Recommender systems play a key role in shaping modern web ecosystems. These systems alternate between (1) making recommendations, (2) collecting user responses to these recommendations, and (3) retraining the recommendation algorithm based on this feedback. During this process, the recommender influences the user behavioral data that is subsequently used to update the recommender itself, thus creating a feedback loop. Recent work has shown that feedback loops may compromise recommendation quality and homogenize user behavior, raising ethical and performance concerns around deploying recommender systems. To address these concerns, we propose the causal adjustment for feedback loops (CAFL) , an algorithm that uses causal inference to break feedback loops for any loss-minimizing recommendation algorithms. The key observation is that a recommender system does not suffer from feedback loops if it reasons about causal quantities, namely the intervention distributions of recommendations on user ratings. Moreover, we can calculate these intervention distributions from observational data by adjusting for the recommender system’s predictions of user preferences. Using simulated environments, we demonstrate that CAFL improves recommendation quality when compared to prior correction methods.

Representation learning constructs low-dimensional representations to summarize essential features of high-dimensional data. This learning problem is often approached by describing various desiderata associated with learned representations; e.g., that they be non-spurious, efficient, or disentangled. It can be challenging, however, to turn these intuitive desiderata into formal criteria that can be measured and enhanced based on observed data. In this paper, we take a causal perspective on representation learning, formalizing desiderata like non-spuriousness and demonstrating their practical utility.

This paper introduces posterior mean matching (PMM), a new method for generative modeling that is grounded in Bayesian inference. PMM uses conjugate pairs of distributions to model complex data of various modalities like images and text, offering a flexible alternative to existing methods like diffusion models. PMM models iteratively refine noisy approximations of the target distribution using updates from online Bayesian inference. PMM is flexible because its mechanics are based on general Bayesian models. We demonstrate this flexibility by developing specialized examples: a generative PMM model of real-valued data using the Normal-Normal model, a generative PMM model of count data using a Gamma-Poisson model, and a generative PMM model of discrete data using a Dirichlet-Categorical model. For the Normal-Normal PMM model, we establish a direct connection to diffusion models by showing that its continuous-time formulation converges to a stochastic differential equation (SDE). Additionally, for the Gamma-Poisson PMM, we derive a novel SDE driven by a Cox process, which is a significant departure from traditional Brownian motion-based generative models. PMMs achieve performance that is competitive with generative models for language modeling and image generation.

Recommender systems are inherently decision-making systems, taking actions that have consequences for the world around them.Some consequences might be desirable (for example, growing the user base for an online platform), others might be unintended (for example, amplifying inequality among item providers).In order to reason about these consequences, we need to resort to methods from the literature on causal inference.Whilst this research area has seen a growing interest in recent years, there is an abundance of open research questions from how we should model large-scale recommender systems in such causal frameworks, to what the limitations are for causal identifiability in general settings, and how we can properly handle confounding variables.The CONSEQUENCES workshop series aims to bring together researchers and practitioners who are interested in this research topic, and wish to help shape its future.

Large language models (LLMs) like transformers demonstrate impressive in-context learning (ICL) capabilities, allowing them to make predictions for new tasks based on prompt exemplars without parameter updates. While existing ICL theories often assume structured training data resembling ICL tasks (e.g., x-y pairs for linear regression), LLMs are typically trained unsupervised on unstructured text, such as web content, which lacks clear parallels to tasks like word analogy. To address this gap, we examine what enables ICL in models trained on unstructured data, focusing on critical sequence model requirements and training data structure. We find that many ICL capabilities can emerge simply from co-occurrence of semantically related word pairs in unstructured data; word analogy completion, for example, can provably arise purely through co-occurrence modeling, using classical language models like continuous bag of words (CBOW), without needing positional information or attention mechanisms. However, positional information becomes crucial for logic reasoning tasks requiring generalization to unseen tokens. Finally, we identify two cases where ICL fails: one in logic reasoning tasks that require generalizing to new, unseen patterns, and another in analogy completion where relevant word pairs appear only in fixed training positions. These findings suggest that LLMs' ICL abilities depend heavily on the structural elements within their training data.

Recommender systems are inherently decision-making systems, taking actions that have consequences for the world around them. Some consequences might be desirable (for example, growing the user base for an online platform), others might be unintended (for example, amplifying inequality among item providers). In order to reason about these consequences, we need to resort to methods from the literature on causal inference. Whilst this research area has seen a growing interest in recent years, there is an abundance of open research questions from how we should model large-scale recommender systems in such causal frameworks, to what the limitations are for causal identifiability in general settings, and how we can properly handle confounding variables. The CONSEQUENCES workshop series aims to bring together researchers and practitioners who are interested in this research topic, and wish to help shape its future.

OBJECTIVE: Healthcare continues to grapple with the persistent issue of treatment disparities, sparking concerns regarding the equitable allocation of treatments in clinical practice. While various fairness metrics have emerged to assess fairness in decision-making processes, a growing focus has been on causality-based fairness concepts due to their capacity to mitigate confounding effects and reason about bias. However, the application of causal fairness notions in evaluating the fairness of clinical decision-making with electronic health record (EHR) data remains an understudied domain. This study aims to address the methodological gap in assessing causal fairness of treatment allocation with electronic health records data. In addition, we investigate the impact of social determinants of health on the assessment of causal fairness of treatment allocation. METHODS: We propose a causal fairness algorithm to assess fairness in clinical decision-making. Our algorithm accounts for the heterogeneity of patient populations and identifies potential unfairness in treatment allocation by conditioning on patients who have the same likelihood to benefit from the treatment. We apply this framework to a patient cohort with coronary artery disease derived from an EHR database to evaluate the fairness of treatment decisions. RESULTS: Our analysis reveals notable disparities in coronary artery bypass grafting (CABG) allocation among different patient groups. Women were found to be 4.4%-7.7% less likely to receive CABG than men in two out of four treatment response strata. Similarly, Black or African American patients were 5.4%-8.7% less likely to receive CABG than others in three out of four response strata. These results were similar when social determinants of health (insurance and area deprivation index) were dropped from the algorithm. These findings highlight the presence of disparities in treatment allocation among similar patients, suggesting potential unfairness in the clinical decision-making process. CONCLUSION: This study introduces a novel approach for assessing the fairness of treatment allocation in healthcare. By incorporating responses to treatment into fairness framework, our method explores the potential of quantifying fairness from a causal perspective using EHR data. Our research advances the methodological development of fairness assessment in healthcare and highlight the importance of causality in determining treatment fairness.

Representation learning constructs low-dimensional representations to summarize essential features of high-dimensional data. This learning problem is often approached by describing various desiderata associated with learned representations; e.g., that they be non-spurious, efficient, or disentangled. It can be challenging, however, to turn these intuitive desiderata into formal criteria that can be measured and enhanced based on observed data. In this paper, we take a causal perspective on representation learning, formalizing non-spuriousness and efficiency (in supervised representation learning) and disentanglement (in unsupervised representation learning) using counterfactual quantities and observable consequences of causal assertions. This yields computable metrics that can be used to assess the degree to which representations satisfy the desiderata of interest and learn non-spurious and disentangled representations from single observational datasets.

In offline reinforcement learning (RL) an optimal policy is learned solely from a priori collected observational data. However, in observational data, actions are often confounded by unobserved variables. Instrumental variables (IVs), in the context of RL, are the variables whose influence on the state variables is all mediated by the action. When a valid instrument is present, we can recover the confounded transition dynamics through observational data. We study a confounded Markov decision process where the transition dynamics admit an additive nonlinear functional form. Using IVs, we derive a conditional moment restriction through which we can identify transition dynamics based on observational data. We propose a provably efficient IV-aided Value Iteration (IVVI) algorithm based on a primal-dual reformulation of the conditional moment restriction. To our knowledge, this is the first provably efficient algorithm for instrument-aided offline RL.

This paper presents a new optimization approach to causal estimation. Given data that contains covariates and an outcome, which covariates are causes of the outcome, and what is the strength of the causality? In classical machine learning (ML), the goal of optimization is to maximize predictive accuracy. However, some covariates might exhibit a non-causal association with the outcome. Such spurious associations provide predictive power for classical ML, but they prevent us from causally interpreting the result. This paper proposes CoCo, an optimization algorithm that bridges the gap between pure prediction and causal inference. CoCo leverages the recently-proposed idea of environments, datasets of covariates/response where the causal relationships remain invariant but where the distribution of the covariates changes from environment to environment. Given datasets from multiple environments—and ones that exhibit sufficient heterogeneity—CoCo maximizes an objective for which the only solution is the causal solution. We describe the theoretical foundations of this approach and demonstrate its effectiveness on simulated and real datasets. Compared to classical ML and existing methods, CoCo provides more accurate estimates of the causal model and more accurate predictions under interventions.

The causal revolution has stimulated interest in understanding complex relationships in various fields. Most of the existing methods aim to discover causal relationships among all variables within a complex large-scale graph. However, in practice, only a small subset of variables in the graph are relevant to the outcomes of interest. Consequently, causal estimation with the full causal graph---particularly given limited data---could lead to numerous *falsely discovered, spurious* variables that exhibit high correlation with, but exert no causal impact on, the target outcome. In this paper, we propose learning a class of *necessary and sufficient causal graphs (NSCG)* that exclusively comprises causally relevant variables for an outcome of interest, which we term *causal features*. The key idea is to employ *probabilities of causation* to systematically evaluate the importance of features in the causal graph, allowing us to identify a subgraph relevant to the outcome of interest. To learn NSCG from data, we develop a *necessary and sufficient causal structural learning (NSCSL)* algorithm, by establishing theoretical properties and relationships between probabilities of causation and natural causal effects of features. Across empirical studies of simulated and real data, we demonstrate that NSCSL outperforms existing algorithms and can reveal crucial yeast genes for target heritable traits of interest.

Recommender systems make algorithmic decisions about what will be shown to whom, billions of times every day across the web. These decisions have consequences that can often be far-reaching. Indeed, users that are exposed to certain items, might be convinced to explore interests that are novel to them. At the same time, exposure is often linked to economic incentives for the item producer, which platform-level metrics will be impacted by as well. Feedback loops in existing systems also imply that algorithmic decisions made by the model itself, have an impact on the data future model iterations will be trained and evaluated on.

Contract theory studies the interactions between a principal and an agent when the two parties transact in the presence of private information [Bolton and Dewatripont, 2004, Faure-Grimaud et al., 2001, Salanié, 2005]. The principal would like to achieve her desired outcomes by hiring agents to work for her. The agent wishes to make money by working for the principal. They develop agreements in the form of a contract, which specifies how much the principal would pay under the different possible outcomes of the agent's work.

Bidirectional attention - composed of the neural network architecture of self-attention with positional encodings, together with the masked language model (MLM) objective - has emerged as a key component of modern large language models (LLMs). Despite its empirical success, few studies have examined its statistical underpinnings: What statistical model is bidirectional attention implicitly fitting? What sets it apart from its non-attention predecessors? We explore these questions in this paper. The key observation is that fitting a single-layer single-head bidirectional attention, upon reparameterization, is equivalent to fitting a continuous bag of words (CBOW) model with mixture-of-experts (MoE) weights. Further, bidirectional attention with multiple heads and multiple layers is equivalent to stacked MoEs and a mixture of MoEs, respectively. This statistical viewpoint reveals the distinct use of MoE in bidirectional attention, which aligns with its practical effectiveness in handling heterogeneous data. It also suggests an immediate extension to categorical tabular data, if we view each word location in a sentence as a tabular feature. Across empirical studies, we find that this extension outperforms existing tabular extensions of transformers in out-of-distribution (OOD) generalization. Finally, this statistical perspective of bidirectional attention enables us to theoretically characterize when linear word analogies are present in its word embeddings. These analyses show that bidirectional attention can require much stronger assumptions to exhibit linear word analogies than its non-attention predecessors.

Large-scale, two-sided matching platforms must find market outcomes that align with user preferences while simultaneously learning these preferences from data. Classical notions of stability (Gale and Shapley, 1962; Shapley and Shubik, 1971) are, unfortunately, of limited value in the learning setting, given that preferences are inherently uncertain and destabilizing while they are being learned. To bridge this gap, we develop a framework and algorithms for learning stable market outcomes under uncertainty. Our primary setting is matching with transferable utilities, where the platform both matches agents and sets monetary transfers between them. We design an incentive-aware learning objective that captures the distance of a market outcome from equilibrium. Using this objective, we analyze the complexity of learning as a function of preference structure, casting learning as a stochastic multi-armed bandit problem. Algorithmically, we show that “optimism in the face of uncertainty,” the principle underlying many bandit algorithms, applies to a primal-dual formulation of matching with transfers and leads to near-optimal regret bounds. Our work takes a first step toward elucidating when and how stable matchings arise in large, data-driven marketplaces.

Multigoal reinforcement learning (RL) extends the typical RL with goal-conditional value functions and policies. One efficient multigoal RL algorithm is the hindsight experience replay (HER). By treating a hindsight goal from failed experiences as the original goal, HER enables the agent to receive rewards frequently. However, a key assumption of HER is that the hindsight goals do not change the likelihood of the sampled transitions and trajectories used in training, which is not the fact according to our analysis. More specifically, we show that using hindsight goals changes such a likelihood and results in a biased learning objective for multigoal RL. We analyze the hindsight bias due to this use of hindsight goals and propose the bias-corrected HER (BHER), an efficient algorithm that corrects the hindsight bias in training. We further show that BHER outperforms several state-of-the-art multigoal RL approaches in challenging robotics tasks.

We study a constructive procedure that approximates Gateaux derivatives for statistical functionals by finite-differencing, with attention to causal inference functionals. We focus on the case where probability distributions are not known a priori but need also to be estimated from data, leading to empirical Gateaux derivatives, and study relationships between empirical, numerical, and analytical Gateaux derivatives. Starting with a case study of counterfactual mean estimation, we verify the exact relationship between finite-differences and the analytical Gateaux derivative. We then derive requirements on the rates of numerical approximation in perturbation and smoothing that preserve statistical benefits. We study more complicated functionals such as dynamic treatment regimes and the linear-programming formulation for policy optimization infinite-horizon Markov decision processes. In the case of the latter, this approach can be used to approximate bias adjustments in the presence of arbitrary constraints, illustrating the usefulness of constructive approaches for Gateaux derivatives. We find that, omitting unfavorable dimension dependence of smoothing, although rate-double robustness permits for coarser rates of perturbation size than implied by generic approximation analysis of finite-differences for the case of the counterfactual mean, this is not the case for the infinite-horizon MDP policy value.

Predictions about people, such as their expected educational achievement or their credit risk, can be performative and shape the outcome that they are designed to predict. Understanding the causal effect of predictions on the eventual outcomes is crucial for foreseeing the implications of future predictive models and selecting which models to deploy. However, this causal estimation task poses unique challenges: model predictions are usually deterministic functions of input features and highly correlated with outcomes, which can make the causal effects of predictions on outcomes impossible to disentangle from the direct effect of the covariates. We study this problem through the lens of causal identifiability. Despite the hardness of this problem in full generality, we highlight three natural scenarios where the causal effect of predictions can be identified from observational data: randomization in predictions, overparameterization of the predictive model deployed during data collection, and discrete prediction outputs. Empirically we show that given our identifiability conditions hold, standard variants of supervised learning that predict from predictions by treating the prediction as an input feature can find transferable functional relationships that allow for conclusions about newly deployed predictive models. These positive results fundamentally rely on model predictions being recorded during data collection, bringing forward the importance of rethinking standard data collection practices to enable progress towards a better understanding of social outcomes and performative feedback loops.

Confounding remains one of the major challenges to causal inference with observational data. This problem is paramount in medicine, where we would like to answer causal questions from large observational datasets like electronic health records (EHRs) and administrative claims. Modern medical data typically contain tens of thousands of covariates. Such a large set carries hope that many of the confounders are directly measured, and further hope that others are indirectly measured through their correlation with measured covariates. How can we exploit these large sets of covariates for causal inference? To help answer this question, this paper examines the performance of the large-scale propensity score (LSPS) approach on causal analysis of medical data. We demonstrate that LSPS may adjust for indirectly measured confounders by including tens of thousands of covariates that may be correlated with them. We present conditions under which LSPS removes bias due to indirectly measured confounders, and we show that LSPS may avoid bias when inadvertently adjusting for variables (like colliders) that otherwise can induce bias. We demonstrate the performance of LSPS with both simulated medical data and real medical data.

Causal inference from observational data can be biased by unobserved confounders. Confounders{—}the variables that affect both the treatments and the outcome{—}induce spurious non-causal correlations between the two. Without additional conditions, unobserved confounders generally make causal quantities hard to identify. In this paper, we focus on the setting where there are many treatments with shared confounding, and we study under what conditions is causal identification possible. The key observation is that we can view subsets of treatments as proxies of the unobserved confounder and identify the intervention distributions of the rest. Moreover, while existing identification formulas for proxy variables involve solving integral equations, we show that one can circumvent the need for such solutions by directly modeling the data. Finally, we extend these results to an expanded class of causal graphs, those with other confounders and selection variables.

Machine learning has allowed many systems that we interact with to improve performance and personalize. Recommender systems in particular are one of the largest users of machine learning in production environments that have improved performance of real-world systems. Learning in these interactive systems requires models that combine very diverse signals, including the logs of the interactive system (indicating if the intervention succeeded or failed) augmented with other data sources including: collaborative filtering, text, and image data. Bayesian inference is a compelling method to combine these diverse signals in a principled manner, but deployment of systems based on Bayesian principles remain challenging. The reward signal in the system logs is often uneven. Accurate estimation of reward is possible for exploiting actions, but often poor for other actions (exploration). Non-Bayesian methods such as inverse propensity score methods, the reinforce algorithm, and other heuristic-based approaches currently dominate practice. These commonly-used heuristics are often ineffective at leveraging diverse data. In contrast, Bayesian methods offer a principled, robust framework for learning from uneven signals and combining different types of information. Drawing upon the bandit and reinforcement learning community, in this workshop we will explore innovations in Bayesian inference for real world interactive systems, and consider advantages and limitations of the Bayesian approach.

Large-scale, two-sided matching platforms must find market outcomes that align with user preferences while simultaneously learning these preferences from data. But since preferences are inherently uncertain during learning, the classical notion of stability (Gale and Shapley, 1962; Shapley and Shubik, 1971) is unattainable in these settings. To bridge this gap, we develop a framework and algorithms for learning stable market outcomes under uncertainty. Our primary setting is matching with transferable utilities, where the platform both matches agents and sets monetary transfers between them. We design an incentive-aware learning objective that captures the distance of a market outcome from equilibrium. Using this objective, we analyze the complexity of learning as a function of preference structure, casting learning as a stochastic multi-armed bandit problem. Algorithmically, we show that "optimism in the face of uncertainty," the principle underlying many bandit algorithms, applies to a primal-dual formulation of matching with transfers and leads to near-optimal regret bounds. Our work takes a first step toward elucidating when and how stable matchings arise in large, data-driven marketplaces.

Variational autoencoders model high-dimensional data by positinglow-dimensional latent variables that are mapped through a flexibledistribution parametrized by a neural network. Unfortunately,variational autoencoders often suffer from posterior collapse: theposterior of the latent variables is equal to its prior, rendering thevariational autoencoder useless as a means to produce meaningfulrepresentations. Existing approaches to posterior collapse oftenattribute it to the use of neural networks or optimization issues dueto variational approximation. In this paper, we consider posteriorcollapse as a problem of latent variable non-identifiability. We provethat the posterior collapses if and only if the latent variables arenon-identifiable in the generative model. This fact implies thatposterior collapse is not a phenomenon specific to the use of flexibledistributions or approximate inference. Rather, it can occur inclassical probabilistic models even with exact inference, which wealso demonstrate. Based on these results, we propose a class oflatent-identifiable variational autoencoders, deep generative modelswhich enforce identifiability without sacrificing flexibility. Thismodel class resolves the problem of latent variablenon-identifiability by leveraging bijective Brenier maps andparameterizing them with input convex neural networks, without specialvariational inference objectives or optimization tricks. Acrosssynthetic and real datasets, latent-identifiable variationalautoencoders outperform existing methods in mitigating posteriorcollapse and providing meaningful representations of the data.

The task of recommender systems is classically framed as a prediction of users’ preferences and users’ ratings. However, its spirit is to answer a counterfactual question: “What would the rating be if we ‘forced’ the user to watch the movie?” This is a question about an intervention, that is a causal inference question. The key challenge of this causal inference is unobserved confounders, variables that affect both which items the users decide to interact with and how they rate them. To this end, we develop an algorithm that leverages classical recommendation models for causal recommendation. Across simulated and real datasets, we demonstrate that the proposed algorithm is more robust to unobserved confounders and improves recommendation.

We consider causal inference in the presence of unobserved confounding. We study the case where a proxy is available for the unobserved confounding in the form of a network connecting the units. For example, the link structure of a social network carries information about its members. We show how to effectively use the proxy to do causal inference. The main idea is to reduce the causal estimation problem to a semi-supervised prediction of both the treatments and outcomes. Networks admit high-quality embedding models that can be used for this semi-supervised prediction. We show that the method yields valid inferences under suitable (weak) conditions on the quality of the predictive model. We validate the method with experiments on a semi-synthetic social network dataset.

Variational Bayes (VB) is a scalable alternative to Markov chain Monte Carlo (MCMC) for Bayesian posterior inference. Though popular, VB comes with few theoretical guarantees, most of which focus on well-specified models. However, models are rarely well-specified in practice. In this work, we study VB under model misspecification. We prove the VB posterior is asymptotically normal and centers at the value that minimizes the Kullback-Leibler (KL) divergence to the true data-generating distribution. Moreover, the VB posterior mean centers at the same value and is also asymptotically normal. These results generalize the variational Bernstein--von Mises theorem [29] to misspecified models. As a consequence of these results, we find that the model misspecification error dominates the variational approximation error in VB posterior predictive distributions. It explains the widely observed phenomenon that VB achieves comparable predictive accuracy with MCMC even though VB uses an approximating family. As illustrations, we study VB under three forms of model misspecification, ranging from model over-/under-dispersion to latent dimensionality misspecification. We conduct two simulation studies that demonstrate the theoretical results.

Analyzing large-scale, multi-experiment studies requires scientists to test each experimental outcome for statistical significance and then assess the results as a whole. We present Black Box FDR (BB-FDR), an empirical-Bayes method for analyzing multi-experiment studies when many covariates are gathered per experiment. BB-FDR learns a series of black box predictive models to boost power and control the false discovery rate (FDR) at two stages of study analysis. In Stage 1, it uses a deep neural network prior to report which experiments yielded significant outcomes. In Stage 2, a separate black box model of each covariate is used to select features that have significant predictive power across all experiments. In benchmarks, BB-FDR outperforms competing state-of-the-art methods in both stages of analysis. We apply BB-FDR to two real studies on cancer drug efficacy. For both studies, BB-FDR increases the proportion of significant outcomes discovered and selects variables that reveal key genomic drivers of drug sensitivity and resistance in cancer.

Probabilistic modeling is cyclical: we specify a model, infer its posterior, and evaluate its performance. Evaluation drives the cycle, as we revise our model based on how it performs. This requires a metric. Traditionally, predictive accuracy prevails. Yet, predictive accuracy does not tell the whole story. We propose to evaluate a model through posterior dispersion. The idea is to analyze how each datapoint fares in relation to posterior uncertainty around the hidden structure. This highlights datapoints the model struggles to explain and provides complimentary insight to datapoints with low predictive accuracy. We present a family of posterior dispersion indices (PDI) that capture this idea. We show how a PDI identifies patterns of model mismatch in three real data examples: voting preferences, supermarket shopping, and population genetics.

Probabilistic models analyze data by relying on a set of assumptions. Data that exhibit deviations from these assumptions can undermine inference and prediction quality. Robust models offer protection against mismatch between a model’s assumptions and reality. We propose a way to systematically detect and mitigate mismatch of a large class of probabilistic models. The idea is to raise the likelihood of each observation to a weight and then to infer both the latent variables and the weights from data. Inferring the weights allows a model to identify observations that match its assumptions and down-weight others. This enables robust inference and improves predictive accuracy. We study four different forms of mismatch with reality, ranging from missing latent groups to structure misspecification. A Poisson factorization analysis of the Movielens 1M dataset shows the benefits of this approach in a practical scenario.