Vanessa Gómez-Verdejo

Vanessa Gómez-Verdejo, Emilio Parrado-Hernández, Manel Martínez-Ramón

Adaptive learning is necessary for non-stationary environments where the learning machine needs to forget past data distribution. Efficient algorithms require a compact model update to not grow in computational burden with the incoming data and with the lowest possible computational cost for online parameter updating. Existing solutions only partially cover these needs. Here, we propose the first adaptive sparse Gaussian Process (GP) able to address all these issues. We first reformulate a variational sparse GP algorithm to make it adaptive through a forgetting factor. Next, to make the model inference as simple as possible, we propose updating a single inducing point of the sparse GP model together with the remaining model parameters every time a new sample arrives. As a result, the algorithm presents a fast convergence of the inference process, which allows an efficient model update (with a single inference iteration) even in highly non-stationary environments. Experimental results demonstrate the capabilities of the proposed algorithm and its good performance in modeling the predictive posterior in mean and confidence interval estimation compared to state-of-the-art approaches.

Alejandro Guerrero-López, Carlos Sevilla-Salcedo, Vanessa Gómez-Verdejo et al.

Purpose: Handling heterogeneous and mixed data types has become increasingly critical with the exponential growth in real-world databases. While deep generative models attempt to merge diverse data views into a common latent space, they often sacrifice interpretability, flexibility, and modularity. This study proposes a novel method to address these limitations by combining Variational AutoEncoders (VAEs) with a Factor Analysis latent space (FA-VAE). Methods: The proposed FA-VAE method employs multiple VAEs to learn a private representation for each heterogeneous data view in a continuous latent space. Information is shared between views using a low-dimensional latent space, generated via a linear projection matrix. This modular design creates a hierarchical dependency between private and shared latent spaces, allowing for the flexible addition of new views and conditioning of pre-trained models. Results: The FA-VAE approach facilitates cross-generation of data from different domains and enables transfer learning between generative models. This allows for effective integration of information across diverse data views while preserving their distinct characteristics. Conclusions: By overcoming the limitations of existing methods, the FA-VAE provides a more interpretable, flexible, and modular solution for managing heterogeneous data types. It offers a pathway to more efficient and scalable data-handling strategies, enhancing the potential for cross-domain data synthesis and model transferability.

Carlos Sevilla-Salcedo, Ascensión Gallardo-Antolín, Vanessa Gómez-Verdejo et al.

This paper introduces a novel approach for multi-task regression that connects Kernel Machines (KMs) and Extreme Learning Machines (ELMs) through the exploitation of the Random Fourier Features (RFFs) approximation of the RBF kernel. In this sense, one of the contributions of this paper shows that for the proposed models, the KM and the ELM formulations can be regarded as two sides of the same coin. These proposed models, termed RFF-BLR, stand on a Bayesian framework that simultaneously addresses two main design goals. On the one hand, it fits multitask regressors based on KMs endowed with RBF kernels. On the other hand, it enables the introduction of a common-across-tasks prior that promotes multioutput sparsity in the ELM view. This Bayesian approach facilitates the simultaneous consideration of both the KM and ELM perspectives enabling (i) the optimisation of the RBF kernel parameter $γ$ within a probabilistic framework, (ii) the optimisation of the model complexity, and (iii) an efficient transfer of knowledge across tasks. The experimental results show that this framework can lead to significant performance improvements compared to the state-of-the-art methods in multitask nonlinear regression.

Lucía González-Zamorano, Nuria Balbás-Esteban, Vanessa Gómez-Verdejo et al.

Multimodal clinical data are characterized by high dimensionality, heterogeneous representations, and structured missingness, posing significant challenges for predictive modeling, data integration, and interpretability. We propose BIONIC (Bayesian Integration of Nonlinear Incomplete Clinical data), a unified probabilistic framework that integrates heterogeneous multimodal data under missingness through a joint generative-discriminative latent architecture. BIONIC uses pretrained embeddings for complex modalities such as medical images and clinical text, while incorporating structured clinical variables directly within a Bayesian multimodal formulation. The proposed framework enables robust learning in partially observed and semi-supervised settings by explicitly modeling modality-level and variable-level missingness, as well as missing labels. We evaluate BIONIC on three multimodal clinical and biomedical datasets, demonstrating strong and consistent discriminative performance compared to representative multimodal baselines, particularly under incomplete data scenarios. Beyond predictive accuracy, BIONIC provides intrinsic interpretability through its latent structure, enabling population-level analysis of modality relevance and supporting clinically meaningful insight.

Albert Belenguer-Llorens, Carlos Sevilla-Salcedo, Janaina Mourao-Miranda et al.

Real-world clinical problems are often characterized by multimodal data, usually associated with incomplete views and limited sample sizes in their cohorts, posing significant limitations for machine learning algorithms. In this work, we propose a Bayesian approach designed to efficiently handle these challenges while providing interpretable solutions. Our approach integrates (1) a generative formulation to capture cross-view relationships with a semi-supervised strategy, and (2) a discriminative task-oriented formulation to identify relevant information for specific downstream objectives. This dual generative-discriminative formulation offers both general understanding and task-specific insights; thus, it provides an automatic imputation of the missing views while enabling robust inference across different data sources. The potential of this approach becomes evident when applied to the multimodal clinical data, where our algorithm is able to capture and disentangle the complex interactions among biological, psychological, and sociodemographic modalities.

Albert Belenguer-Llorens, Carlos Sevilla-Salcedo, Jussi Tohka et al.

We present BALDUR, a novel Bayesian algorithm designed to deal with multi-modal datasets and small sample sizes in high-dimensional settings while providing explainable solutions. To do so, the proposed model combines within a common latent space the different data views to extract the relevant information to solve the classification task and prune out the irrelevant/redundant features/data views. Furthermore, to provide generalizable solutions in small sample size scenarios, BALDUR efficiently integrates dual kernels over the views with a small sample-to-feature ratio. Finally, its linear nature ensures the explainability of the model outcomes, allowing its use for biomarker identification. This model was tested over two different neurodegeneration datasets, outperforming the state-of-the-art models and detecting features aligned with markers already described in the scientific literature.

Albert Belenguer-Llorens, Carlos Sevilla-Salcedo, Emilio Parrado-Hernández et al.

This paper presents the Relevance Feature and Vector Machine (RFVM), a novel model that addresses the challenges of the fat-data problem when dealing with clinical prospective studies. The fat-data problem refers to the limitations of Machine Learning (ML) algorithms when working with databases in which the number of features is much larger than the number of samples (a common scenario in certain medical fields). To overcome such limitations, the RFVM incorporates different characteristics: (1) A Bayesian formulation which enables the model to infer its parameters without overfitting thanks to the Bayesian model averaging. (2) A joint optimisation that overcomes the limitations arising from the fat-data characteristic by simultaneously including the variables that define the primal space (features) and those that define the dual space (observations). (3) An integrated prunning that removes the irrelevant features and samples during the training iterative optimization. Also, this last point turns out crucial when performing medical prospective studies, enabling researchers to exclude unnecessary medical tests, reducing costs and inconvenience for patients, and identifying the critical patients/subjects that characterize the disorder and, subsequently, optimize the patient recruitment process that leads to a balanced cohort. The model capabilities are tested against state-of-the-art models in several medical datasets with fat-data problems. These experimental works show that RFVM is capable of achieving competitive classification accuracies while providing the most compact subset of data (in both terms of features and samples). Moreover, the selected features (medical tests) seem to be aligned with the existing medical literature.

Carlos Sevilla-Salcedo, Vandad Imani, Pablo M. Olmos et al.

Machine learning techniques typically applied to dementia forecasting lack in their capabilities to jointly learn several tasks, handle time dependent heterogeneous data and missing values. In this paper, we propose a framework using the recently presented SSHIBA model for jointly learning different tasks on longitudinal data with missing values. The method uses Bayesian variational inference to impute missing values and combine information of several views. This way, we can combine different data-views from different time-points in a common latent space and learn the relations between each time-point while simultaneously modelling and predicting several output variables. We apply this model to predict together diagnosis, ventricle volume, and clinical scores in dementia. The results demonstrate that SSHIBA is capable of learning a good imputation of the missing values and outperforming the baselines while simultaneously predicting three different tasks.

Sergio Muñoz-Romero, Jerónimo Arenas García, Vanessa Gómez-Verdejo

Audio or visual data analysis tasks usually have to deal with high-dimensional and nonnegative signals. However, most data analysis methods suffer from overfitting and numerical problems when data have more than a few dimensions needing a dimensionality reduction preprocessing. Moreover, interpretability about how and why filters work for audio or visual applications is a desired property, especially when energy or spectral signals are involved. In these cases, due to the nature of these signals, the nonnegativity of the filter weights is a desired property to better understand its working. Because of these two necessities, we propose different methods to reduce the dimensionality of data while the nonnegativity and interpretability of the solution are assured. In particular, we propose a generalized methodology to design filter banks in a supervised way for applications dealing with nonnegative data, and we explore different ways of solving the proposed objective function consisting of a nonnegative version of the orthonormalized partial least-squares method. We analyze the discriminative power of the features obtained with the proposed methods for two different and widely studied applications: texture and music genre classification. Furthermore, we compare the filter banks achieved by our methods with other state-of-the-art methods specifically designed for feature extraction.

Sergio Muñoz-Romero, Vanessa Gómez-Verdejo, Jerónimo Arenas-García

Multivariate Analysis (MVA) comprises a family of well-known methods for feature extraction which exploit correlations among input variables representing the data. One important property that is enjoyed by most such methods is uncorrelation among the extracted features. Recently, regularized versions of MVA methods have appeared in the literature, mainly with the goal to gain interpretability of the solution. In these cases, the solutions can no longer be obtained in a closed manner, and more complex optimization methods that rely on the iteration of two steps are frequently used. This paper recurs to an alternative approach to solve efficiently this iterative problem. The main novelty of this approach lies in preserving several properties of the original methods, most notably the uncorrelation of the extracted features. Under this framework, we propose a novel method that takes advantage of the l-21 norm to perform variable selection during the feature extraction process. Experimental results over different problems corroborate the advantages of the proposed formulation in comparison to state of the art formulations.

Óscar García-Hinde, Vanessa Gómez-Verdejo, Manel Martínez-Ramón

Multitask Gaussian processes (MTGP) are the Gaussian process (GP) framework's solution for multioutput regression problems in which the $T$ elements of the regressors cannot be considered conditionally independent given the observations. Standard MTGP models assume that there exist both a multitask covariance matrix as a function of an intertask matrix, and a noise covariance matrix. These matrices need to be approximated by a low rank simplification of order $P$ in order to reduce the number of parameters to be learnt from $T^2$ to $TP$. Here we introduce a novel approach that simplifies the multitask learning by reducing it to a set of conditioned univariate GPs without the need for any low rank approximations, therefore completely eliminating the requirement to select an adequate value for hyperparameter $P$. At the same time, by extending this approach with both a hierarchical and an approximate model, the proposed extensions are capable of recovering the multitask covariance and noise matrices after learning only $2T$ parameters, avoiding the validation of any model hyperparameter and reducing the overall complexity of the model as well as the risk of overfitting. Experimental results over synthetic and real problems confirm the advantages of this inference approach in its ability to accurately recover the original noise and signal matrices, as well as the achieved performance improvement in comparison to other state of art MTGP approaches. We have also integrated the model with standard GP toolboxes, showing that it is computationally competitive with state of the art options.

Carlos Sevilla-Salcedo, Alejandro Guerrero-López, Pablo M. Olmos et al.

Multi-view problems can be faced with latent variable models since they are able to find low-dimensional projections that fairly capture the correlations among the multiple views that characterise each datum. On the other hand, high-dimensionality and non-linear issues are traditionally handled by kernel methods, inducing a (non)-linear function between the latent projection and the data itself. However, they usually come with scalability issues and exposition to overfitting. Here, we propose merging both approaches into single model so that we can exploit the best features of multi-view latent models and kernel methods and, moreover, overcome their limitations. In particular, we combine probabilistic factor analysis with what we refer to as kernelized observations, in which the model focuses on reconstructing not the data itself, but its relationship with other data points measured by a kernel function. This model can combine several types of views (kernelized or not), and it can handle heterogeneous data and work in semi-supervised settings. Additionally, by including adequate priors, it can provide compact solutions for the kernelized observations -- based in a automatic selection of Bayesian Relevance Vectors (RVs) -- and can include feature selection capabilities. Using several public databases, we demonstrate the potential of our approach (and its extensions) w.r.t. common multi-view learning models such as kernel canonical correlation analysis or manifold relevance determination.

Carlos Sevilla-Salcedo, Vanessa Gómez-Verdejo, Pablo M. Olmos

The Bayesian approach to feature extraction, known as factor analysis (FA), has been widely studied in machine learning to obtain a latent representation of the data. An adequate selection of the probabilities and priors of these bayesian models allows the model to better adapt to the data nature (i.e. heterogeneity, sparsity), obtaining a more representative latent space. The objective of this article is to propose a general FA framework capable of modelling any problem. To do so, we start from the Bayesian Inter-Battery Factor Analysis (BIBFA) model, enhancing it with new functionalities to be able to work with heterogeneous data, include feature selection, and handle missing values as well as semi-supervised problems. The performance of the proposed model, Sparse Semi-supervised Heterogeneous Interbattery Bayesian Analysis (SSHIBA) has been tested on 4 different scenarios to evaluate each one of its novelties, showing not only a great versatility and an interpretability gain, but also outperforming most of the state-of-the-art algorithms.

Sergio Muñoz-Romero, Vanessa Gómez-Verdejo, Jerónimo Arenas-García

Multivariate Analysis (MVA) comprises a family of well-known methods for feature extraction that exploit correlations among input variables of the data representation. One important property that is enjoyed by most such methods is uncorrelation among the extracted features. Recently, regularized versions of MVA methods have appeared in the literature, mainly with the goal to gain interpretability of the solution. In these cases, the solutions can no longer be obtained in a closed manner, and it is frequent to recur to the iteration of two steps, one of them being an orthogonal Procrustes problem. This letter shows that the Procrustes solution is not optimal from the perspective of the overall MVA method, and proposes an alternative approach based on the solution of an eigenvalue problem. Our method ensures the preservation of several properties of the original methods, most notably the uncorrelation of the extracted features, as demonstrated theoretically and through a collection of selected experiments.