Rafael Molina

S. Derin Babacan, Martin Luessi, Rafael Molina et al.

Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesting practical applications. A number of methods have been developed for this recovery problem. However, a principled method for choosing the unknown target rank is generally not provided. In this paper, we present novel recovery algorithms for estimating low-rank matrices in matrix completion and robust principal component analysis based on sparse Bayesian learning (SBL) principles. Starting from a matrix factorization formulation and enforcing the low-rank constraint in the estimates as a sparsity constraint, we develop an approach that is very effective in determining the correct rank while providing high recovery performance. We provide connections with existing methods in other similar problems and empirical results and comparisons with current state-of-the-art methods that illustrate the effectiveness of this approach.

Yunan Wu, Francisco M. Castro-Macías, Pablo Morales-Álvarez et al.

Multiple Instance Learning (MIL) has been widely applied to medical imaging diagnosis, where bag labels are known and instance labels inside bags are unknown. Traditional MIL assumes that instances in each bag are independent samples from a given distribution. However, instances are often spatially or sequentially ordered, and one would expect similar diagnostic importance for neighboring instances. To address this, in this study, we propose a smooth attention deep MIL (SA-DMIL) model. Smoothness is achieved by the introduction of first and second order constraints on the latent function encoding the attention paid to each instance in a bag. The method is applied to the detection of intracranial hemorrhage (ICH) on head CT scans. The results show that this novel SA-DMIL: (a) achieves better performance than the non-smooth attention MIL at both scan (bag) and slice (instance) levels; (b) learns spatial dependencies between slices; and (c) outperforms current state-of-the-art MIL methods on the same ICH test set.

Arne Schmidt, Pablo Morales-Álvarez, Rafael Molina

Medical image segmentation is a challenging task, particularly due to inter- and intra-observer variability, even between medical experts. In this paper, we propose a novel model, called Probabilistic Inter-Observer and iNtra-Observer variation NetwOrk (Pionono). It captures the labeling behavior of each rater with a multidimensional probability distribution and integrates this information with the feature maps of the image to produce probabilistic segmentation predictions. The model is optimized by variational inference and can be trained end-to-end. It outperforms state-of-the-art models such as STAPLE, Probabilistic U-Net, and models based on confusion matrices. Additionally, Pionono predicts multiple coherent segmentation maps that mimic the rater's expert opinion, which provides additional valuable information for the diagnostic process. Experiments on real-world cancer segmentation datasets demonstrate the high accuracy and efficiency of Pionono, making it a powerful tool for medical image analysis.

Arne Schmidt, Pablo Morales-Álvarez, Rafael Molina

Multiple Instance Learning (MIL) is a weakly supervised learning paradigm that is becoming increasingly popular because it requires less labeling effort than fully supervised methods. This is especially interesting for areas where the creation of large annotated datasets remains challenging, as in medicine. Although recent deep learning MIL approaches have obtained state-of-the-art results, they are fully deterministic and do not provide uncertainty estimations for the predictions. In this work, we introduce the Attention Gaussian Process (AGP) model, a novel probabilistic attention mechanism based on Gaussian Processes for deep MIL. AGP provides accurate bag-level predictions as well as instance-level explainability, and can be trained end-to-end. Moreover, its probabilistic nature guarantees robustness to overfitting on small datasets and uncertainty estimations for the predictions. The latter is especially important in medical applications, where decisions have a direct impact on the patient's health. The proposed model is validated experimentally as follows. First, its behavior is illustrated in two synthetic MIL experiments based on the well-known MNIST and CIFAR-10 datasets, respectively. Then, it is evaluated in three different real-world cancer detection experiments. AGP outperforms state-of-the-art MIL approaches, including deterministic deep learning ones. It shows a strong performance even on a small dataset with less than 100 labels and generalizes better than competing methods on an external test set. Moreover, we experimentally show that predictive uncertainty correlates with the risk of wrong predictions, and therefore it is a good indicator of reliability in practice. Our code is publicly available.

Pablo Morales-Álvarez, Arne Schmidt, José Miguel Hernández-Lobato et al.

In the last years, the weakly supervised paradigm of multiple instance learning (MIL) has become very popular in many different areas. A paradigmatic example is computational pathology, where the lack of patch-level labels for whole-slide images prevents the application of supervised models. Probabilistic MIL methods based on Gaussian Processes (GPs) have obtained promising results due to their excellent uncertainty estimation capabilities. However, these are general-purpose MIL methods that do not take into account one important fact: in (histopathological) images, the labels of neighboring patches are expected to be correlated. In this work, we extend a state-of-the-art GP-based MIL method, which is called VGPMIL-PR, to exploit such correlation. To do so, we develop a novel coupling term inspired by the statistical physics Ising model. We use variational inference to estimate all the model parameters. Interestingly, the VGPMIL-PR formulation is recovered when the weight that regulates the strength of the Ising term vanishes. The performance of the proposed method is assessed in two real-world problems of prostate cancer detection. We show that our model achieves better results than other state-of-the-art probabilistic MIL methods. We also provide different visualizations and analysis to gain insights into the influence of the novel Ising term. These insights are expected to facilitate the application of the proposed model to other research areas.

Fernando Pérez-Bueno, Luz García, Gabriel Maciá-Fernández et al.

Network anomaly detection is a very relevant research area nowadays, especially due to its multiple applications in the field of network security. The boost of new models based on variational autoencoders and generative adversarial networks has motivated a reevaluation of traditional techniques for anomaly detection. It is, however, essential to be able to understand these new models from the perspective of the experience attained from years of evaluating network security data for anomaly detection. In this paper, we revisit anomaly detection techniques based on PCA from a probabilistic generative model point of view, and contribute a mathematical model that relates them. Specifically, we start with the probabilistic PCA model and explain its connection to the Multivariate Statistical Network Monitoring (MSNM) framework. MSNM was recently successfully proposed as a means of incorporating industrial process anomaly detection experience into the field of networking. We have evaluated the mathematical model using two different datasets. The first, a synthetic dataset created to better understand the analysis proposed, and the second, UGR'16, is a specifically designed real-traffic dataset for network security anomaly detection. We have drawn conclusions that we consider to be useful when applying generative models to network security detection.

Francisco M. Castro-Macías, Francisco J. Sáez-Maldonado, Pablo Morales-Álvarez et al.

Multiple Instance Learning (MIL) is a powerful framework for weakly supervised learning, particularly useful when fine-grained annotations are unavailable. Despite growing interest in deep MIL methods, the field lacks standardized tools for model development, evaluation, and comparison, which hinders reproducibility and accessibility. To address this, we present torchmil, an open-source Python library built on PyTorch. torchmil offers a unified, modular, and extensible framework, featuring basic building blocks for MIL models, a standardized data format, and a curated collection of benchmark datasets and models. The library includes comprehensive documentation and tutorials to support both practitioners and researchers. torchmil aims to accelerate progress in MIL and lower the entry barrier for new users. Available at https://torchmil.readthedocs.io.

Michael Iliadis, Haohong Wang, Rafael Molina et al.

In this paper we propose an iterative method to address the face identification problem with block occlusions. Our approach utilizes a robust representation based on two characteristics in order to model contiguous errors (e.g., block occlusion) effectively. The first fits to the errors a distribution described by a tailored loss function. The second describes the error image as having a specific structure (resulting in low-rank in comparison to image size). We will show that this joint characterization is effective for describing errors with spatial continuity. Our approach is computationally efficient due to the utilization of the Alternating Direction Method of Multipliers (ADMM). A special case of our fast iterative algorithm leads to the robust representation method which is normally used to handle non-contiguous errors (e.g., pixel corruption). Extensive results on representative face databases (in constrained and unconstrained environments) document the effectiveness of our method over existing robust representation methods with respect to both identification rates and computational time. Code is available at Github, where you can find implementations of the F-LR-IRNNLS and F-IRNNLS (fast version of the RRC) : https://github.com/miliadis/FIRC

Francisco M. Castro-Macías, Pablo Morales-Álvarez, Saifuddin Syed et al.

Sampling from unnormalized multimodal distributions with limited density evaluations remains a fundamental challenge in machine learning and natural sciences. Successful approaches construct a bridge between a tractable reference and the target distribution. Parallel Tempering (PT) serves as the gold standard, while recent diffusion-based approaches offer a continuous alternative at the cost of neural training. In this work, we introduce Conditional Diffusion Sampling (CDS), a framework that combines these two paradigms. To this end, we derive Conditional Interpolants, a class of stochastic processes whose transport dynamics are governed by an exact, closed-form stochastic differential equation (SDE), requiring no neural approximation. Although these dynamics require sampling from a non-trivial initialization distribution, we show both theoretically and empirically that the cost of this initialization diminishes for sufficiently short diffusion times. CDS leverages this by a two-stage procedure: (1) PT is used to efficiently sample the initial distribution, and then (2) samples are transported via the transport SDE. This combination couples the robust global exploration of PT with efficient local transport. Experiments suggest that CDS has the potential to achieve a superior trade-off between sample quality and density evaluation cost compared to state-of-the-art samplers.

Arne Schmidt, Pablo Morales-Álvarez, Lee A. D. Cooper et al.

Active Learning (AL) has the potential to solve a major problem of digital pathology: the efficient acquisition of labeled data for machine learning algorithms. However, existing AL methods often struggle in realistic settings with artifacts, ambiguities, and class imbalances, as commonly seen in the medical field. The lack of precise uncertainty estimations leads to the acquisition of images with a low informative value. To address these challenges, we propose Focused Active Learning (FocAL), which combines a Bayesian Neural Network with Out-of-Distribution detection to estimate different uncertainties for the acquisition function. Specifically, the weighted epistemic uncertainty accounts for the class imbalance, aleatoric uncertainty for ambiguous images, and an OoD score for artifacts. We perform extensive experiments to validate our method on MNIST and the real-world Panda dataset for the classification of prostate cancer. The results confirm that other AL methods are 'distracted' by ambiguities and artifacts which harm the performance. FocAL effectively focuses on the most informative images, avoiding ambiguities and artifacts during acquisition. For both experiments, FocAL outperforms existing AL approaches, reaching a Cohen's kappa of 0.764 with only 0.69% of the labeled Panda data.

Francisco M. Castro-Macías, Pablo Morales-Álvarez, Yunan Wu et al.

The Multiple Instance Learning (MIL) paradigm is attracting plenty of attention in medical imaging classification, where labeled data is scarce. MIL methods cast medical images as bags of instances (e.g. patches in whole slide images, or slices in CT scans), and only bag labels are required for training. Deep MIL approaches have obtained promising results by aggregating instance-level representations via an attention mechanism to compute the bag-level prediction. These methods typically capture both local interactions among adjacent instances and global, long-range dependencies through various mechanisms. However, they treat attention values deterministically, potentially overlooking uncertainty in the contribution of individual instances. In this work we propose a novel probabilistic framework that estimates a probability distribution over the attention values, and accounts for both global and local interactions. In a comprehensive evaluation involving {\color{review} eleven} state-of-the-art baselines and three medical datasets, we show that our approach achieves top predictive performance in different metrics. Moreover, the probabilistic treatment of the attention provides uncertainty maps that are interpretable in terms of illness localization.

Xijun Wang, Santiago López-Tapia, Alice Lucas et al.

Generative Adversarial Networks (GANs) have shown great performance on super-resolution problems since they can generate more visually realistic images and video frames. However, these models often introduce side effects into the outputs, such as unexpected artifacts and noises. To reduce these artifacts and enhance the perceptual quality of the results, in this paper, we propose a general method that can be effectively used in most GAN-based super-resolution (SR) models by introducing essential spatial information into the training process. We extract spatial information from the input data and incorporate it into the training loss, making the corresponding loss a spatially adaptive (SA) one. After that, we utilize it to guide the training process. We will show that the proposed approach is independent of the methods used to extract the spatial information and independent of the SR tasks and models. This method consistently guides the training process towards generating visually pleasing SR images and video frames, substantially mitigating artifacts and noise, ultimately leading to enhanced perceptual quality.

Julio Silva-Rodríguez, Adrián Colomer, María A. Sales et al.

The Gleason scoring system is the primary diagnostic and prognostic tool for prostate cancer. In recent years, with the development of digitisation devices, the use of computer vision techniques for the analysis of biopsies has increased. However, to the best of the authors' knowledge, the development of algorithms to automatically detect individual cribriform patterns belonging to Gleason grade 4 has not yet been studied in the literature. The objective of the work presented in this paper is to develop a deep-learning-based system able to support pathologists in the daily analysis of prostate biopsies. The methodological core of this work is a patch-wise predictive model based on convolutional neural networks able to determine the presence of cancerous patterns. In particular, we train from scratch a simple self-design architecture. The cribriform pattern is detected by retraining the set of filters of the last convolutional layer in the network. From the reconstructed prediction map, we compute the percentage of each Gleason grade in the tissue to feed a multi-layer perceptron which provides a biopsy-level score.mIn our SICAPv2 database, composed of 182 annotated whole slide images, we obtained a Cohen's quadratic kappa of 0.77 in the test set for the patch-level Gleason grading with the proposed architecture trained from scratch. Our results outperform previous ones reported in the literature. Furthermore, this model reaches the level of fine-tuned state-of-the-art architectures in a patient-based four groups cross validation. In the cribriform pattern detection task, we obtained an area under ROC curve of 0.82. Regarding the biopsy Gleason scoring, we achieved a quadratic Cohen's Kappa of 0.81 in the test subset. Shallow CNN architectures trained from scratch outperform current state-of-the-art methods for Gleason grades classification.

Daniel Heestermans Svendsen, Pablo Morales-Alvarez, Ana Belen Ruescas et al.

Parameter retrieval and model inversion are key problems in remote sensing and Earth observation. Currently, different approximations exist: a direct, yet costly, inversion of radiative transfer models (RTMs); the statistical inversion with in situ data that often results in problems with extrapolation outside the study area; and the most widely adopted hybrid modeling by which statistical models, mostly nonlinear and non-parametric machine learning algorithms, are applied to invert RTM simulations. We will focus on the latter. Among the different existing algorithms, in the last decade kernel based methods, and Gaussian Processes (GPs) in particular, have provided useful and informative solutions to such RTM inversion problems. This is in large part due to the confidence intervals they provide, and their predictive accuracy. However, RTMs are very complex, highly nonlinear, and typically hierarchical models, so that often a shallow GP model cannot capture complex feature relations for inversion. This motivates the use of deeper hierarchical architectures, while still preserving the desirable properties of GPs. This paper introduces the use of deep Gaussian Processes (DGPs) for bio-geo-physical model inversion. Unlike shallow GP models, DGPs account for complicated (modular, hierarchical) processes, provide an efficient solution that scales well to big datasets, and improve prediction accuracy over their single layer counterpart. In the experimental section, we provide empirical evidence of performance for the estimation of surface temperature and dew point temperature from infrared sounding data, as well as for the prediction of chlorophyll content, inorganic suspended matter, and coloured dissolved matter from multispectral data acquired by the Sentinel-3 OLCI sensor. The presented methodology allows for more expressive forms of GPs in remote sensing model inversion problems.

Daniel Heestermans Svendsen, Pablo Morales-Álvarez, Rafael Molina et al.

This paper introduces deep Gaussian processes (DGPs) for geophysical parameter retrieval. Unlike the standard full GP model, the DGP accounts for complicated (modular, hierarchical) processes, provides an efficient solution that scales well to large datasets, and improves prediction accuracy over standard full and sparse GP models. We give empirical evidence of performance for estimation of surface dew point temperature from infrared sounding data.

Alice Lucas, Santiago Lopez-Tapia, Rafael Molina et al.

While Convolutional Neural Networks (CNNs) trained for image and video super-resolution (SR) regularly achieve new state-of-the-art performance, they also suffer from significant drawbacks. One of their limitations is their lack of robustness to unseen image formation models during training. Other limitations include the generation of artifacts and hallucinated content when training Generative Adversarial Networks (GANs) for SR. While the Deep Learning literature focuses on presenting new training schemes and settings to resolve these various issues, we show that one can avoid training and correct for SR results with a fully self-supervised fine-tuning approach. More specifically, at test time, given an image and its known image formation model, we fine-tune the parameters of the trained network and iteratively update them using a data fidelity loss. We apply our fine-tuning algorithm on multiple image and video SR CNNs and show that it can successfully correct for a sub-optimal SR solution by entirely relying on internal learning at test time. We apply our method on the problem of fine-tuning for unseen image formation models and on removal of artifacts introduced by GANs.

Pablo Morales-Álvarez, Pablo Ruiz, Scott Coughlin et al.

In the last years, crowdsourcing is transforming the way classification training sets are obtained. Instead of relying on a single expert annotator, crowdsourcing shares the labelling effort among a large number of collaborators. For instance, this is being applied to the data acquired by the laureate Laser Interferometer Gravitational Waves Observatory (LIGO), in order to detect glitches which might hinder the identification of true gravitational-waves. The crowdsourcing scenario poses new challenging difficulties, as it deals with different opinions from a heterogeneous group of annotators with unknown degrees of expertise. Probabilistic methods, such as Gaussian Processes (GP), have proven successful in modeling this setting. However, GPs do not scale well to large data sets, which hampers their broad adoption in real practice (in particular at LIGO). This has led to the recent introduction of deep learning based crowdsourcing methods, which have become the state-of-the-art. However, the accurate uncertainty quantification of GPs has been partially sacrificed. This is an important aspect for astrophysicists in LIGO, since a glitch detection system should provide very accurate probability distributions of its predictions. In this work, we leverage the most popular sparse GP approximation to develop a novel GP based crowdsourcing method that factorizes into mini-batches. This makes it able to cope with previously-prohibitive data sets. The approach, which we refer to as Scalable Variational Gaussian Processes for Crowdsourcing (SVGPCR), brings back GP-based methods to the state-of-the-art, and excels at uncertainty quantification. SVGPCR is shown to outperform deep learning based methods and previous probabilistic approaches when applied to the LIGO data. Moreover, its behavior and main properties are carefully analyzed in a controlled experiment based on the MNIST data set.

Santiago López-Tapia, Alice Lucas, Rafael Molina et al.

The popularity of high and ultra-high definition displays has led to the need for methods to improve the quality of videos already obtained at much lower resolutions. Current Video Super-Resolution methods are not robust to mismatch between training and testing degradation models since they are trained against a single degradation model (usually bicubic downsampling). This causes their performance to deteriorate in real-life applications. At the same time, the use of only the Mean Squared Error during learning causes the resulting images to be too smooth. In this work we propose a new Convolutional Neural Network for video super resolution which is robust to multiple degradation models. During training, which is performed on a large dataset of scenes with slow and fast motions, it uses the pseudo-inverse image formation model as part of the network architecture in conjunction with perceptual losses, in addition to a smoothness constraint that eliminates the artifacts originating from these perceptual losses. The experimental validation shows that our approach outperforms current state-of-the-art methods and is robust to multiple degradations.

Alice Lucas, Santiago Lopez Tapia, Rafael Molina et al.

Video super-resolution (VSR) has become one of the most critical problems in video processing. In the deep learning literature, recent works have shown the benefits of using adversarial-based and perceptual losses to improve the performance on various image restoration tasks; however, these have yet to be applied for video super-resolution. In this work, we propose a Generative Adversarial Network(GAN)-based formulation for VSR. We introduce a new generator network optimized for the VSR problem, named VSRResNet, along with a new discriminator architecture to properly guide VSRResNet during the GAN training. We further enhance our VSR GAN formulation with two regularizers, a distance loss in feature-space and pixel-space, to obtain our final VSRResFeatGAN model. We show that pre-training our generator with the Mean-Squared-Error loss only quantitatively surpasses the current state-of-the-art VSR models. Finally, we employ the PercepDist metric (Zhang et al., 2018) to compare state-of-the-art VSR models. We show that this metric more accurately evaluates the perceptual quality of SR solutions obtained from neural networks, compared with the commonly used PSNR/SSIM metrics. Finally, we show that our proposed model, the VSRResFeatGAN model, outperforms current state-of-the-art SR models, both quantitatively and qualitatively.

Pablo Morales-Alvarez, Adrian Perez-Suay, Rafael Molina et al.

Current remote sensing image classification problems have to deal with an unprecedented amount of heterogeneous and complex data sources. Upcoming missions will soon provide large data streams that will make land cover/use classification difficult. Machine learning classifiers can help at this, and many methods are currently available. A popular kernel classifier is the Gaussian process classifier (GPC), since it approaches the classification problem with a solid probabilistic treatment, thus yielding confidence intervals for the predictions as well as very competitive results to state-of-the-art neural networks and support vector machines. However, its computational cost is prohibitive for large scale applications, and constitutes the main obstacle precluding wide adoption. This paper tackles this problem by introducing two novel efficient methodologies for Gaussian Process (GP) classification. We first include the standard random Fourier features approximation into GPC, which largely decreases its computational cost and permits large scale remote sensing image classification. In addition, we propose a model which avoids randomly sampling a number of Fourier frequencies, and alternatively learns the optimal ones within a variational Bayes approach. The performance of the proposed methods is illustrated in complex problems of cloud detection from multispectral imagery and infrared sounding data. Excellent empirical results support the proposal in both computational cost and accuracy.