], and recently a Variational Bayesian (VB) approximation has been studied [4, 5, 6, 7, 9]. The most challenging part of implementing the VB method is performing inference over h1:T , and previous authors have developed their own specialized routines, based on Belief Propagation, since standard LGSSM inference routines appear, at first sight, not to be applicable. 1 2 Also called Kalman Filters/Smoothers, Linear Dynamical Systems. v1:T denotes v1 , . . . , vT . A key contribution of this paper is to show how the Variational Bayesian treatment of the LGSSM can be implemented using standard LGSSM inference routines. Based on the insight we provide, any standard inference method may be applied, including those specifically addressed to improve numerical stability [2, 10, 11]. In this article, we decided to describe the predictor-corrector and Rauch-Tung-Striebel recursions [2], and also suggest a small modification that reduces computational cost. The Bayesian LGSSM is particularly of interest when strong prior constraints are needed to find adequate solutions. One such case is in EEG signal analysis, whereby we wish to extract sources that evolve independently through time. Since EEG is particularly noisy [12], a prior that encourages sources to have preferential dynamics is advantageous. This application is discussed in Section 4, and demonstrates the ease of applying our VB framework. 2 Bayesian Linear Gaussian State-Space Models In the Bayesian treatment of the LGSSM, instead of considering the model parameters as fixed, ^ ^ we define a prior distribution p(|), where is a set of hyperparameters. Then: ^ ^ p(v1:T |) = p(v1:T |)p(|) . (1) In a full Bayesian treatment we would define additional prior distributions over the hyperparameters ^ . Here we take instead the ML-II (`evidence') framework, in which the optimal set of hyperpa^ ^ rameters is found by maximizing p(v1:T |) with respect to [6, 7, 9]. For the parameter priors, here we define Gaussians on the columns of A and B 3 : p(A|, H ) jH e- j 2