Santiago Zazo

Santiago Zazo, Sergio Valcarcel Macua, Matilde Sánchez-Fernández et al. · microsoft-research

In a noncooperative dynamic game, multiple agents operating in a changing environment aim to optimize their utilities over an infinite time horizon. Time-varying environments allow to model more realistic scenarios (e.g., mobile devices equipped with batteries, wireless communications over a fading channel, etc.). However, solving a dynamic game is a difficult task that requires dealing with multiple coupled optimal control problems. We focus our analysis on a class of problems, named \textit{dynamic potential games}, whose solution can be found through a single multivariate optimal control problem. Our analysis generalizes previous studies by considering that the set of environment's states and the set of players' actions are constrained, as it is required by most of the applications. And the theoretical results are the natural extension of the analysis for static potential games. We apply the analysis and provide numerical methods to solve four key example problems, with different features each: energy demand control in a smart-grid network, network flow optimization in which the relays have bounded link capacity and limited battery life, uplink multiple access communication with users that have to optimize the use of their batteries, and two optimal scheduling games with nonstationary channels.

Alejandro Almodóvar, Mar Elizo, Patricia A. Apellániz et al.

Causal generative models provide a principled framework for answering observational, interventional, and counterfactual queries from observational data. However, many deep causal models rely on highly expressive architectures with opaque mechanisms, limiting auditability in high-stakes domains. We propose KaCGM, a causal generative model for mixed-type tabular data where each structural equation is parameterized by a Kolmogorov--Arnold Network (KAN). This decomposition enables direct inspection of learned causal mechanisms, including symbolic approximations and visualization of parent--child relationships, while preserving query-agnostic generative semantics. We introduce a validation pipeline based on distributional matching and independence diagnostics of inferred exogenous variables, allowing assessment using observational data alone. Experiments on synthetic and semi-synthetic benchmarks show competitive performance against state-of-the-art methods. A real-world cardiovascular case study further demonstrates the extraction of simplified structural equations and interpretable causal effects. These results suggest that expressive causal generative modeling and functional transparency can be achieved jointly, supporting trustworthy deployment in tabular decision-making settings. Code: https://github.com/aalmodovares/kacgm

Javier Zazo, Santiago Zazo, Sergio Valcarcel Macua

Demand-side management presents significant benefits in reducing the energy load in smart grids by balancing consumption demands or including energy generation and/or storage devices in the user's side. These techniques coordinate the energy load so that users minimize their monetary expenditure. However, these methods require accurate predictions in the energy consumption profiles, which make them inflexible to real demand variations. In this paper we propose a realistic model that accounts for uncertainty in these variations and calculates a robust price for all users in the smart grid. We analyze the existence of solutions for this novel scenario, propose convergent distributed algorithms to find them, and perform simulations considering energy expenditure. We show that this model can effectively reduce the monetary expenses for all users in a real-time market, while at the same time it provides a reliable production cost estimate to the energy supplier.

Patricia A. Apellániz, Ana Jiménez, Borja Arroyo Galende et al.

While synthetic tabular data generation using Deep Generative Models (DGMs) offers a compelling solution to data scarcity and privacy concerns, their effectiveness relies on the availability of substantial training data, often lacking in real-world scenarios. To overcome this limitation, we propose a novel methodology that explicitly integrates artificial inductive biases into the generative process to improve data quality in low-data regimes. Our framework leverages transfer learning and meta-learning techniques to construct and inject informative inductive biases into DGMs. We evaluate four approaches (pre-training, model averaging, Model-Agnostic Meta-Learning (MAML), and Domain Randomized Search (DRS)) and analyze their impact on the quality of the generated text. Experimental results show that incorporating inductive bias substantially improves performance, with transfer learning methods outperforming meta-learning, achieving up to 60\% gains in Jensen-Shannon divergence. The methodology is model-agnostic and especially relevant in domains such as healthcare and finance, where high-quality synthetic data are essential, and data availability is often limited.

Alejandro Almodóvar, Patricia A. Apellániz, Santiago Zazo et al.

Deep neural networks achieve state-of-the-art performance in estimating heterogeneous treatment effects, but their opacity limits trust and adoption in sensitive domains such as medicine, economics, and public policy. Building on well-established and high-performing causal neural architectures, we propose causalKANs, a framework that transforms neural estimators of conditional average treatment effects (CATEs) into Kolmogorov--Arnold Networks (KANs). By incorporating pruning and symbolic simplification, causalKANs yields interpretable closed-form formulas while preserving predictive accuracy. Experiments on benchmark datasets demonstrate that causalKANs perform on par with neural baselines in CATE error metrics, and that even simple KAN variants achieve competitive performance, offering a favorable accuracy--interpretability trade-off. By combining reliability with analytic accessibility, causalKANs provide auditable estimators supported by closed-form expressions and interpretable plots, enabling trustworthy individualized decision-making in high-stakes settings. We release the code for reproducibility at https://github.com/aalmodovares/causalkans .

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

Patricia A. Apellániz, Juan Parras, Santiago Zazo

The rising use of machine learning in various fields requires robust methods to create synthetic tabular data. Data should preserve key characteristics while addressing data scarcity challenges. Current approaches based on Generative Adversarial Networks, such as the state-of-the-art CTGAN model, struggle with the complex structures inherent in tabular data. These data often contain both continuous and discrete features with non-Gaussian distributions. Therefore, we propose a novel Variational Autoencoder (VAE)-based model that addresses these limitations. Inspired by the TVAE model, our approach incorporates a Bayesian Gaussian Mixture model (BGM) within the VAE architecture. This avoids the limitations imposed by assuming a strictly Gaussian latent space, allowing for a more accurate representation of the underlying data distribution during data generation. Furthermore, our model offers enhanced flexibility by allowing the use of various differentiable distributions for individual features, making it possible to handle both continuous and discrete data types. We thoroughly validate our model on three real-world datasets with mixed data types, including two medically relevant ones, based on their resemblance and utility. This evaluation demonstrates significant outperformance against CTGAN and TVAE, establishing its potential as a valuable tool for generating synthetic tabular data in various domains, particularly in healthcare.

Patricia A. Apellániz, Ana Jiménez, Borja Arroyo Galende et al.

The ever-increasing use of generative models in various fields where tabular data is used highlights the need for robust and standardized validation metrics to assess the similarity between real and synthetic data. Current methods lack a unified framework and rely on diverse and often inconclusive statistical measures. Divergences, which quantify discrepancies between data distributions, offer a promising avenue for validation. However, traditional approaches calculate divergences independently for each feature due to the complexity of joint distribution modeling. This paper addresses this challenge by proposing a novel approach that uses divergence estimation to overcome the limitations of marginal comparisons. Our core contribution lies in applying a divergence estimator to build a validation metric considering the joint distribution of real and synthetic data. We leverage a probabilistic classifier to approximate the density ratio between datasets, allowing the capture of complex relationships. We specifically calculate two divergences: the well-known Kullback-Leibler (KL) divergence and the Jensen-Shannon (JS) divergence. KL divergence offers an established use in the field, while JS divergence is symmetric and bounded, providing a reliable metric. The efficacy of this approach is demonstrated through a series of experiments with varying distribution complexities. The initial phase involves comparing estimated divergences with analytical solutions for simple distributions, setting a benchmark for accuracy. Finally, we validate our method on a real-world dataset and its corresponding synthetic counterpart, showcasing its effectiveness in practical applications. This research offers a significant contribution with applicability beyond tabular data and the potential to improve synthetic data validation in various fields.

Patricia A. Apellániz, Juan Parras, Santiago Zazo

As in many fields of medical research, survival analysis has witnessed a growing interest in the application of deep learning techniques to model complex, high-dimensional, heterogeneous, incomplete, and censored medical data. Current methods often make assumptions about the relations between data that may not be valid in practice. In response, we introduce SAVAE (Survival Analysis Variational Autoencoder), a novel approach based on Variational Autoencoders. SAVAE contributes significantly to the field by introducing a tailored ELBO formulation for survival analysis, supporting various parametric distributions for covariates and survival time (as long as the log-likelihood is differentiable). It offers a general method that consistently performs well on various metrics, demonstrating robustness and stability through different experiments. Our proposal effectively estimates time-to-event, accounting for censoring, covariate interactions, and time-varying risk associations. We validate our model in diverse datasets, including genomic, clinical, and demographic data, with varying levels of censoring. This approach demonstrates competitive performance compared to state-of-the-art techniques, as assessed by the Concordance Index and the Integrated Brier Score. SAVAE also offers an interpretable model that parametrically models covariates and time. Moreover, its generative architecture facilitates further applications such as clustering, data imputation, and the generation of synthetic patient data through latent space inference from survival data.

Alejandro Almodóvar, Patricia A. Apellániz, Alba Garrido et al.

Why should a clinician trust an Artificial Intelligence (AI) prediction? Despite the increasing accuracy of machine learning methods in medicine, the lack of transparency continues to hinder their adoption in clinical practice. In this work, we explore Kolmogorov-Arnold Networks (KANs) for clinical classification tasks on tabular data. In contrast to traditional neural networks, KANs are function-based architectures that offer intrinsic interpretability through transparent, symbolic representations. We introduce \emph{Logistic-KAN}, a flexible generalization of logistic regression, and \emph{Kolmogorov-Arnold Additive Model (KAAM)}, a simplified additive variant that delivers transparent, symbolic formulas. Unlike ``black-box'' models that require post-hoc explainability tools, our models support built-in patient-level insights, intuitive visualizations, and nearest-patient retrieval. Across multiple health datasets, our models match or outperform standard baselines, while remaining fully interpretable. These results position KANs as a promising step toward trustworthy AI that clinicians can understand, audit, and act upon. We release the code for reproducibility in \codeurl.

Alba Garrido, Alejandro Almodóvar, Patricia A. Apellániz et al.

Accurate survival prediction is critical in oncology for prognosis and treatment planning. Traditional approaches often rely on a single data modality, limiting their ability to capture the complexity of tumor biology. To address this challenge, we introduce a multimodal deep learning framework for survival analysis capable of modeling both single and competing risks scenarios, evaluating the impact of integrating multiple medical data sources on survival predictions. We propose SAMVAE (Survival Analysis Multimodal Variational Autoencoder), a novel deep learning architecture designed for survival prediction that integrates six data modalities: clinical variables, four molecular profiles, and histopathological images. SAMVAE leverages modality specific encoders to project inputs into a shared latent space, enabling robust survival prediction while preserving modality specific information. Its parametric formulation enables the derivation of clinically meaningful statistics from the output distributions, providing patient-specific insights through interactive multimedia that contribute to more informed clinical decision-making and establish a foundation for interpretable, data-driven survival analysis in oncology. We evaluate SAMVAE on two cancer cohorts breast cancer and lower grade glioma applying tailored preprocessing, dimensionality reduction, and hyperparameter optimization. The results demonstrate the successful integration of multimodal data for both standard survival analysis and competing risks scenarios across different datasets. Our model achieves competitive performance compared to state-of-the-art multimodal survival models. Notably, this is the first parametric multimodal deep learning architecture to incorporate competing risks while modeling continuous time to a specific event, using both tabular and image data.

Sergio Valcarcel Macua, Javier Zazo, Santiago Zazo

Multiagent systems where agents interact among themselves and with a stochastic environment can be formalized as stochastic games. We study a subclass named Markov potential games (MPGs) that appear often in economic and engineering applications when the agents share a common resource. We consider MPGs with continuous state-action variables, coupled constraints and nonconvex rewards. Previous analysis followed a variational approach that is only valid for very simple cases (convex rewards, invertible dynamics, and no coupled constraints); or considered deterministic dynamics and provided open-loop (OL) analysis, studying strategies that consist in predefined action sequences, which are not optimal for stochastic environments. We present a closed-loop (CL) analysis for MPGs and consider parametric policies that depend on the current state. We provide easily verifiable, sufficient and necessary conditions for a stochastic game to be an MPG, even for complex parametric functions (e.g., deep neural networks); and show that a closed-loop Nash equilibrium (NE) can be found (or at least approximated) by solving a related optimal control problem (OCP). This is useful since solving an OCP--which is a single-objective problem--is usually much simpler than solving the original set of coupled OCPs that form the game--which is a multiobjective control problem. This is a considerable improvement over the previously standard approach for the CL analysis of MPGs, which gives no approximate solution if no NE belongs to the chosen parametric family, and which is practical only for simple parametric forms. We illustrate the theoretical contributions with an example by applying our approach to a noncooperative communications engineering game. We then solve the game with a deep reinforcement learning algorithm that learns policies that closely approximates an exact variational NE of the game.

Sergio Valcarcel Macua, Aleksi Tukiainen, Daniel García-Ocaña Hernández et al.

We propose a fully distributed actor-critic algorithm approximated by deep neural networks, named \textit{Diff-DAC}, with application to single-task and to average multitask reinforcement learning (MRL). Each agent has access to data from its local task only, but it aims to learn a policy that performs well on average for the whole set of tasks. During the learning process, agents communicate their value-policy parameters to their neighbors, diffusing the information across the network, so that they converge to a common policy, with no need for a central node. The method is scalable, since the computational and communication costs per agent grow with its number of neighbors. We derive Diff-DAC's from duality theory and provide novel insights into the standard actor-critic framework, showing that it is actually an instance of the dual ascent method that approximates the solution of a linear program. Experiments suggest that Diff-DAC can outperform the single previous distributed MRL approach (i.e., Dist-MTLPS) and even the centralized architecture.

Sergio Valcarcel Macua, Jianshu Chen, Santiago Zazo et al.

We apply diffusion strategies to develop a fully-distributed cooperative reinforcement learning algorithm in which agents in a network communicate only with their immediate neighbors to improve predictions about their environment. The algorithm can also be applied to off-policy learning, meaning that the agents can predict the response to a behavior different from the actual policies they are following. The proposed distributed strategy is efficient, with linear complexity in both computation time and memory footprint. We provide a mean-square-error performance analysis and establish convergence under constant step-size updates, which endow the network with continuous learning capabilities. The results show a clear gain from cooperation: when the individual agents can estimate the solution, cooperation increases stability and reduces bias and variance of the prediction error; but, more importantly, the network is able to approach the optimal solution even when none of the individual agents can (e.g., when the individual behavior policies restrict each agent to sample a small portion of the state space).