Isabel Valera

Adrián Javaloy, Pablo Sánchez-Martín, Isabel Valera

In this work, we deepen on the use of normalizing flows for causal reasoning. Specifically, we first leverage recent results on non-linear ICA to show that causal models are identifiable from observational data given a causal ordering, and thus can be recovered using autoregressive normalizing flows (NFs). Second, we analyze different design and learning choices for causal normalizing flows to capture the underlying causal data-generating process. Third, we describe how to implement the do-operator in causal NFs, and thus, how to answer interventional and counterfactual questions. Finally, in our experiments, we validate our design and training choices through a comprehensive ablation study; compare causal NFs to other approaches for approximating causal models; and empirically demonstrate that causal NFs can be used to address real-world problems, where the presence of mixed discrete-continuous data and partial knowledge on the causal graph is the norm. The code for this work can be found at https://github.com/psanch21/causal-flows.

Yifan Wang, Jinyi Mu, Mayank Jobanputra et al.

Preference modeling plays a central role in reinforcement learning from human feedback (RLHF), enabling large language models (LLMs) to align with human values. However, most existing approaches assume a universal reward function, neglecting the diversity and heterogeneity of human preferences. To address this limitation without additional annotation costs, recent work has proposed learning multiple preference components from binary data and combining them to model individual preferences. Nevertheless, these components often fail to capture coherent and disentangled patterns, limiting their interpretability and effectiveness for personalization. In this work, we propose a sparse Mixture-of-Experts (MoE) reward model that encourages sparse routing and expert diversity during training on binary preference data. Across controlled and real-world experiments, sparse MoE learns interpretable routing patterns and specialized experts. It also improves test-time personalization, and post-adaptation shifts in expert weights provide a qualitative lens for analyzing how the model adapts to personalized preferences.

Miriam Rateike, Ayan Majumdar, Olga Mineeva et al.

Decision making algorithms, in practice, are often trained on data that exhibits a variety of biases. Decision-makers often aim to take decisions based on some ground-truth target that is assumed or expected to be unbiased, i.e., equally distributed across socially salient groups. In many practical settings, the ground-truth cannot be directly observed, and instead, we have to rely on a biased proxy measure of the ground-truth, i.e., biased labels, in the data. In addition, data is often selectively labeled, i.e., even the biased labels are only observed for a small fraction of the data that received a positive decision. To overcome label and selection biases, recent work proposes to learn stochastic, exploring decision policies via i) online training of new policies at each time-step and ii) enforcing fairness as a constraint on performance. However, the existing approach uses only labeled data, disregarding a large amount of unlabeled data, and thereby suffers from high instability and variance in the learned decision policies at different times. In this paper, we propose a novel method based on a variational autoencoder for practical fair decision-making. Our method learns an unbiased data representation leveraging both labeled and unlabeled data and uses the representations to learn a policy in an online process. Using synthetic data, we empirically validate that our method converges to the optimal (fair) policy according to the ground-truth with low variance. In real-world experiments, we further show that our training approach not only offers a more stable learning process but also yields policies with higher fairness as well as utility than previous approaches.

Adrián Javaloy, Maryam Meghdadi, Isabel Valera

A number of variational autoencoders (VAEs) have recently emerged with the aim of modeling multimodal data, e.g., to jointly model images and their corresponding captions. Still, multimodal VAEs tend to focus solely on a subset of the modalities, e.g., by fitting the image while neglecting the caption. We refer to this limitation as modality collapse. In this work, we argue that this effect is a consequence of conflicting gradients during multimodal VAE training. We show how to detect the sub-graphs in the computational graphs where gradients conflict (impartiality blocks), as well as how to leverage existing gradient-conflict solutions from multitask learning to mitigate modality collapse. That is, to ensure impartial optimization across modalities. We apply our training framework to several multimodal VAE models, losses and datasets from the literature, and empirically show that our framework significantly improves the reconstruction performance, conditional generation, and coherence of the latent space across modalities.

Adrián Javaloy, Pablo Sanchez-Martin, Amit Levi et al.

Existing Graph Neural Networks (GNNs) compute the message exchange between nodes by either aggregating uniformly (convolving) the features of all the neighboring nodes, or by applying a non-uniform score (attending) to the features. Recent works have shown the strengths and weaknesses of the resulting GNN architectures, respectively, GCNs and GATs. In this work, we aim at exploiting the strengths of both approaches to their full extent. To this end, we first introduce the graph convolutional attention layer (CAT), which relies on convolutions to compute the attention scores. Unfortunately, as in the case of GCNs and GATs, we show that there exists no clear winner between the three (neither theoretically nor in practice) as their performance directly depends on the nature of the data (i.e., of the graph and features). This result brings us to the main contribution of our work, the learnable graph convolutional attention network (L-CAT): a GNN architecture that automatically interpolates between GCN, GAT and CAT in each layer, by adding only two scalar parameters. Our results demonstrate that L-CAT is able to efficiently combine different GNN layers along the network, outperforming competing methods in a wide range of datasets, and resulting in a more robust model that reduces the need of cross-validating.

Batuhan Koyuncu, Pablo Sanchez-Martin, Ignacio Peis et al.

Recent approaches build on implicit neural representations (INRs) to propose generative models over function spaces. However, they are computationally costly when dealing with inference tasks, such as missing data imputation, or directly cannot tackle them. In this work, we propose a novel deep generative model, named VAMoH. VAMoH combines the capabilities of modeling continuous functions using INRs and the inference capabilities of Variational Autoencoders (VAEs). In addition, VAMoH relies on a normalizing flow to define the prior, and a mixture of hypernetworks to parametrize the data log-likelihood. This gives VAMoH a high expressive capability and interpretability. Through experiments on a diverse range of data types, such as images, voxels, and climate data, we show that VAMoH can effectively learn rich distributions over continuous functions. Furthermore, it can perform inference-related tasks, such as conditional super-resolution generation and in-painting, as well or better than previous approaches, while being less computationally demanding.

Giovani Valdrighi, Isabel Valera, Marcos Medeiros Raimundo

Long-term fairness algorithms aim to satisfy fairness beyond static and short-term notions by accounting for the dynamics between decision-making policies and population behavior. Most previous approaches evaluate performance and fairness measures from observable features and a label, which is assumed to be fully observed. However, in scenarios such as hiring or lending, the labels (e.g., ability to repay the loan) are selective labels as they are only revealed based on positive decisions (e.g., when a loan is granted). In this paper, we study long-term fairness in the selective labels setting and analytically show that naive solutions do not guarantee fairness. To address this gap, we then introduce a novel framework that leverages both the observed data and a label predictor model to estimate the true fairness measure value by decomposing it into the observed fairness and bias from label predictions. This allows us to derive sufficient conditions to satisfy true fairness from observable quantities by using the confidence in the predictor model. Finally, we rely on our theoretical results to propose a novel reinforcement learning algorithm for effective long-term fair decision-making with selective labels. In semisynthetic environments, the proposed algorithm reached comparable fairness and performance to an agent with oracle access to the true labels.

Kavya Gupta, Nektarios Kalampalikis, Christoph Heitz et al.

Fairness in algorithmic decision-making is often defined in the predictive space, where predictive performance - used as a proxy for decision-maker (DM) utility - is traded off against prediction-based fairness notions, such as demographic parity or equality of opportunity. This perspective, however, ignores how predictions translate into decisions and ultimately into utilities and welfare for both DM and decision subjects (DS), as well as their allocation across social-salient groups. In this paper, we propose a multi-stakeholder framework for fair algorithmic decision-making grounded in welfare economics and distributive justice, explicitly modeling the utilities of both the DM and DS, and defining fairness via a social planner's utility that captures inequalities in DS utilities across groups under different justice-based fairness notions (e.g., Egalitarian, Rawlsian). We formulate fair decision-making as a post-hoc multi-objective optimization problem, characterizing the achievable performance-fairness trade-offs in the two-dimensional utility space of DM utility and the social planner's utility, under different decision policy classes (deterministic vs. stochastic, shared vs. group-specific). Using the proposed framework, we then identify conditions (in terms of the stakeholders' utilities) under which stochastic policies are more optimal than deterministic ones, and empirically demonstrate that simple stochastic policies can yield superior performance-fairness trade-offs by leveraging outcome uncertainty. Overall, we advocate a shift from prediction-centric fairness to a transparent, justice-based, multi-stakeholder approach that supports the collaborative design of decision-making policies.

Miriam Rateike, Isabel Valera, Patrick Forré

Neglecting the effect that decisions have on individuals (and thus, on the underlying data distribution) when designing algorithmic decision-making policies may increase inequalities and unfairness in the long term - even if fairness considerations were taken in the policy design process. In this paper, we propose a novel framework for achieving long-term group fairness in dynamical systems, in which current decisions may affect an individual's features in the next step, and thus, future decisions. Specifically, our framework allows us to identify a time-independent policy that converges, if deployed, to the targeted fair stationary state of the system in the long term, independently of the initial data distribution. We model the system dynamics with a time-homogeneous Markov chain and optimize the policy leveraging the Markov chain convergence theorem to ensure unique convergence. We provide examples of different targeted fair states of the system, encompassing a range of long-term goals for society and policymakers. Furthermore, we show how our approach facilitates the evaluation of different long-term targets by examining their impact on the group-conditional population distribution in the long term and how it evolves until convergence.

Nicola J. Müller, Moritz Oster, Isabel Valera et al.

Learning per-domain generalizing policies is a key challenge in learning for planning. Standard approaches learn state-value functions represented as graph neural networks using supervised learning on optimal plans generated by a teacher planner. In this work, we advocate for learning Q-value functions instead. Such policies are drastically cheaper to evaluate for a given state, as they need to process only the current state rather than every successor. Surprisingly, vanilla supervised learning of Q-values performs poorly as it does not learn to distinguish between the actions taken and those not taken by the teacher. We address this by using regularization terms that enforce this distinction, resulting in Q-value policies that consistently outperform state-value policies across a range of 10 domains and are competitive with the planner LAMA-first.

Alejandro Almodóvar, Adrián Javaloy, Juan Parras et al.

We introduce DeCaFlow, a deconfounding causal generative model. Training once per dataset using just observational data and the underlying causal graph, DeCaFlow enables accurate causal inference on continuous variables under the presence of hidden confounders. Specifically, we extend previous results on causal estimation under hidden confounding to show that a single instance of DeCaFlow provides correct estimates for all causal queries identifiable with do-calculus, leveraging proxy variables to adjust for the causal effects when do-calculus alone is insufficient. Moreover, we show that counterfactual queries are identifiable as long as their interventional counterparts are identifiable, and thus are also correctly estimated by DeCaFlow. Our empirical results on diverse settings (including the Ecoli70 dataset, with 3 independent hidden confounders, tens of observed variables and hundreds of causal queries) show that DeCaFlow outperforms existing approaches, while demonstrating its out-of-the-box applicability to any given causal graph. An implementation can be found in https://github.com/aalmodovares/DeCaFlow

Adrián Javaloy, Isabel Valera

Multitask learning is being increasingly adopted in applications domains like computer vision and reinforcement learning. However, optimally exploiting its advantages remains a major challenge due to the effect of negative transfer. Previous works have tracked down this issue to the disparities in gradient magnitudes and directions across tasks, when optimizing the shared network parameters. While recent work has acknowledged that negative transfer is a two-fold problem, existing approaches fall short as they only focus on either homogenizing the gradient magnitude across tasks; or greedily change the gradient directions, overlooking future conflicts. In this work, we introduce RotoGrad, an algorithm that tackles negative transfer as a whole: it jointly homogenizes gradient magnitudes and directions, while ensuring training convergence. We show that RotoGrad outperforms competing methods in complex problems, including multi-label classification in CelebA and computer vision tasks in the NYUv2 dataset. A Pytorch implementation can be found in https://github.com/adrianjav/rotograd.

Adrián Javaloy, Isabel Valera

Probabilistic learning is increasingly being tackled as an optimization problem, with gradient-based approaches as predominant methods. When modelling multivariate likelihoods, a usual but undesirable outcome is that the learned model fits only a subset of the observed variables, overlooking the rest. In this work, we study this problem through the lens of multitask learning (MTL), where similar effects have been broadly studied. While MTL solutions do not directly apply in the probabilistic setting (as they cannot handle the likelihood constraints) we show that similar ideas may be leveraged during data preprocessing. First, we show that data standardization often helps under common continuous likelihoods, but it is not enough in the general case, specially under mixed continuous and discrete likelihood models. In order for balance multivariate learning, we then propose a novel data preprocessing, Lipschitz standardization, which balances the local Lipschitz smoothness across variables. Our experiments on real-world datasets show that Lipschitz standardization leads to more accurate multivariate models than the ones learned using existing data preprocessing techniques. The models and datasets employed in the experiments can be found in https://github.com/adrianjav/lipschitz-standardization.

Huyen Vo, Isabel Valera

Multimodal variational autoencoders (VAEs) are widely used for weakly supervised generative learning with multiple modalities. Predominant methods aggregate unimodal inference distributions using either a product of experts (PoE), a mixture of experts (MoE), or their combinations to approximate the joint posterior. In this work, we revisit multimodal inference through the lens of probabilistic opinion pooling, an optimization-based approach. We start from Hölder pooling with $α=0.5$, which corresponds to the unique symmetric member of the $α\text{-divergence}$ family, and derive a moment-matching approximation, termed Hellinger. We then leverage such an approximation to propose HELVAE, a multimodal VAE that avoids sub-sampling, yielding an efficient yet effective model that: (i) learns more expressive latent representations as additional modalities are observed; and (ii) empirically achieves better trade-offs between generative coherence and quality, outperforming state-of-the-art multimodal VAE models.

Lena Marie Budde, Ayan Majumdar, Richard Uth et al.

Algorithmic recourse aims to provide actionable recommendations that enable individuals to change unfavorable model outcomes, and prior work has extensively studied properties such as efficiency, robustness, and fairness. However, the role of personalization in recourse remains largely implicit and underexplored. While existing approaches incorporate elements of personalization through user interactions, they typically lack an explicit definition of personalization and do not systematically analyze its downstream effects on other recourse desiderata. In this paper, we formalize personalization as individual actionability, characterized along two dimensions: hard constraints that specify which features are individually actionable, and soft, individualized constraints that capture preferences over action values and costs. We operationalize these dimensions within the causal algorithmic recourse framework, adopting a pre-hoc user-prompting approach in which individuals express preferences via rankings or scores prior to the generation of any recourse recommendation. Through extensive empirical evaluation, we investigate how personalization interacts with key recourse desiderata, including validity, cost, and plausibility. Our results highlight important trade-offs: individual actionability constraints, particularly hard ones, can substantially degrade the plausibility and validity of recourse recommendations across amortized and non-amortized approaches. Notably, we also find that incorporating individual actionability can reveal disparities in the cost and plausibility of recourse actions across socio-demographic groups. These findings underscore the need for principled definitions, careful operationalization, and rigorous evaluation of personalization in algorithmic recourse.

Pablo Sanchez-Martin, Kinaan Aamir Khan, Isabel Valera

Graph Neural Networks (GNNs) have achieved state-of-the-art performance in solving graph classification tasks. However, most GNN architectures aggregate information from all nodes and edges in a graph, regardless of their relevance to the task at hand, thus hindering the interpretability of their predictions. In contrast to prior work, in this paper we propose a GNN \emph{training} approach that jointly i) finds the most predictive subgraph by removing edges and/or nodes -- -\emph{without making assumptions about the subgraph structure} -- while ii) optimizing the performance of the graph classification task. To that end, we rely on reinforcement learning to solve the resulting bi-level optimization with a reward function based on conformal predictions to account for the current in-training uncertainty of the classifier. Our empirical results on nine different graph classification datasets show that our method competes in performance with baselines while relying on significantly sparser subgraphs, leading to more interpretable GNN-based predictions.

Martina Cinquini, Isacco Beretta, Salvatore Ruggieri et al.

In this paper, we focus on estimating the causal effect of an intervention over time on a dynamical system. To that end, we formally define causal interventions and their effects over time on discrete-time stochastic processes (DSPs). Then, we show under which conditions the equilibrium states of a DSP, both before and after a causal intervention, can be captured by a structural causal model (SCM). With such an equivalence at hand, we provide an explicit mapping from vector autoregressive models (VARs), broadly applied in econometrics, to linear, but potentially cyclic and/or affected by unmeasured confounders, SCMs. The resulting causal VAR framework allows us to perform causal inference over time from observational time series data. Our experiments on synthetic and real-world datasets show that the proposed framework achieves strong performance in terms of observational forecasting while enabling accurate estimation of the causal effect of interventions on dynamical systems. We demonstrate, through a case study, the potential practical questions that can be addressed using the proposed causal VAR framework.

Nektarios Kalampalikis, Kavya Gupta, Georgi Vitanov et al.

In this paper, we propose $\textbf{C}$oncept $\textbf{REA}$soning $\textbf{M}$odels (CREAM), a novel family of Concept Bottleneck Models (CBMs) that: (i) explicitly encodes concept-concept (${\texttt{C-C}}$) and concept-task (${\texttt{C$\rightarrow$Y}}$) relationships to enforce a desired model reasoning; and (ii) use a regularized side-channel to achieve competitive task performance, while keeping high concept importance. Specifically, CREAM architecturally embeds (bi)directed concept-concept, and concept to task relationships specified by a human expert, while severing undesired information flows (e.g., to handle mutually exclusive concepts). Moreover, CREAM integrates a black-box side-channel that is regularized to encourage task predictions to be grounded in the relevant concepts, thereby utilizing the side-channel only when necessary to enhance performance. Our experiments show that: (i) CREAM mainly relies on concepts while achieving task performance on par with black-box models; and (ii) the embedded ${\texttt{C-C}}$ and ${\texttt{C$\rightarrow$Y}}$ relationships ease model interventions and mitigate concept leakage.

Timo P. Gros, Nicola J. Müller, Daniel Fiser et al.

Recent work has shown that successful per-domain generalizing action policies can be learned. Scaling behavior, from small training instances to large test instances, is the key objective; and the use of validation instances larger than training instances is one key to achieve it. Prior work has used fixed validation sets. Here, we introduce a method generating the validation set dynamically, on the fly, increasing instance size so long as informative and feasible.We also introduce refined methodology for evaluating scaling behavior, generating test instances systematically to guarantee a given confidence in coverage performance for each instance size. In experiments, dynamic validation improves scaling behavior of GNN policies in all 9 domains used.

Ignacio Peis, Batuhan Koyuncu, Isabel Valera et al.

We introduce a novel generative framework for functions by integrating Implicit Neural Representations (INRs) and Transformer-based hypernetworks into latent variable models. Unlike prior approaches that rely on MLP-based hypernetworks with scalability limitations, our method employs a Transformer-based decoder to generate INR parameters from latent variables, addressing both representation capacity and computational efficiency. Our framework extends latent diffusion models (LDMs) to INR generation by replacing standard decoders with a Transformer-based hypernetwork, which can be trained either from scratch or via hyper-transforming: a strategy that fine-tunes only the decoder while freezing the pre-trained latent space. This enables efficient adaptation of existing generative models to INR-based representations without requiring full retraining. We validate our approach across multiple modalities, demonstrating improved scalability, expressiveness, and generalization over existing INR-based generative models. Our findings establish a unified and flexible framework for learning structured function representations.

Yifan Wang, Mayank Jobanputra, Ji-Ung Lee et al.

Natural language processing (NLP) models often replicate or amplify social bias from training data, raising concerns about fairness. At the same time, their black-box nature makes it difficult for users to recognize biased predictions and for developers to effectively mitigate them. While some studies suggest that input-based explanations can help detect and mitigate bias, others question their reliability in ensuring fairness. Existing research on explainability in fair NLP has been predominantly qualitative, with limited large-scale quantitative analysis. In this work, we conduct the first systematic study of the relationship between explainability and fairness in hate speech detection, focusing on both encoder- and decoder-only models. We examine three key dimensions: (1) identifying biased predictions, (2) selecting fair models, and (3) mitigating bias during model training. Our findings show that input-based explanations can effectively detect biased predictions and serve as useful supervision for reducing bias during training, but they are unreliable for selecting fair models among candidates.

Israel Abebe Azime, Deborah D. Kanubala, Tejumade Afonja et al.

Large Language Models (LLMs) are increasingly employed in high-stakes decision-making tasks, such as loan approvals. While their applications expand across domains, LLMs struggle to process tabular data, ensuring fairness and delivering reliable predictions. In this work, we assess the performance and fairness of LLMs on serialized loan approval datasets from three geographically distinct regions: Ghana, Germany, and the United States. Our evaluation focuses on the model's zero-shot and in-context learning (ICL) capabilities. Our results reveal that the choice of serialization (Serialization refers to the process of converting tabular data into text formats suitable for processing by LLMs.) format significantly affects both performance and fairness in LLMs, with certain formats such as GReat and LIFT yielding higher F1 scores but exacerbating fairness disparities. Notably, while ICL improved model performance by 4.9-59.6% relative to zero-shot baselines, its effect on fairness varied considerably across datasets. Our work underscores the importance of effective tabular data representation methods and fairness-aware models to improve the reliability of LLMs in financial decision-making.

Batuhan Koyuncu, Rachael DeVries, Ole Winther et al.

We introduce Temporal Variational Implicit Neural Representations (TV-INRs), a probabilistic framework for modeling irregular multivariate time series that enables efficient individualized imputation and forecasting. By integrating implicit neural representations with latent variable models, TV-INRs learn distributions over time-continuous generator functions conditioned on signal-specific covariates. Unlike existing approaches that require extensive training, fine-tuning or meta-learning, our method achieves accurate individualized predictions through a single forward pass. Our experiments demonstrate that with a single TV-INRs instance, we can accurately solve diverse imputation and forecasting tasks, offering a computationally efficient and scalable solution for real-world applications. TV-INRs excel especially in low-data regimes, where it outperforms existing methods by an order of magnitude in mean squared error for imputation task.

Ayan Majumdar, Deborah D. Kanubala, Kavya Gupta et al.

Fairness studies of algorithmic decision-making systems often simplify complex decision processes, such as bail or loan approvals, into binary classification tasks. However, these approaches overlook that such decisions are not inherently binary (e.g., approve or not approve bail or loan); they also involve non-binary treatment decisions (e.g., bail conditions or loan terms) that can influence the downstream outcomes (e.g., loan repayment or reoffending). In this paper, we argue that non-binary treatment decisions are integral to the decision process and controlled by decision-makers and, therefore, should be central to fairness analyses in algorithmic decision-making. We propose a causal framework that extends fairness analyses and explicitly distinguishes between decision-subjects' covariates and the treatment decisions. This specification allows decision-makers to use our framework to (i) measure treatment disparity and its downstream effects in historical data and, using counterfactual reasoning, (ii) mitigate the impact of past unfair treatment decisions when automating decision-making. We use our framework to empirically analyze four widely used loan approval datasets to reveal potential disparity in non-binary treatment decisions and their discriminatory impact on outcomes, highlighting the need to incorporate treatment decisions in fairness assessments. Moreover, by intervening in treatment decisions, we show that our framework effectively mitigates treatment discrimination from historical data to ensure fair risk score estimation and (non-binary) decision-making processes that benefit all stakeholders.

Adrián Javaloy, Antonio Vergari, Isabel Valera

In machine learning (ML), we often need to choose one among hundreds of trained ML models at hand, based on various objectives such as accuracy, robustness, fairness or scalability. However, it is often unclear how to compare, aggregate and, ultimately, trade-off these objectives, making it a time-consuming task that requires expert knowledge, as objectives may be measured in different units and scales. In this work, we investigate how objectives can be automatically normalized and aggregated to systematically help the user navigate their Pareto front. To this end, we make incomparable objectives comparable using their cumulative functions, approximated by their relative rankings. As a result, our proposed approach, COPA, can aggregate them while matching user-specific preferences, allowing practitioners to meaningfully navigate and search for models in the Pareto front. We demonstrate the potential impact of COPA in both model selection and benchmarking tasks across diverse ML areas such as fair ML, domain generalization, AutoML and foundation models, where classical ways to normalize and aggregate objectives fall short.

Pablo Sanchez-Martin, Miriam Rateike, Isabel Valera

In this paper, we introduce VACA, a novel class of variational graph autoencoders for causal inference in the absence of hidden confounders, when only observational data and the causal graph are available. Without making any parametric assumptions, VACA mimics the necessary properties of a Structural Causal Model (SCM) to provide a flexible and practical framework for approximating interventions (do-operator) and abduction-action-prediction steps. As a result, and as shown by our empirical results, VACA accurately approximates the interventional and counterfactual distributions on diverse SCMs. Finally, we apply VACA to evaluate counterfactual fairness in fair classification problems, as well as to learn fair classifiers without compromising performance.

Jakob Schoeffer, Niklas Kuehl, Isabel Valera

Algorithmic decision systems are increasingly used in areas such as hiring, school admission, or loan approval. Typically, these systems rely on labeled data for training a classification model. However, in many scenarios, ground-truth labels are unavailable, and instead we have only access to imperfect labels as the result of (potentially biased) human-made decisions. Despite being imperfect, historical decisions often contain some useful information on the unobserved true labels. In this paper, we focus on scenarios where only imperfect labels are available and propose a new fair ranking-based decision system based on monotonic relationships between legitimate features and the outcome. Our approach is both intuitive and easy to implement, and thus particularly suitable for adoption in real-world settings. More in detail, we introduce a distance-based decision criterion, which incorporates useful information from historical decisions and accounts for unwanted correlation between protected and legitimate features. Through extensive experiments on synthetic and real-world data, we show that our method is fair in the sense that a) it assigns the desirable outcome to the most qualified individuals, and b) it removes the effect of stereotypes in decision-making, thereby outperforming traditional classification algorithms. Additionally, we are able to show theoretically that our method is consistent with a prominent concept of individual fairness which states that "similar individuals should be treated similarly."

Julius von Kügelgen, Amir-Hossein Karimi, Umang Bhatt et al.

Algorithmic fairness is typically studied from the perspective of predictions. Instead, here we investigate fairness from the perspective of recourse actions suggested to individuals to remedy an unfavourable classification. We propose two new fairness criteria at the group and individual level, which -- unlike prior work on equalising the average group-wise distance from the decision boundary -- explicitly account for causal relationships between features, thereby capturing downstream effects of recourse actions performed in the physical world. We explore how our criteria relate to others, such as counterfactual fairness, and show that fairness of recourse is complementary to fairness of prediction. We study theoretically and empirically how to enforce fair causal recourse by altering the classifier and perform a case study on the Adult dataset. Finally, we discuss whether fairness violations in the data generating process revealed by our criteria may be better addressed by societal interventions as opposed to constraints on the classifier.

Kiarash Mohammadi, Amir-Hossein Karimi, Gilles Barthe et al.

Counterfactual explanations (CFE) are being widely used to explain algorithmic decisions, especially in consequential decision-making contexts (e.g., loan approval or pretrial bail). In this context, CFEs aim to provide individuals affected by an algorithmic decision with the most similar individual (i.e., nearest individual) with a different outcome. However, while an increasing number of works propose algorithms to compute CFEs, such approaches either lack in optimality of distance (i.e., they do not return the nearest individual) and perfect coverage (i.e., they do not provide a CFE for all individuals); or they cannot handle complex models, such as neural networks. In this work, we provide a framework based on Mixed-Integer Programming (MIP) to compute nearest counterfactual explanations with provable guarantees and with runtimes comparable to gradient-based approaches. Our experiments on the Adult, COMPAS, and Credit datasets show that, in contrast with previous methods, our approach allows for efficiently computing diverse CFEs with both distance guarantees and perfect coverage.

Amir-Hossein Karimi, Gilles Barthe, Bernhard Schölkopf et al.

Machine learning is increasingly used to inform decision-making in sensitive situations where decisions have consequential effects on individuals' lives. In these settings, in addition to requiring models to be accurate and robust, socially relevant values such as fairness, privacy, accountability, and explainability play an important role for the adoption and impact of said technologies. In this work, we focus on algorithmic recourse, which is concerned with providing explanations and recommendations to individuals who are unfavourably treated by automated decision-making systems. We first perform an extensive literature review, and align the efforts of many authors by presenting unified definitions, formulations, and solutions to recourse. Then, we provide an overview of the prospective research directions towards which the community may engage, challenging existing assumptions and making explicit connections to other ethical challenges such as security, privacy, and fairness.

Amir-Hossein Karimi, Julius von Kügelgen, Bernhard Schölkopf et al.

Recent work has discussed the limitations of counterfactual explanations to recommend actions for algorithmic recourse, and argued for the need of taking causal relationships between features into consideration. Unfortunately, in practice, the true underlying structural causal model is generally unknown. In this work, we first show that it is impossible to guarantee recourse without access to the true structural equations. To address this limitation, we propose two probabilistic approaches to select optimal actions that achieve recourse with high probability given limited causal knowledge (e.g., only the causal graph). The first captures uncertainty over structural equations under additive Gaussian noise, and uses Bayesian model averaging to estimate the counterfactual distribution. The second removes any assumptions on the structural equations by instead computing the average effect of recourse actions on individuals similar to the person who seeks recourse, leading to a novel subpopulation-based interventional notion of recourse. We then derive a gradient-based procedure for selecting optimal recourse actions, and empirically show that the proposed approaches lead to more reliable recommendations under imperfect causal knowledge than non-probabilistic baselines.

Amir-Hossein Karimi, Bernhard Schölkopf, Isabel Valera

As machine learning is increasingly used to inform consequential decision-making (e.g., pre-trial bail and loan approval), it becomes important to explain how the system arrived at its decision, and also suggest actions to achieve a favorable decision. Counterfactual explanations -- "how the world would have (had) to be different for a desirable outcome to occur" -- aim to satisfy these criteria. Existing works have primarily focused on designing algorithms to obtain counterfactual explanations for a wide range of settings. However, one of the main objectives of "explanations as a means to help a data-subject act rather than merely understand" has been overlooked. In layman's terms, counterfactual explanations inform an individual where they need to get to, but not how to get there. In this work, we rely on causal reasoning to caution against the use of counterfactual explanations as a recommendable set of actions for recourse. Instead, we propose a shift of paradigm from recourse via nearest counterfactual explanations to recourse through minimal interventions, moving the focus from explanations to recommendations. Finally, we provide the reader with an extensive discussion on how to realistically achieve recourse beyond structural interventions.

Amir-Hossein Karimi, Gilles Barthe, Borja Balle et al.

Predictive models are being increasingly used to support consequential decision making at the individual level in contexts such as pretrial bail and loan approval. As a result, there is increasing social and legal pressure to provide explanations that help the affected individuals not only to understand why a prediction was output, but also how to act to obtain a desired outcome. To this end, several works have proposed optimization-based methods to generate nearest counterfactual explanations. However, these methods are often restricted to a particular subset of models (e.g., decision trees or linear models) and differentiable distance functions. In contrast, we build on standard theory and tools from formal verification and propose a novel algorithm that solves a sequence of satisfiability problems, where both the distance function (objective) and predictive model (constraints) are represented as logic formulae. As shown by our experiments on real-world data, our algorithm is: i) model-agnostic ({non-}linear, {non-}differentiable, {non-}convex); ii) data-type-agnostic (heterogeneous features); iii) distance-agnostic ($\ell_0, \ell_1, \ell_\infty$, and combinations thereof); iv) able to generate plausible and diverse counterfactuals for any sample (i.e., 100% coverage); and v) at provably optimal distances.

Niki Kilbertus, Manuel Gomez-Rodriguez, Bernhard Schölkopf et al.

Consequential decisions are increasingly informed by sophisticated data-driven predictive models. However, to consistently learn accurate predictive models, one needs access to ground truth labels. Unfortunately, in practice, labels may only exist conditional on certain decisions---if a loan is denied, there is not even an option for the individual to pay back the loan. Hence, the observed data distribution depends on how decisions are being made. In this paper, we show that in this selective labels setting, learning a predictor directly only from available labeled data is suboptimal in terms of both fairness and utility. To avoid this undesirable behavior, we propose to directly learn decision policies that maximize utility under fairness constraints and thereby take into account how decisions affect which data is observed in the future. Our results suggest the need for a paradigm shift in the context of fair machine learning from the currently prevalent idea of simply building predictive models from a single static dataset via risk minimization, to a more interactive notion of "learning to decide". In particular, such policies should not entirely neglect part of the input space, drawing connections to explore/exploit tradeoffs in reinforcement learning, data missingness, and potential outcomes in causal inference. Experiments on synthetic and real-world data illustrate the favorable properties of learning to decide in terms of utility and fairness.

Francisco J. R. Ruiz, Isabel Valera, Lennart Svensson et al.

New communication standards need to deal with machine-to-machine communications, in which users may start or stop transmitting at any time in an asynchronous manner. Thus, the number of users is an unknown and time-varying parameter that needs to be accurately estimated in order to properly recover the symbols transmitted by all users in the system. In this paper, we address the problem of joint channel parameter and data estimation in a multiuser communication channel in which the number of transmitters is not known. For that purpose, we develop the infinite factorial finite state machine model, a Bayesian nonparametric model based on the Markov Indian buffet that allows for an unbounded number of transmitters with arbitrary channel length. We propose an inference algorithm that makes use of slice sampling and particle Gibbs with ancestor sampling. Our approach is fully blind as it does not require a prior channel estimation step, prior knowledge of the number of transmitters, or any signaling information. Our experimental results, loosely based on the LTE random access channel, show that the proposed approach can effectively recover the data-generating process for a wide range of scenarios, with varying number of transmitters, number of receivers, constellation order, channel length, and signal-to-noise ratio.

Antonio Vergari, Alejandro Molina, Robert Peharz et al.

Making sense of a dataset in an automatic and unsupervised fashion is a challenging problem in statistics and AI. Classical approaches for {exploratory data analysis} are usually not flexible enough to deal with the uncertainty inherent to real-world data: they are often restricted to fixed latent interaction models and homogeneous likelihoods; they are sensitive to missing, corrupt and anomalous data; moreover, their expressiveness generally comes at the price of intractable inference. As a result, supervision from statisticians is usually needed to find the right model for the data. However, since domain experts are not necessarily also experts in statistics, we propose Automatic Bayesian Density Analysis (ABDA) to make exploratory data analysis accessible at large. Specifically, ABDA allows for automatic and efficient missing value estimation, statistical data type and likelihood discovery, anomaly detection and dependency structure mining, on top of providing accurate density estimation. Extensive empirical evidence shows that ABDA is a suitable tool for automatic exploratory analysis of mixed continuous and discrete tabular data.

Alfredo Nazabal, Pablo M. Olmos, Zoubin Ghahramani et al.

Variational autoencoders (VAEs), as well as other generative models, have been shown to be efficient and accurate for capturing the latent structure of vast amounts of complex high-dimensional data. However, existing VAEs can still not directly handle data that are heterogenous (mixed continuous and discrete) or incomplete (with missing data at random), which is indeed common in real-world applications. In this paper, we propose a general framework to design VAEs suitable for fitting incomplete heterogenous data. The proposed HI-VAE includes likelihood models for real-valued, positive real valued, interval, categorical, ordinal and count data, and allows accurate estimation (and potentially imputation) of missing data. Furthermore, HI-VAE presents competitive predictive performance in supervised tasks, outperforming supervised models when trained on incomplete data.

Francesco Locatello, Gideon Dresdner, Rajiv Khanna et al.

Approximating a probability density in a tractable manner is a central task in Bayesian statistics. Variational Inference (VI) is a popular technique that achieves tractability by choosing a relatively simple variational family. Borrowing ideas from the classic boosting framework, recent approaches attempt to \emph{boost} VI by replacing the selection of a single density with a greedily constructed mixture of densities. In order to guarantee convergence, previous works impose stringent assumptions that require significant effort for practitioners. Specifically, they require a custom implementation of the greedy step (called the LMO) for every probabilistic model with respect to an unnatural variational family of truncated distributions. Our work fixes these issues with novel theoretical and algorithmic insights. On the theoretical side, we show that boosting VI satisfies a relaxed smoothness assumption which is sufficient for the convergence of the functional Frank-Wolfe (FW) algorithm. Furthermore, we rephrase the LMO problem and propose to maximize the Residual ELBO (RELBO) which replaces the standard ELBO optimization in VI. These theoretical enhancements allow for black box implementation of the boosting subroutine. Finally, we present a stopping criterion drawn from the duality gap in the classic FW analyses and exhaustive experiments to illustrate the usefulness of our theoretical and algorithmic contributions.

Isabel Valera, Adish Singla, Manuel Gomez Rodriguez

Societies often rely on human experts to take a wide variety of decisions affecting their members, from jail-or-release decisions taken by judges and stop-and-frisk decisions taken by police officers to accept-or-reject decisions taken by academics. In this context, each decision is taken by an expert who is typically chosen uniformly at random from a pool of experts. However, these decisions may be imperfect due to limited experience, implicit biases, or faulty probabilistic reasoning. Can we improve the accuracy and fairness of the overall decision making process by optimizing the assignment between experts and decisions? In this paper, we address the above problem from the perspective of sequential decision making and show that, for different fairness notions from the literature, it reduces to a sequence of (constrained) weighted bipartite matchings, which can be solved efficiently using algorithms with approximation guarantees. Moreover, these algorithms also benefit from posterior sampling to actively trade off exploitation---selecting expert assignments which lead to accurate and fair decisions---and exploration---selecting expert assignments to learn about the experts' preferences and biases. We demonstrate the effectiveness of our algorithms on both synthetic and real-world data and show that they can significantly improve both the accuracy and fairness of the decisions taken by pools of experts.

Isabel Valera, Melanie F. Pradier, Zoubin Ghahramani

This paper introduces a general Bayesian non- parametric latent feature model suitable to per- form automatic exploratory analysis of heterogeneous datasets, where the attributes describing each object can be either discrete, continuous or mixed variables. The proposed model presents several important properties. First, it accounts for heterogeneous data while can be inferred in linear time with respect to the number of objects and attributes. Second, its Bayesian nonparametric nature allows us to automatically infer the model complexity from the data, i.e., the number of features necessary to capture the latent structure in the data. Third, the latent features in the model are binary-valued variables, easing the interpretability of the obtained latent features in data exploration tasks.

Muhammad Bilal Zafar, Isabel Valera, Manuel Gomez Rodriguez et al.

The adoption of automated, data-driven decision making in an ever expanding range of applications has raised concerns about its potential unfairness towards certain social groups. In this context, a number of recent studies have focused on defining, detecting, and removing unfairness from data-driven decision systems. However, the existing notions of fairness, based on parity (equality) in treatment or outcomes for different social groups, tend to be quite stringent, limiting the overall decision making accuracy. In this paper, we draw inspiration from the fair-division and envy-freeness literature in economics and game theory and propose preference-based notions of fairness -- given the choice between various sets of decision treatments or outcomes, any group of users would collectively prefer its treatment or outcomes, regardless of the (dis)parity as compared to the other groups. Then, we introduce tractable proxies to design margin-based classifiers that satisfy these preference-based notions of fairness. Finally, we experiment with a variety of synthetic and real-world datasets and show that preference-based fairness allows for greater decision accuracy than parity-based fairness.

Isabel Valera, Melanie F. Pradier, Maria Lomeli et al.

Latent feature modeling allows capturing the latent structure responsible for generating the observed properties of a set of objects. It is often used to make predictions either for new values of interest or missing information in the original data, as well as to perform data exploratory analysis. However, although there is an extensive literature on latent feature models for homogeneous datasets, where all the attributes that describe each object are of the same (continuous or discrete) nature, there is a lack of work on latent feature modeling for heterogeneous databases. In this paper, we introduce a general Bayesian nonparametric latent feature model suitable for heterogeneous datasets, where the attributes describing each object can be either discrete, continuous or mixed variables. The proposed model presents several important properties. First, it accounts for heterogeneous data while keeping the properties of conjugate models, which allow us to infer the model in linear time with respect to the number of objects and attributes. Second, its Bayesian nonparametric nature allows us to automatically infer the model complexity from the data, i.e., the number of features necessary to capture the latent structure in the data. Third, the latent features in the model are binary-valued variables, easing the interpretability of the obtained latent features in data exploratory analysis. We show the flexibility of the proposed model by solving both prediction and data analysis tasks on several real-world datasets. Moreover, a software package of the GLFM is publicly available for other researcher to use and improve it.

Utkarsh Upadhyay, Isabel Valera, Manuel Gomez-Rodriguez

Learning from the crowd has become increasingly popular in the Web and social media. There is a wide variety of crowdlearning sites in which, on the one hand, users learn from the knowledge that other users contribute to the site, and, on the other hand, knowledge is reviewed and curated by the same users using assessment measures such as upvotes or likes. In this paper, we present a probabilistic modeling framework of crowdlearning, which uncovers the evolution of a user's expertise over time by leveraging other users' assessments of her contributions. The model allows for both off-site and on-site learning and captures forgetting of knowledge. We then develop a scalable estimation method to fit the model parameters from millions of recorded learning and contributing events. We show the effectiveness of our model by tracing activity of ~25 thousand users in Stack Overflow over a 4.5 year period. We find that answers with high knowledge value are rare. Newbies and experts tend to acquire less knowledge than users in the middle range. Prolific learners tend to be also proficient contributors that post answers with high knowledge value.

Muhammad Bilal Zafar, Isabel Valera, Manuel Gomez Rodriguez et al.

Automated data-driven decision making systems are increasingly being used to assist, or even replace humans in many settings. These systems function by learning from historical decisions, often taken by humans. In order to maximize the utility of these systems (or, classifiers), their training involves minimizing the errors (or, misclassifications) over the given historical data. However, it is quite possible that the optimally trained classifier makes decisions for people belonging to different social groups with different misclassification rates (e.g., misclassification rates for females are higher than for males), thereby placing these groups at an unfair disadvantage. To account for and avoid such unfairness, in this paper, we introduce a new notion of unfairness, disparate mistreatment, which is defined in terms of misclassification rates. We then propose intuitive measures of disparate mistreatment for decision boundary-based classifiers, which can be easily incorporated into their formulation as convex-concave constraints. Experiments on synthetic as well as real world datasets show that our methodology is effective at avoiding disparate mistreatment, often at a small cost in terms of accuracy.

Behzad Tabibian, Isabel Valera, Mehrdad Farajtabar et al.

Online knowledge repositories typically rely on their users or dedicated editors to evaluate the reliability of their content. These evaluations can be viewed as noisy measurements of both information reliability and information source trustworthiness. Can we leverage these noisy evaluations, often biased, to distill a robust, unbiased and interpretable measure of both notions? In this paper, we argue that the temporal traces left by these noisy evaluations give cues on the reliability of the information and the trustworthiness of the sources. Then, we propose a temporal point process modeling framework that links these temporal traces to robust, unbiased and interpretable notions of information reliability and source trustworthiness. Furthermore, we develop an efficient convex optimization procedure to learn the parameters of the model from historical traces. Experiments on real-world data gathered from Wikipedia and Stack Overflow show that our modeling framework accurately predicts evaluation events, provides an interpretable measure of information reliability and source trustworthiness, and yields interesting insights about real-world events.

Charalampos Mavroforakis, Isabel Valera, Manuel Gomez Rodriguez

People are increasingly relying on the Web and social media to find solutions to their problems in a wide range of domains. In this online setting, closely related problems often lead to the same characteristic learning pattern, in which people sharing these problems visit related pieces of information, perform almost identical queries or, more generally, take a series of similar actions. In this paper, we introduce a novel modeling framework for clustering continuous-time grouped streaming data, the hierarchical Dirichlet Hawkes process (HDHP), which allows us to automatically uncover a wide variety of learning patterns from detailed traces of learning activity. Our model allows for efficient inference, scaling to millions of actions taken by thousands of users. Experiments on real data gathered from Stack Overflow reveal that our framework can recover meaningful learning patterns in terms of both content and temporal dynamics, as well as accurately track users' interests and goals over time.

Muhammad Bilal Zafar, Isabel Valera, Manuel Gomez Rodriguez et al.

Algorithmic decision making systems are ubiquitous across a wide variety of online as well as offline services. These systems rely on complex learning methods and vast amounts of data to optimize the service functionality, satisfaction of the end user and profitability. However, there is a growing concern that these automated decisions can lead, even in the absence of intent, to a lack of fairness, i.e., their outcomes can disproportionately hurt (or, benefit) particular groups of people sharing one or more sensitive attributes (e.g., race, sex). In this paper, we introduce a flexible mechanism to design fair classifiers by leveraging a novel intuitive measure of decision boundary (un)fairness. We instantiate this mechanism with two well-known classifiers, logistic regression and support vector machines, and show on real-world data that our mechanism allows for a fine-grained control on the degree of fairness, often at a small cost in terms of accuracy.

Francisco J. R. Ruiz, Isabel Valera, Carlos Blanco et al.

The analysis of comorbidity is an open and complex research field in the branch of psychiatry, where clinical experience and several studies suggest that the relation among the psychiatric disorders may have etiological and treatment implications. In this paper, we are interested in applying latent feature modeling to find the latent structure behind the psychiatric disorders that can help to examine and explain the relationships among them. To this end, we use the large amount of information collected in the National Epidemiologic Survey on Alcohol and Related Conditions (NESARC) database and propose to model these data using a nonparametric latent model based on the Indian Buffet Process (IBP). Due to the discrete nature of the data, we first need to adapt the observation model for discrete random variables. We propose a generative model in which the observations are drawn from a multinomial-logit distribution given the IBP matrix. The implementation of an efficient Gibbs sampler is accomplished using the Laplace approximation, which allows integrating out the weighting factors of the multinomial-logit likelihood model. We also provide a variational inference algorithm for this model, which provides a complementary (and less expensive in terms of computational complexity) alternative to the Gibbs sampler allowing us to deal with a larger number of data. Finally, we use the model to analyze comorbidity among the psychiatric disorders diagnosed by experts from the NESARC database.