Roberto Santana

Andrea Bonfanti, Roberto Santana, Marco Ellero et al.

Physics-Informed Neural Networks (PINNs) are Neural Network architectures trained to emulate solutions of differential equations without the necessity of solution data. They are currently ubiquitous in the scientific literature due to their flexible and promising settings. However, very little of the available research provides practical studies that aim for a better quantitative understanding of such architecture and its functioning. In this paper, we perform an empirical analysis of the behavior of PINN predictions outside their training domain. The primary goal is to investigate the scenarios in which a PINN can provide consistent predictions outside the training area. Thereinafter, we assess whether the algorithmic setup of PINNs can influence their potential for generalization and showcase the respective effect on the prediction. The results obtained in this study returns insightful and at times counterintuitive perspectives which can be highly relevant for architectures which combines PINNs with domain decomposition and/or adaptive training strategies.

Roberto Santana, Ivan Hidalgo-Cenalmor, Unai Garciarena et al.

In some machine learning applications the availability of labeled instances for supervised classification is limited while unlabeled instances are abundant. Semi-supervised learning algorithms deal with these scenarios and attempt to exploit the information contained in the unlabeled examples. In this paper, we address the question of how to evolve neural networks for semi-supervised problems. We introduce neuroevolutionary approaches that exploit unlabeled instances by using neuron coverage metrics computed on the neural network architecture encoded by each candidate solution. Neuron coverage metrics resemble code coverage metrics used to test software, but are oriented to quantify how the different neural network components are covered by test instances. In our neuroevolutionary approach, we define fitness functions that combine classification accuracy computed on labeled examples and neuron coverage metrics evaluated using unlabeled examples. We assess the impact of these functions on semi-supervised problems with a varying amount of labeled instances. Our results show that the use of neuron coverage metrics helps neuroevolution to become less sensitive to the scarcity of labeled data, and can lead in some cases to a more robust generalization of the learned classifiers.

Madhuri Shanbhogue, Zhe Li, Shanfeng Zhang et al.

We introduce Gemini Embedding 2, a native multimodal embedding model that allows embedding video, audio, image, and text modalities in a unified representation space. We leverage the multimodal capabilities of Gemini to produce embeddings for arbitrary combinations of interleaved inputs across all these modalities that generalize well across a wide variety of tasks. Applying large-scale contrastive learning in a multi-task multi-stage training setup, we achieve state-of-the-art performance on key embedding benchmarks including unimodal, cross-modal, and multimodal retrieval spanning a diverse set of tasks. We show that our embedding model demonstrates strong performance (with a score of 62.9 R@1 on MSCOCO, 68.8 NDCG@10 on Vatex, 69.9 on MTEB multilingual and 84.0 on MTEB Code) across a variety of tasks surpassing the performance of specialized models. These unified capabilities make Gemini Embedding 2 a promising candidate for downstream use cases such as RAG, recommendation and search. Furthermore, its robust zero-shot performance across distinct fields - from astronomy and bioscience to fine arts and the culinary arts - establishes it as a highly reliable, out-of-the-box representation even for specialized domains.

Arkaitz Bidaurrazaga, Aritz Pérez, Roberto Santana

Restricted Boltzmann Machines are generative models that consist of a layer of hidden variables connected to another layer of visible units, and they are used to model the distribution over visible variables. In order to gain a higher representability power, many hidden units are commonly used, which, in combination with a large number of visible units, leads to a high number of trainable parameters. In this work we introduce the Structural Restricted Boltzmann Machine model, which taking advantage of the structure of the data in hand, constrains connections of hidden units to subsets of visible units in order to reduce significantly the number of trainable parameters, without compromising performance. As a possible area of application, we focus on image modelling. Based on the nature of the images, the structure of the connections is given in terms of spatial neighbourhoods over the pixels of the image that constitute the visible variables of the model. We conduct extensive experiments on various image domains. Image denoising is evaluated with corrupted images from the MNIST dataset. The generative power of our models is compared to vanilla RBMs, as well as their classification performance, which is assessed with five different image domains. Results show that our proposed model has a faster and more stable training, while also obtaining better results compared to an RBM with no constrained connections between its visible and hidden units.

Zochil González Arenas, Juan Carlos Jimenez, Li-Vang Lozada-Chang et al.

Estimation of Distribution Algorithms (EDAs) and Innovation Method are recognized methods for solving global optimization problems and for the estimation of parameters in diffusion processes, respectively. Well known is also that the quality of the Innovation Estimator strongly depends on an adequate selection of the initial value for the parameters when a local optimization algorithm is used in its computation. Alternatively, in this paper, we study the feasibility of a specific EDA - a continuous version of the Univariate Marginal Distribution Algorithm (UMDAc) - for the computation of the Innovation Estimators. Numerical experiments are performed for two different models with a high level of complexity. The numerical simulations show that the considered global optimization algorithms substantially improves the effectiveness of the Innovation Estimators for different types of diffusion processes with complex nonlinear and stochastic dynamics.

Imanol Echeverria, Maialen Murua, Roberto Santana

In scheduling problems common in the industry and various real-world scenarios, responding in real-time to disruptive events is essential. Recent methods propose the use of deep reinforcement learning (DRL) to learn policies capable of generating solutions under this constraint. The objective of this paper is to introduce a new DRL method for solving the flexible job-shop scheduling problem, particularly for large instances. The approach is based on the use of heterogeneous graph neural networks to a more informative graph representation of the problem. This novel modeling of the problem enhances the policy's ability to capture state information and improve its decision-making capacity. Additionally, we introduce two novel approaches to enhance the performance of the DRL approach: the first involves generating a diverse set of scheduling policies, while the second combines DRL with dispatching rules (DRs) constraining the action space. Experimental results on two public benchmarks show that our approach outperforms DRs and achieves superior results compared to three state-of-the-art DRL methods, particularly for large instances.

Alexander Olza, David Soto, Roberto Santana

In cognitive neuroscience and brain-computer interface research, accurately predicting imagined stimuli is crucial. This study investigates the effectiveness of Domain Adaptation (DA) in enhancing imagery prediction using primarily visual data from fMRI scans of 18 subjects. Initially, we train a baseline model on visual stimuli to predict imagined stimuli, utilizing data from 14 brain regions. We then develop several models to improve imagery prediction, comparing different DA methods. Our results demonstrate that DA significantly enhances imagery prediction in binary classification on our dataset, as well as in multiclass classification on a publicly available dataset. We then conduct a DA-enhanced searchlight analysis, followed by permutation-based statistical tests to identify brain regions where imagery decoding is consistently above chance across subjects. Our DA-enhanced searchlight predicts imagery contents in a highly distributed set of brain regions, including the visual cortex and the frontoparietal cortex, thereby outperforming standard cross-domain classification methods. The complete code and data for this paper have been made openly available for the use of the scientific community.

Alexander Olza, Roberto Santana, David Soto

Decoded Neurofeedback (DecNef) is a flourishing non-invasive approach to brain modulation with wide-ranging applications in neuromedicine and cognitive neuroscience. However, progress in DecNef research remains constrained by subject-dependent learning variability, reliance on indirect measures to quantify progress, and the high cost and time demands of experimentation. We present DecNefLab, a modular and interpretable simulation framework that formalizes DecNef as a machine learning problem. Beyond providing a virtual laboratory, DecNefLab enables researchers to model, analyze and understand neurofeedback dynamics. Using latent variable generative models as simulated participants, DecNefLab allows direct observation of internal cognitive states and systematic evaluation of how different protocol designs and subject characteristics influence learning. We demonstrate how this approach can (i) reproduce empirical phenomena of DecNef learning, (ii) identify conditions under which DecNef feedback fails to induce learning, and (iii) guide the design of more robust and reliable DecNef protocols in silico before human implementation. In summary, DecNefLab bridges computational modeling and cognitive neuroscience, offering a principled foundation for methodological innovation, robust protocol design, and ultimately, a deeper understanding of DecNef-based brain modulation.

Andrea Bonfanti, Ismael Medina, Roman List et al.

Recent advances in Scientific Machine Learning have shown that second-order methods can enhance the training of Physics-Informed Neural Networks (PINNs), making them a suitable alternative to traditional numerical methods for Partial Differential Equations (PDEs). However, second-order methods induce large memory requirements, making them scale poorly with the model size. In this paper, we define a local Mixture of Experts (MoE) combining the parameter-efficiency of ensemble models and sparse coding to enable the use of second-order training. Our model -- \textsc{PINN Balls} -- also features a fully learnable domain decomposition structure, achieved through the use of Adversarial Adaptive Sampling (AAS), which adapts the DD to the PDE and its domain. \textsc{PINN Balls} achieves better accuracy than the state-of-the-art in scientific machine learning, while maintaining invaluable scalability properties and drawing from a sound theoretical background.

Imanol Echeverria, Maialen Murua, Roberto Santana

Combinatorial optimization problems, such as scheduling and route planning, are crucial in various industries but are computationally intractable due to their NP-hard nature. Neural Combinatorial Optimization methods leverage machine learning to address these challenges but often depend on sequential decision-making, which is prone to error accumulation as small mistakes propagate throughout the process. Inspired by self-evaluation techniques in Large Language Models, we propose a novel framework that generates and evaluates subsets of assignments, moving beyond traditional stepwise approaches. Applied to the Job-Shop Scheduling Problem, our method integrates a heterogeneous graph neural network with a Transformer to build a policy model and a self-evaluation function. Experimental validation on challenging, well-known benchmarks demonstrates the effectiveness of our approach, surpassing state-of-the-art methods.

Imanol Echeverria, Maialen Murua, Roberto Santana

Recent advances in deep learning have shown significant potential for solving combinatorial optimization problems in real-time. Unlike traditional methods, deep learning can generate high-quality solutions efficiently, which is crucial for applications like routing and scheduling. However, existing approaches like deep reinforcement learning (RL) and behavioral cloning have notable limitations, with deep RL suffering from slow learning and behavioral cloning relying solely on expert actions, which can lead to generalization issues and neglect of the optimization objective. This paper introduces a novel offline RL method designed for combinatorial optimization problems with complex constraints, where the state is represented as a heterogeneous graph and the action space is variable. Our approach encodes actions in edge attributes and balances expected rewards with the imitation of expert solutions. We demonstrate the effectiveness of this method on job-shop scheduling and flexible job-shop scheduling benchmarks, achieving superior performance compared to state-of-the-art techniques.

Roberto Santana, Mauricio Romero Sicre

In this paper we introduce a word embedding composition method based on the intuitive idea that a fair embedding representation for a given set of words should satisfy that the new vector will be at the same distance of the vector representation of each of its constituents, and this distance should be minimized. The embedding composition method can work with static and contextualized word representations, it can be applied to create representations of sentences and learn also representations of sets of words that are not necessarily organized as a sequence. We theoretically characterize the conditions for the existence of this type of representation and derive the solution. We evaluate the method in data augmentation and sentence classification tasks, investigating several design choices of embeddings and composition methods. We show that our approach excels in solving probing tasks designed to capture simple linguistic features of sentences.

Jon Vadillo, Roberto Santana, Jose A. Lozano et al.

The lack of transparency of Deep Neural Networks continues to be a limitation that severely undermines their reliability and usage in high-stakes applications. Promising approaches to overcome such limitations are Prototype-Based Self-Explainable Neural Networks (PSENNs), whose predictions rely on the similarity between the input at hand and a set of prototypical representations of the output classes, offering therefore a deep, yet transparent-by-design, architecture. In this paper, we introduce a probabilistic reformulation of PSENNs, called Prob-PSENN, which replaces point estimates for the prototypes with probability distributions over their values. This provides not only a more flexible framework for an end-to-end learning of prototypes, but can also capture the explanatory uncertainty of the model, which is a missing feature in previous approaches. In addition, since the prototypes determine both the explanation and the prediction, Prob-PSENNs allow us to detect when the model is making uninformed or uncertain predictions, and to obtain valid explanations for them. Our experiments demonstrate that Prob-PSENNs provide more meaningful and robust explanations than their non-probabilistic counterparts, while remaining competitive in terms of predictive performance, thus enhancing the explainability and reliability of the models.

Imanol Echeverria, Maialen Murua, Roberto Santana

Recent advancements in the flexible job-shop scheduling problem (FJSSP) are primarily based on deep reinforcement learning (DRL) due to its ability to generate high-quality, real-time solutions. However, DRL approaches often fail to fully harness the strengths of existing techniques such as exact methods or constraint programming (CP), which can excel at finding optimal or near-optimal solutions for smaller instances. This paper aims to integrate CP within a deep learning (DL) based methodology, leveraging the benefits of both. In this paper, we introduce a method that involves training a DL model using optimal solutions generated by CP, ensuring the model learns from high-quality data, thereby eliminating the need for the extensive exploration typical in DRL and enhancing overall performance. Further, we integrate CP into our DL framework to jointly construct solutions, utilizing DL for the initial complex stages and transitioning to CP for optimal resolution as the problem is simplified. Our hybrid approach has been extensively tested on three public FJSSP benchmarks, demonstrating superior performance over five state-of-the-art DRL approaches and a widely-used CP solver. Additionally, with the objective of exploring the application to other combinatorial optimization problems, promising preliminary results are presented on applying our hybrid approach to the traveling salesman problem, combining an exact method with a well-known DRL method.

Jon Vadillo, Roberto Santana, Jose A. Lozano

Reliable deployment of machine learning models such as neural networks continues to be challenging due to several limitations. Some of the main shortcomings are the lack of interpretability and the lack of robustness against adversarial examples or out-of-distribution inputs. In this exploratory review, we explore the possibilities and limits of adversarial attacks for explainable machine learning models. First, we extend the notion of adversarial examples to fit in explainable machine learning scenarios, in which the inputs, the output classifications and the explanations of the model's decisions are assessed by humans. Next, we propose a comprehensive framework to study whether (and how) adversarial examples can be generated for explainable models under human assessment, introducing and illustrating novel attack paradigms. In particular, our framework considers a wide range of relevant yet often ignored factors such as the type of problem, the user expertise or the objective of the explanations, in order to identify the attack strategies that should be adopted in each scenario to successfully deceive the model (and the human). The intention of these contributions is to serve as a basis for a more rigorous and realistic study of adversarial examples in the field of explainable machine learning.

Unai Garciarena, Roberto Santana, Alexander Mendiburu

With neural architecture search methods gaining ground on manually designed deep neural networks -even more rapidly as model sophistication escalates-, the research trend shifts towards arranging different and often increasingly complex neural architecture search spaces. In this conjuncture, delineating algorithms which can efficiently explore these search spaces can result in a significant improvement over currently used methods, which, in general, randomly select the structural variation operator, hoping for a performance gain. In this paper, we investigate the effect of different variation operators in a complex domain, that of multi-network heterogeneous neural models. These models have an extensive and complex search space of structures as they require multiple sub-networks within the general model in order to answer to different output types. From that investigation, we extract a set of general guidelines, whose application is not limited to that particular type of model, and are useful to determine the direction in which an architecture optimization method could find the largest improvement. To deduce the set of guidelines, we characterize both the variation operators, according to their effect on the complexity and performance of the model; and the models, relying on diverse metrics which estimate the quality of the different parts composing it.

Unai Garciarena, Nuno Lourenço, Penousal Machado et al.

Neuroevolutionary algorithms, automatic searches of neural network structures by means of evolutionary techniques, are computationally costly procedures. In spite of this, due to the great performance provided by the architectures which are found, these methods are widely applied. The final outcome of neuroevolutionary processes is the best structure found during the search, and the rest of the procedure is commonly omitted in the literature. However, a good amount of residual information consisting of valuable knowledge that can be extracted is also produced during these searches. In this paper, we propose an approach that extracts this information from neuroevolutionary runs, and use it to build a metamodel that could positively impact future neural architecture searches. More specifically, by inspecting the best structures found during neuroevolutionary searches of generative adversarial networks with varying characteristics (e.g., based on dense or convolutional layers), we propose a Bayesian network-based model which can be used to either find strong neural structures right away, conveniently initialize different structural searches for different problems, or help future optimization of structures of any type to keep finding increasingly better structures where uninformed methods get stuck into local optima.

Jon Vadillo, Roberto Santana, Jose A. Lozano

The reasons why Deep Neural Networks are susceptible to being fooled by adversarial examples remains an open discussion. Indeed, many different strategies can be employed to efficiently generate adversarial attacks, some of them relying on different theoretical justifications. Among these strategies, universal (input-agnostic) perturbations are of particular interest, due to their capability to fool a network independently of the input in which the perturbation is applied. In this work, we investigate an intriguing phenomenon of universal perturbations, which has been reported previously in the literature, yet without a proven justification: universal perturbations change the predicted classes for most inputs into one particular (dominant) class, even if this behavior is not specified during the creation of the perturbation. In order to justify the cause of this phenomenon, we propose a number of hypotheses and experimentally test them using a speech command classification problem in the audio domain as a testbed. Our analyses reveal interesting properties of universal perturbations, suggest new methods to generate such attacks and provide an explanation of dominant classes, under both a geometric and a data-feature perspective.

Jon Vadillo, Roberto Santana, Jose A. Lozano

Despite the remarkable performance and generalization levels of deep learning models in a wide range of artificial intelligence tasks, it has been demonstrated that these models can be easily fooled by the addition of imperceptible yet malicious perturbations to natural inputs. These altered inputs are known in the literature as adversarial examples. In this paper, we propose a novel probabilistic framework to generalize and extend adversarial attacks in order to produce a desired probability distribution for the classes when we apply the attack method to a large number of inputs. This novel attack paradigm provides the adversary with greater control over the target model, thereby exposing, in a wide range of scenarios, threats against deep learning models that cannot be conducted by the conventional paradigms. We introduce four different strategies to efficiently generate such attacks, and illustrate our approach by extending multiple adversarial attack algorithms. We also experimentally validate our approach for the spoken command classification task and the Tweet emotion classification task, two exemplary machine learning problems in the audio and text domain, respectively. Our results demonstrate that we can closely approximate any probability distribution for the classes while maintaining a high fooling rate and even prevent the attacks from being detected by label-shift detection methods.

Jon Vadillo, Roberto Santana

Human-machine interaction is increasingly dependent on speech communication. Machine Learning models are usually applied to interpret human speech commands. However, these models can be fooled by adversarial examples, which are inputs intentionally perturbed to produce a wrong prediction without being noticed. While much research has been focused on developing new techniques to generate adversarial perturbations, less attention has been given to aspects that determine whether and how the perturbations are noticed by humans. This question is relevant since high fooling rates of proposed adversarial perturbation strategies are only valuable if the perturbations are not detectable. In this paper we investigate to which extent the distortion metrics proposed in the literature for audio adversarial examples, and which are commonly applied to evaluate the effectiveness of methods for generating these attacks, are a reliable measure of the human perception of the perturbations. Using an analytical framework, and an experiment in which 18 subjects evaluate audio adversarial examples, we demonstrate that the metrics employed by convention are not a reliable measure of the perceptual similarity of adversarial examples in the audio domain.

Jon Vadillo, Roberto Santana

Adversarial examples are inputs intentionally perturbed with the aim of forcing a machine learning model to produce a wrong prediction, while the changes are not easily detectable by a human. Although this topic has been intensively studied in the image domain, classification tasks in the audio domain have received less attention. In this paper we address the existence of universal perturbations for speech command classification. We provide evidence that universal attacks can be generated for speech command classification tasks, which are able to generalize across different models to a significant extent. Additionally, a novel analytical framework is proposed for the evaluation of universal perturbations under different levels of universality, demonstrating that the feasibility of generating effective perturbations decreases as the universality level increases. Finally, we propose a more detailed and rigorous framework to measure the amount of distortion introduced by the perturbations, demonstrating that the methods employed by convention are not realistic in audio-based problems.

Ibai Roman, Roberto Santana, Alexander Mendiburu et al.

Choosing the most adequate kernel is crucial in many Machine Learning applications. Gaussian Process is a state-of-the-art technique for regression and classification that heavily relies on a kernel function. However, in the Gaussian Process literature, kernels have usually been either ad hoc designed, selected from a predefined set, or searched for in a space of compositions of kernels which have been defined a priori. In this paper, we propose a Genetic-Programming algorithm that represents a kernel function as a tree of elementary mathematical expressions. By means of this representation, a wider set of kernels can be modeled, where potentially better solutions can be found, although new challenges also arise. The proposed algorithm is able to overcome these difficulties and find kernels that accurately model the characteristics of the data. This method has been tested in several real-world time-series extrapolation problems, improving the state-of-the-art results while reducing the complexity of the kernels.

Ibai Roman, Alexander Mendiburu, Roberto Santana et al.

Sentiment analysis consists of evaluating opinions or statements from the analysis of text. Among the methods used to estimate the degree in which a text expresses a given sentiment, are those based on Gaussian Processes. However, traditional Gaussian Processes methods use a predefined kernel with hyperparameters that can be tuned but whose structure can not be adapted. In this paper, we propose the application of Genetic Programming for evolving Gaussian Process kernels that are more precise for sentiment analysis. We use use a very flexible representation of kernels combined with a multi-objective approach that simultaneously considers two quality metrics and the computational time spent by the kernels. Our results show that the algorithm can outperform Gaussian Processes with traditional kernels for some of the sentiment analysis tasks considered.

Unai Garciarena, Alexander Mendiburu, Roberto Santana

Multi-task learning, as it is understood nowadays, consists of using one single model to carry out several similar tasks. From classifying hand-written characters of different alphabets to figuring out how to play several Atari games using reinforcement learning, multi-task models have been able to widen their performance range across different tasks, although these tasks are usually of a similar nature. In this work, we attempt to widen this range even further, by including heterogeneous tasks in a single learning procedure. To do so, we firstly formally define a multi-network model, identifying the necessary components and characteristics to allow different adaptations of said model depending on the tasks it is required to fulfill. Secondly, employing the formal definition as a starting point, we develop an illustrative model example consisting of three different tasks (classification, regression and data sampling). The performance of this model implementation is then analyzed, showing its capabilities. Motivated by the results of the analysis, we enumerate a set of open challenges and future research lines over which the full potential of the proposed model definition can be exploited.

Marcella S. R. Martins, Mohamed El Yafrani, Roberto Santana et al.

Fitness landscape analysis investigates features with a high influence on the performance of optimization algorithms, aiming to take advantage of the addressed problem characteristics. In this work, a fitness landscape analysis using problem features is performed for a Multi-objective Bayesian Optimization Algorithm (mBOA) on instances of MNK-landscape problem for 2, 3, 5 and 8 objectives. We also compare the results of mBOA with those provided by NSGA-III through the analysis of their estimated runtime necessary to identify an approximation of the Pareto front. Moreover, in order to scrutinize the probabilistic graphic model obtained by mBOA, the Pareto front is examined according to a probabilistic view. The fitness landscape study shows that mBOA is moderately or loosely influenced by some problem features, according to a simple and a multiple linear regression model, which is being proposed to predict the algorithms performance in terms of the estimated runtime. Besides, we conclude that the analysis of the probabilistic graphic model produced at the end of evolution can be useful to understand the convergence and diversity performances of the proposed approach.

Unai Garciarena, Alexander Mendiburu, Roberto Santana

Automated Machine Learning encompasses a set of meta-algorithms intended to design and apply machine learning techniques (e.g., model selection, hyperparameter tuning, model assessment, etc.). TPOT, a software for optimizing machine learning pipelines based on genetic programming (GP), is a novel example of this kind of applications. Recently we have proposed a way to introduce imputation methods as part of TPOT. While our approach was able to deal with problems with missing data, it can produce a high number of unfeasible pipelines. In this paper we propose a strongly-typed-GP based approach that enforces constraint satisfaction by GP solutions. The enhancement we introduce is based on the redefinition of the operators and implicit enforcement of constraints in the generation of the GP trees. We evaluate the method to introduce imputation methods as part of TPOT. We show that the method can notably increase the efficiency of the GP search for optimal pipelines.

Roberto Santana

The concept of gray-box optimization, in juxtaposition to black-box optimization, revolves about the idea of exploiting the problem structure to implement more efficient evolutionary algorithms (EAs). Work on factorized distribution algorithms (FDAs), whose factorizations are directly derived from the problem structure, has also contributed to show how exploiting the problem structure produces important gains in the efficiency of EAs. In this paper we analyze the general question of using problem structure in EAs focusing on confronting work done in gray-box optimization with related research accomplished in FDAs. This contrasted analysis helps us to identify, in current studies on the use problem structure in EAs, two distinct analytical characterizations of how these algorithms work. Moreover, we claim that these two characterizations collide and compete at the time of providing a coherent framework to investigate this type of algorithms. To illustrate this claim, we present a contrasted analysis of formalisms, questions, and results produced in FDAs and gray-box optimization. Common underlying principles in the two approaches, which are usually overlooked, are identified and discussed. Besides, an extensive review of previous research related to different uses of the problem structure in EAs is presented. The paper also elaborates on some of the questions that arise when extending the use of problem structure in EAs, such as the question of evolvability, high cardinality of the variables and large definition sets, constrained and multi-objective problems, etc. Finally, emergent approaches that exploit neural models to capture the problem structure are covered.

Unai Garciarena, Roberto Santana, Alexander Mendiburu

Missing data has a ubiquitous presence in real-life applications of machine learning techniques. Imputation methods are algorithms conceived for restoring missing values in the data, based on other entries in the database. The choice of the imputation method has an influence on the performance of the machine learning technique, e.g., it influences the accuracy of the classification algorithm applied to the data. Therefore, selecting and applying the right imputation method is important and usually requires a substantial amount of human intervention. In this paper we propose the use of genetic programming techniques to search for the right combination of imputation and classification algorithms. We build our work on the recently introduced Python-based TPOT library, and incorporate a heterogeneous set of imputation algorithms as part of the machine learning pipeline search. We show that genetic programming can automatically find increasingly better pipelines that include the most effective combinations of imputation methods, feature pre-processing, and classifiers for a variety of classification problems with missing data.

Roberto Santana

Word-vector representations associate a high dimensional real-vector to every word from a corpus. Recently, neural-network based methods have been proposed for learning this representation from large corpora. This type of word-to-vector embedding is able to keep, in the learned vector space, some of the syntactic and semantic relationships present in the original word corpus. This, in turn, serves to address different types of language classification tasks by doing algebraic operations defined on the vectors. The general practice is to assume that the semantic relationships between the words can be inferred by the application of a-priori specified algebraic operations. Our general goal in this paper is to show that it is possible to learn methods for word composition in semantic spaces. Instead of expressing the compositional method as an algebraic operation, we will encode it as a program, which can be linear, nonlinear, or involve more intricate expressions. More remarkably, this program will be evolved from a set of initial random programs by means of genetic programming (GP). We show that our method is able to reproduce the same behavior as human-designed algebraic operators. Using a word analogy task as benchmark, we also show that GP-generated programs are able to obtain accuracy values above those produced by the commonly used human-designed rule for algebraic manipulation of word vectors. Finally, we show the robustness of our approach by executing the evolved programs on the word2vec GoogleNews vectors, learned over 3 billion running words, and assessing their accuracy in the same word analogy task.

Roberto Santana, Zheng Zhu, Helmut G. Katzgraber

Chimera graphs define the topology of one of the first commercially available quantum computers. A variety of optimization problems have been mapped to this topology to evaluate the behavior of quantum enhanced optimization heuristics in relation to other optimizers, being able to efficiently solve problems classically to use them as benchmarks for quantum machines. In this paper we investigate for the first time the use of Evolutionary Algorithms (EAs) on Ising spin glass instances defined on the Chimera topology. Three genetic algorithms (GAs) and three estimation of distribution algorithms (EDAs) are evaluated over $1000$ hard instances of the Ising spin glass constructed from Sidon sets. We focus on determining whether the information about the topology of the graph can be used to improve the results of EAs and on identifying the characteristics of the Ising instances that influence the success rate of GAs and EDAs.

Roberto Santana, Alexander Mendiburu, Jose A. Lozano

NM-landscapes have been recently introduced as a class of tunable rugged models. They are a subset of the general interaction models where all the interactions are of order less or equal $M$. The Boltzmann distribution has been extensively applied in single-objective evolutionary algorithms to implement selection and study the theoretical properties of model-building algorithms. In this paper we propose the combination of the multi-objective NM-landscape model and the Boltzmann distribution to obtain Pareto-front approximations. We investigate the joint effect of the parameters of the NM-landscapes and the probabilistic factorizations in the shape of the Pareto front approximations.

Murilo Zangari de Souza, Roberto Santana, Aurora Trinidad Ramirez Pozo et al.

Evolutionary algorithms based on modeling the statistical dependencies (interactions) between the variables have been proposed to solve a wide range of complex problems. These algorithms learn and sample probabilistic graphical models able to encode and exploit the regularities of the problem. This paper investigates the effect of using probabilistic modeling techniques as a way to enhance the behavior of MOEA/D framework. MOEA/D is a decomposition based evolutionary algorithm that decomposes a multi-objective optimization problem (MOP) in a number of scalar single-objective subproblems and optimizes them in a collaborative manner. MOEA/D framework has been widely used to solve several MOPs. The proposed algorithm, MOEA/D using probabilistic Graphical Models (MOEA/D-GM) is able to instantiate both univariate and multi-variate probabilistic models for each subproblem. To validate the introduced framework algorithm, an experimental study is conducted on a multi-objective version of the deceptive function Trap5. The results show that the variant of the framework (MOEA/D-Tree), where tree models are learned from the matrices of the mutual information between the variables, is able to capture the structure of the problem. MOEA/D-Tree is able to achieve significantly better results than both MOEA/D using genetic operators and MOEA/D using univariate probability models, in terms of the approximation to the true Pareto front.

Roberto Santana, Ross B. McDonald, Helmut G. Katzgraber

Topological quantum computing is an alternative framework for avoiding the quantum decoherence problem in quantum computation. The problem of executing a gate in this framework can be posed as the problem of braiding quasiparticles. Because these are not Abelian, the problem can be reduced to finding an optimal product of braid generators where the optimality is defined in terms of the gate approximation and the braid's length. In this paper we propose the use of different variants of estimation of distribution algorithms to deal with the problem. Furthermore, we investigate how the regularities of the braid optimization problem can be translated into statistical regularities by means of the Boltzmann distribution. We show that our best algorithm is able to produce many solutions that approximates the target gate with an accuracy in the order of $10^{-6}$, and have lengths up to 9 times shorter than those expected from braids of the same accuracy obtained with other methods.