Eduardo C. Garrido-Merchán

Eduardo C. Garrido-Merchán

The human-dignity-centric digital social contract grounds personal data in human dignity, data personalism, and data sovereignty, and articulates six dimensions of data governance: technological oversight, automation limits, economic justice, political legitimacy, social cohesion, and legal guarantees. It presupposes, however, that enforcement falls to State regulators, licensed fiduciaries, and multi-stakeholder bodies embedded in existing legal systems. This paper asks whether its normative content can instead be realized not as rules imposed on the owners of the AI stack from without, but as a commons-governed infrastructure that any person, firm, or State may use and fund while its governance stays horizontal, polycentric, and subsidiary. We construct the Dignity Stack, a six-layer architecture mapping each dimension onto a layer of commons-governed AI infrastructure, with protocols drawn from the Liberation Stack framework and from the cooperative, mutualist, and libertarian-municipalist traditions. The commons is State-agnostic rather than anti-State, anarchist in its horizontal means but not in the abolition of the State. Its central device is a decoupling of capital from control, by which the stack functions as a shared civic battery, charged by many contributors yet steered by none in proportion to its charge. We prove that this defeats formal capture through votes or surplus, and show that structural capture, the leverage of a dominant supplier free to withdraw what it provides, is resisted only insofar as operational supply is polycentric and substitutable, a condition demanding at the lower layers and perhaps presently unattainable at chip fabrication. We conclude, with explicit attention to its limits, that commons-governed AI realizes the values the contract proclaims more faithfully than the regulation it presupposes.

Florian Karl, Tobias Pielok, Julia Moosbauer et al.

Hyperparameter optimization constitutes a large part of typical modern machine learning workflows. This arises from the fact that machine learning methods and corresponding preprocessing steps often only yield optimal performance when hyperparameters are properly tuned. But in many applications, we are not only interested in optimizing ML pipelines solely for predictive accuracy; additional metrics or constraints must be considered when determining an optimal configuration, resulting in a multi-objective optimization problem. This is often neglected in practice, due to a lack of knowledge and readily available software implementations for multi-objective hyperparameter optimization. In this work, we introduce the reader to the basics of multi-objective hyperparameter optimization and motivate its usefulness in applied ML. Furthermore, we provide an extensive survey of existing optimization strategies, both from the domain of evolutionary algorithms and Bayesian optimization. We illustrate the utility of MOO in several specific ML applications, considering objectives such as operating conditions, prediction time, sparseness, fairness, interpretability and robustness.

Alejo Jose G. Sison, Marco Tulio Daza, Roberto Gozalo-Brizuela et al.

This article explores the ethical problems arising from the use of ChatGPT as a kind of generative AI and suggests responses based on the Human-Centered Artificial Intelligence (HCAI) framework. The HCAI framework is appropriate because it understands technology above all as a tool to empower, augment, and enhance human agency while referring to human wellbeing as a grand challenge, thus perfectly aligning itself with ethics, the science of human flourishing. Further, HCAI provides objectives, principles, procedures, and structures for reliable, safe, and trustworthy AI which we apply to our ChatGPT assessments. The main danger ChatGPT presents is the propensity to be used as a weapon of mass deception (WMD) and an enabler of criminal activities involving deceit. We review technical specifications to better comprehend its potentials and limitations. We then suggest both technical (watermarking, styleme, detectors, and fact-checkers) and non-technical measures (terms of use, transparency, educator considerations, HITL) to mitigate ChatGPT misuse or abuse and recommend best uses (creative writing, non-creative writing, teaching and learning). We conclude with considerations regarding the role of humans in ensuring the proper use of ChatGPT for individual and social wellbeing.

Roberto Gozalo-Brizuela, Eduardo C. Garrido-Merchán

Generative AI has experienced remarkable growth in recent years, leading to a wide array of applications across diverse domains. In this paper, we present a comprehensive survey of more than 350 generative AI applications, providing a structured taxonomy and concise descriptions of various unimodal and even multimodal generative AIs. The survey is organized into sections, covering a wide range of unimodal generative AI applications such as text, images, video, gaming and brain information. Our survey aims to serve as a valuable resource for researchers and practitioners to navigate the rapidly expanding landscape of generative AI, facilitating a better understanding of the current state-of-the-art and fostering further innovation in the field.

Eduardo C. Garrido-Merchán, Esther Vaquero Lafuente, Elisa Aracil

The integration of Artificial Intelligence into sustainable finance represents a transformative paradigm shift in how Environmental, Social, and Governance factors are analyzed, predicted, and incorporated into investment decisions. This review provides a comprehensive taxonomy of AI approaches applicable to sustainable investment decision-making, categorizing methodologies based on their underlying algorithms and their impact on ESG-related financial processes. The proposed AI Taxonomy includes machine learning paradigms -- including supervised, unsupervised, and reinforcement learning -- as well as natural language processing techniques and optimization algorithms, examining their specific applications in ESG score prediction, controversy detection, portfolio management, and sustainability report analysis. By synthesizing findings from the recent literature, a framework emerges on AI-powered sustainable finance that identifies technological applications to overcome ESG data barriers.

Juan Ballesteros Gómez, Eduardo C. Garrido-Merchán, Pedro Pablo Pérez-Velasco

Operational risk capital estimation under Basel II/III requires quantifying aggregate losses at extreme confidence levels of 99.9% and beyond, yet the standard Loss Distribution Approach (LDA) assumes independence between loss frequency and severity, an assumption frequently violated during stress episodes. Furthermore, MLE of tail parameters ignores parameter uncertainty, leading to overconfident risk estimates at extreme quantiles. We propose a Bayesian framework that combines Extreme Value Theory with a dynamic dependence architecture, the Hawkes-AR-Gumbel model, for operational risk Conditional Value-at-Risk (CVaR) estimation at confidence levels up to 99.995%. The model integrates three mechanisms that capture empirically documented features of operational losses: an autoregressive latent stress process that captures persistence of crisis regimes, a Hawkes selfexcitation component for frequency that generates event clustering and overdispersion, and a Gumbel copula for upper-tail dependence that links frequency and severity innovations through an asymmetric copula concentrating dependence in the extreme tail. Inference is performed via Hamiltonian Monte Carlo using PyMC, yielding full posterior distributions for all parameters, and CVaR at arbitrary confidence levels is estimated through posterior predictive Monte Carlo simulation. We compare three models on simulated operational risk data: the independent model (standard LDA), a shared latent factor model with symmetric dependence, and the proposed Hawkes-AR-Gumbel model. The independent model underestimates CVaR at 99.995% by approximately 40%, while the shared factor model fails to capture temporal persistence, event clustering, and upper-tail asymmetry. The HawkesAR-Gumbel model recovers the true dependence structure and correctly estimates CVaR at extreme levels.

Eduardo C. Garrido-Merchán, Sol Mora-Figueroa-Cruz-Guzmán, María Coronado-Vaca

This paper investigates the application of Deep Reinforcement Learning (DRL) for Environment, Social, and Governance (ESG) financial portfolio management, with a specific focus on the potential benefits of ESG score-based market regulation. We leveraged an Advantage Actor-Critic (A2C) agent and conducted our experiments using environments encoded within the OpenAI Gym, adapted from the FinRL platform. The study includes a comparative analysis of DRL agent performance under standard Dow Jones Industrial Average (DJIA) market conditions and a scenario where returns are regulated in line with company ESG scores. In the ESG-regulated market, grants were proportionally allotted to portfolios based on their returns and ESG scores, while taxes were assigned to portfolios below the mean ESG score of the index. The results intriguingly reveal that the DRL agent within the ESG-regulated market outperforms the standard DJIA market setup. Furthermore, we considered the inclusion of ESG variables in the agent state space, and compared this with scenarios where such data were excluded. This comparison adds to the understanding of the role of ESG factors in portfolio management decision-making. We also analyze the behaviour of the DRL agent in IBEX 35 and NASDAQ-100 indexes. Both the A2C and Proximal Policy Optimization (PPO) algorithms were applied to these additional markets, providing a broader perspective on the generalization of our findings. This work contributes to the evolving field of ESG investing, suggesting that market regulation based on ESG scoring can potentially improve DRL-based portfolio management, with significant implications for sustainable investing strategies.

Eduardo C. Garrido-Merchán, Cristina González-Barthe, María Coronado Vaca

In recent years there has been a growing demand from financial agents, especially from particular and institutional investors, for companies to report on climate-related financial risks. A vast amount of information, in text format, can be expected to be disclosed in the short term by firms in order to identify these types of risks in their financial and non financial reports, particularly in response to the growing regulation that is being passed on the matter. To this end, this paper applies state-of-the-art NLP techniques to achieve the detection of climate change in text corpora. We use transfer learning to fine-tune two transformer models, BERT and ClimateBert -a recently published DistillRoBERTa-based model that has been specifically tailored for climate text classification-. These two algorithms are based on the transformer architecture which enables learning the contextual relationships between words in a text. We carry out the fine-tuning process of both models on the novel Clima-Text database, consisting of data collected from Wikipedia, 10K Files Reports and web-based claims. Our text classification model obtained from the ClimateBert fine-tuning process on ClimaText, outperforms the models created with BERT and the current state-of-the-art transformer in this particular problem. Our study is the first one to implement on the ClimaText database the recently published ClimateBert algorithm. Based on our results, it can be said that ClimateBert fine-tuned on ClimaText is an outstanding tool within the NLP pre-trained transformer models that may and should be used by investors, institutional agents and companies themselves to monitor the disclosure of climate risk in financial reports. In addition, our transfer learning methodology is cheap in computational terms, thus allowing any organization to perform it.

Eduardo C. Garrido-Merchán, Carlos Blanco

Are intelligent machines really intelligent? Is the underlying philosophical concept of intelligence satisfactory for describing how the present systems work? Is understanding a necessary and sufficient condition for intelligence? If a machine could understand, should we attribute subjectivity to it? This paper addresses the problem of deciding whether the so-called "intelligent machines" are capable of understanding, instead of merely processing signs. It deals with the relationship between syntaxis and semantics. The main thesis concerns the inevitability of semantics for any discussion about the possibility of building conscious machines, condensed into the following two tenets: "If a machine is capable of understanding (in the strong sense), then it must be capable of combining rules and intuitions"; "If semantics cannot be reduced to syntaxis, then a machine cannot understand." Our conclusion states that it is not necessary to attribute understanding to a machine in order to explain its exhibited "intelligent" behavior; a merely syntactic and mechanistic approach to intelligence as a task-solving tool suffices to justify the range of operations that it can display in the current state of technological development.

Eduardo C. Garrido-Merchán, Gabriel González Piris, Maria Coronado Vaca

Financial experts and analysts seek to predict the variability of financial markets. In particular, the correct prediction of this variability ensures investors successful investments. However, there has been a big trend in finance in the last years, which are the ESG criteria. Concretely, ESG (Economic, Social and Governance) criteria have become more significant in finance due to the growing importance of investments being socially responsible, and because of the financial impact companies suffer when not complying with them. Consequently, creating a stock portfolio should not only take into account its performance but compliance with ESG criteria. Hence, this paper combines mathematical modelling, with ESG and finance. In more detail, we use Bayesian optimization (BO), a sequential state-of-the-art design strategy to optimize black-boxes with unknown analytical and costly-to compute expressions, to maximize the performance of a stock portfolio under the presence of ESG criteria soft constraints incorporated to the objective function. In an illustrative experiment, we use the Sharpe ratio, that takes into consideration the portfolio returns and its variance, in other words, it balances the trade-off between maximizing returns and minimizing risks. In the present work, ESG criteria have been divided into fourteen independent categories used in a linear combination to estimate a firm total ESG score. Most importantly, our presented approach would scale to alternative black-box methods of estimating the performance and ESG compliance of the stock portfolio. In particular, this research has opened the door to many new research lines, as it has proved that a portfolio can be optimized using a BO that takes into consideration financial performance and the accomplishment of ESG criteria.

Eduardo C. Garrido-Merchán, Jose L. Arroyo-Barrigüete, Francisco Borrás-Pala et al.

Large Language Models (LLMs), as the case of OpenAI ChatGPT-4 Turbo, are revolutionizing several industries, including higher education. In this context, LLMs can be personalized through a fine-tuning process to meet the student demands on every particular subject, like statistics. Recently, OpenAI has launched the possibility to fine-tune their model with a natural language web interface, enabling the possibility to create customized GPT version deliberately conditioned to meet the demands of a specific task. The objective of this research is to assess the potential of the customized GPTs that have recently been launched by OpenAI. After developing a Business Statistics Virtual Professor (BSVP), tailored for students at the Universidad Pontificia Comillas, its behavior was evaluated and compared with that of ChatGPT-4 Turbo. The results lead to several conclusions. Firstly, a substantial modification in the style of communication was observed. Following the instructions it was trained with, BSVP provided responses in a more relatable and friendly tone, even incorporating a few minor jokes. Secondly, and this is a matter of relevance, when explicitly asked for something like, "I would like to practice a programming exercise similar to those in R practice 4," BSVP was capable of providing a far superior response: having access to contextual documentation, it could fulfill the request, something beyond ChatGPT-4 Turbo's capabilities. On the downside, the response times were generally higher. Lastly, regarding overall performance, quality, depth, and alignment with the specific content of the course, no statistically significant differences were observed in the responses between BSVP and ChatGPT-4 Turbo. It appears that customized assistants trained with prompts present advantages as virtual aids for students, yet they do not constitute a substantial improvement over ChatGPT-4 Turbo.

Eduardo C. Garrido-Merchán, Javier Sánchez-Cañizares

Integrated information theory (IIT) is a theoretical framework that provides a quantitative measure to estimate when a physical system is conscious, its degree of consciousness, and the complexity of the qualia space that the system is experiencing. Formally, IIT rests on the assumption that if a surrogate physical system can fully embed the phenomenological properties of consciousness, then the system properties must be constrained by the properties of the qualia being experienced. Following this assumption, IIT represents the physical system as a network of interconnected elements that can be thought of as a probabilistic causal graph, $\mathcal{G}$, where each node has an input-output function and all the graph is encoded in a transition probability matrix. Consequently, IIT's quantitative measure of consciousness, $Φ$, is computed with respect to the transition probability matrix and the present state of the graph. In this paper, we provide a random search algorithm that is able to optimize $Φ$ in order to investigate, as the number of nodes increases, the structure of the graphs that have higher $Φ$. We also provide arguments that show the difficulties of applying more complex black-box search algorithms, such as Bayesian optimization or metaheuristics, in this particular problem. Additionally, we suggest specific research lines for these techniques to enhance the search algorithm that guarantees maximal $Φ$.

Claudia Benavides Cantos, Eduardo C. Garrido-Merchán

We study how four widely used large language models, namely Claude, GPT-4o, DeepSeek and Grok, distribute a fixed national social budget across twelve macro-areas of public expenditure under two European national contexts, Spain and Germany. Each combination of model and country is queried six times under identical prompts and generation parameters, producing forty-eight independent allocations that are compared against approximate Organisation for Economic Co-operation and Development (OECD) reference budgets and against each other. We formalise five hypotheses regarding geopolitical bias, housing under-allocation, structural convergence, sensitivity to national context, and under-representation of politically sensitive categories. The differences between models are then validated through Kruskal-Wallis tests on each macro-area, with post-hoc Mann-Whitney U comparisons under Bonferroni correction, and complemented by an analysis of pairwise Pearson correlations and a lexical examination of the textual justifications produced by each model. The results show that all four models share a systematic implicit social policy that diverges from real European spending structures: pensions are under-allocated by a factor close to three, while housing and employment are over-allocated by factors of four and two respectively. The principal axis of differentiation between models is not geopolitical, since Claude and DeepSeek are the most correlated pair across both countries, but rather a contrast between concentration and dispersion of the budget. Only Claude exhibits substantive sensitivity to the national context. The conclusions delimit the conditions under which language models may responsibly support, but not replace, expert deliberation in public budgeting.

Nicolás Villagrán Prieto, Eduardo C. Garrido-Merchán

Bayesian Optimization (BO) is a standard tool for hyperparameter tuning thanks to its sample efficiency on expensive black-box functions. While most BO pipelines begin with uniform random initialization, default hyperparameter values shipped with popular ML libraries such as scikit-learn encode implicit expert knowledge and could serve as informative starting points that accelerate convergence. This hypothesis, despite its intuitive appeal, has remained largely unexamined. We formalize the idea by initializing BO with points drawn from truncated Gaussian distributions centered at library defaults and compare the resulting trajectories against a uniform-random baseline. We conduct an extensive empirical evaluation spanning three BO back-ends (BoTorch, Optuna, Scikit-Optimize), three model families (Random Forests, Support Vector Machines, Multilayer Perceptrons), and five benchmark datasets covering classification and regression tasks. Performance is assessed through convergence speed and final predictive quality, and statistical significance is determined via one-sided binomial tests. Across all conditions, default-informed initialization yields no statistically significant advantage over purely random sampling, with p-values ranging from 0.141 to 0.908. A sensitivity analysis on the prior variance confirms that, while tighter concentration around the defaults improves early evaluations, this transient benefit vanishes as optimization progresses, leaving final performance unchanged. Our results provide no evidence that default hyperparameters encode useful directional information for optimization. We therefore recommend that practitioners treat hyperparameter tuning as an integral part of model development and favor principled, data-driven search strategies over heuristic reliance on library defaults.

Eduardo C. Garrido-Merchán

Several scenarios require the optimization of non-convex black-box functions, that are noisy expensive to evaluate functions with unknown analytical expression, whose gradients are hence not accessible. For example, the hyper-parameter tuning problem of machine learning models. Bayesian optimization is a class of methods with state-of-the-art performance delivering a solution to this problem in real scenarios. It uses an iterative process that employs a probabilistic surrogate model, typically a Gaussian process, of the objective function to be optimized computing a posterior predictive distribution of the black-box function. Based on the information given by this posterior predictive distribution, Bayesian optimization includes the computation of an acquisition function that represents, for every input space point, the utility of evaluating that point in the next iteraiton if the objective of the process is to retrieve a global extremum. This paper is a survey of the information theoretical acquisition functions, whose performance typically outperforms the rest of acquisition functions. The main concepts of the field of information theory are also described in detail to make the reader aware of why information theory acquisition functions deliver great results in Bayesian optimization and how can we approximate them when they are intractable. We also cover how information theory acquisition functions can be adapted to complex optimization scenarios such as the multi-objective, constrained, non-myopic, multi-fidelity, parallel and asynchronous settings and provide further lines of research.

Daniel Fernández-Sánchez, Eduardo C. Garrido-Merchán, Daniel Hernández-Lobato

Bayesian optimization (BO) methods based on information theory have obtained state-of-the-art results in several tasks. These techniques heavily rely on the Kullback-Leibler (KL) divergence to compute the acquisition function. In this work, we introduce a novel information-based class of acquisition functions for BO called Alpha Entropy Search (AES). AES is based on the α-divergence, that generalizes the KL divergence. Iteratively, AES selects the next evaluation point as the one whose associated target value has the highest level of the dependency with respect to the location and associated value of the global maximum of the optimization problem. Dependency is measured in terms of the α-divergence, as an alternative to the KL divergence. Intuitively, this favors the evaluation of the objective function at the most informative points about the global maximum. The α-divergence has a free parameter α, which determines the behavior of the divergence, trading-off evaluating differences between distributions at a single mode, and evaluating differences globally. Therefore, different values of α result in different acquisition functions. AES acquisition lacks a closed-form expression. However, we propose an efficient and accurate approximation using a truncated Gaussian distribution. In practice, the value of α can be chosen by the practitioner, but here we suggest to use a combination of acquisition functions obtained by simultaneously considering a range of values of α. We provide an implementation of AES in BOTorch and we evaluate its performance in both synthetic, benchmark and real-world experiments involving the tuning of the hyper-parameters of a deep neural network. These experiments show that the performance of AES is competitive with respect to other information-based acquisition functions such as JES, MES or PES.

Eduardo C. Garrido-Merchán, Maria Coronado-Vaca, Álvaro López-López et al.

Traditional economic models often rely on fixed assumptions about market dynamics, limiting their ability to capture the complexities and stochastic nature of real-world scenarios. However, reality is more complex and includes noise, making traditional models assumptions not met in the market. In this paper, we explore the application of deep reinforcement learning (DRL) to obtain optimal production strategies in microeconomic market environments to overcome the limitations of traditional models. Concretely, we propose a DRL-based approach to obtain an effective policy in competitive markets with multiple producers, each optimizing their production decisions in response to fluctuating demand, supply, prices, subsidies, fixed costs, total production curve, elasticities and other effects contaminated by noise. Our framework enables agents to learn adaptive production policies to several simulations that consistently outperform static and random strategies. As the deep neural networks used by the agents are universal approximators of functions, DRL algorithms can represent in the network complex patterns of data learnt by trial and error that explain the market. Through extensive simulations, we demonstrate how DRL can capture the intricate interplay between production costs, market prices, and competitor behavior, providing insights into optimal decision-making in dynamic economic settings. The results show that agents trained with DRL can strategically adjust production levels to maximize long-term profitability, even in the face of volatile market conditions. We believe that the study bridges the gap between theoretical economic modeling and practical market simulation, illustrating the potential of DRL to revolutionize decision-making in market strategies.

Eduardo C. Garrido-Merchán, Cristina Puente

The development of large language models (LLMs) has successfully transformed knowledge-based systems such as open domain question nswering, which can automatically produce vast amounts of seemingly coherent information. Yet, those models have several disadvantages like hallucinations or confident generation of incorrect or unverifiable facts. In this paper, we introduce a new approach to the development of expert systems using LLMs in a controlled and transparent way. By limiting the domain and employing a well-structured prompt-based extraction approach, we produce a symbolic representation of knowledge in Prolog, which can be validated and corrected by human experts. This approach also guarantees interpretability, scalability and reliability of the developed expert systems. Via quantitative and qualitative experiments with Claude Sonnet 3.7 and GPT-4.1, we show strong adherence to facts and semantic coherence on our generated knowledge bases. We present a transparent hybrid solution that combines the recall capacity of LLMs with the precision of symbolic systems, thereby laying the foundation for dependable AI applications in sensitive domains.

Eduardo C. Garrido-Merchán, José Luis Arroyo-Barrigüete, Roberto Gozalo-Brizuela

In this paper, we present a novel approach to simulating H.P. Lovecraft's horror literature using the ChatGPT large language model, specifically the GPT-4 architecture. Our study aims to generate text that emulates Lovecraft's unique writing style and themes, while also examining the effectiveness of prompt engineering techniques in guiding the model's output. To achieve this, we curated a prompt containing several specialized literature references and employed advanced prompt engineering methods. We conducted an empirical evaluation of the generated text by administering a survey to a sample of undergraduate students. Utilizing statistical hypothesis testing, we assessed the students ability to distinguish between genuine Lovecraft works and those generated by our model. Our findings demonstrate that the participants were unable to reliably differentiate between the two, indicating the effectiveness of the GPT-4 model and our prompt engineering techniques in emulating Lovecraft's literary style. In addition to presenting the GPT model's capabilities, this paper provides a comprehensive description of its underlying architecture and offers a comparative analysis with related work that simulates other notable authors and philosophers, such as Dennett. By exploring the potential of large language models in the context of literary emulation, our study contributes to the body of research on the applications and limitations of these models in various creative domains.

Lucia Asencio Martín, Eduardo C. Garrido-Merchán

Some real problems require the evaluation of expensive and noisy objective functions. Moreover, the analytical expression of these objective functions may be unknown. These functions are known as black-boxes, for example, estimating the generalization error of a machine learning algorithm and computing its prediction time in terms of its hyper-parameters. Multi-objective Bayesian optimization (MOBO) is a set of methods that has been successfully applied for the simultaneous optimization of black-boxes. Concretely, BO methods rely on a probabilistic model of the objective functions, typically a Gaussian process. This model generates a predictive distribution of the objectives. However, MOBO methods have problems when the number of objectives in a multi-objective optimization problem are 3 or more, which is the many objective setting. In particular, the BO process is more costly as more objectives are considered, computing the quality of the solution via the hyper-volume is also more costly and, most importantly, we have to evaluate every objective function, wasting expensive computational, economic or other resources. However, as more objectives are involved in the optimization problem, it is highly probable that some of them are redundant and not add information about the problem solution. A measure that represents how similar are GP predictive distributions is proposed. We also propose a many objective Bayesian optimization algorithm that uses this metric to determine whether two objectives are redundant. The algorithm stops evaluating one of them if the similarity is found, saving resources and not hurting the performance of the multi-objective BO algorithm. We show empirical evidence in a set of toy, synthetic, benchmark and real experiments that GPs predictive distributions of the effectiveness of the metric and the algorithm.

Lucia Asencio-Martín, Eduardo C. Garrido-Merchán

Some scenarios require the computation of a predictive distribution of a new value evaluated on an objective function conditioned on previous observations. We are interested on using a model that makes valid assumptions on the objective function whose values we are trying to predict. Some of these assumptions may be smoothness or stationarity. Gaussian process (GPs) are probabilistic models that can be interpreted as flexible distributions over functions. They encode the assumptions through covariance functions, making hypotheses about new data through a predictive distribution by being fitted to old observations. We can face the case where several GPs are used to model different objective functions. GPs are non-parametric models whose complexity is cubic on the number of observations. A measure that represents how similar is one GP predictive distribution with respect to another would be useful to stop using one GP when they are modelling functions of the same input space. We are really inferring that two objective functions are correlated, so one GP is enough to model both of them by performing a transformation of the prediction of the other function in case of inverse correlation. We show empirical evidence in a set of synthetic and benchmark experiments that GPs predictive distributions can be compared and that one of them is enough to predict two correlated functions in the same input space. This similarity metric could be extremely useful used to discard objectives in Bayesian many-objective optimization.

Eduardo C. Garrido-Merchán, Martin Molina, Francisco M. Mendoza

This work seeks to study the beneficial properties that an autonomous agent can obtain by implementing a cognitive architecture similar to the one of conscious beings. Along this document, a conscious model of autonomous agent based in a global workspace architecture is presented. We describe how this agent is viewed from different perspectives of philosophy of mind, being inspired by their ideas. The goal of this model is to create autonomous agents able to navigate within an environment composed of multiple independent magnitudes, adapting to its surroundings in order to find the best possible position in base of its inner preferences. The purpose of the model is to test the effectiveness of many cognitive mechanisms that are incorporated, such as an attention mechanism for magnitude selection, pos-session of inner feelings and preferences, usage of a memory system to storage beliefs and past experiences, and incorporating a global workspace which controls and integrates information processed by all the subsystem of the model. We show in a large experiment set how an autonomous agent can benefit from having a cognitive architecture such as the one described.

Daniel Fernández-Sánchez, Eduardo C. Garrido-Merchán, Daniel Hernández-Lobato

We present MESMOC+, an improved version of Max-value Entropy search for Multi-Objective Bayesian optimization with Constraints (MESMOC). MESMOC+ can be used to solve constrained multi-objective problems when the objectives and the constraints are expensive to evaluate. MESMOC+ works by minimizing the entropy of the solution of the optimization problem in function space, i.e., the Pareto frontier, to guide the search for the optimum. The cost of MESMOC+ is linear in the number of objectives and constraints. Furthermore, it is often significantly smaller than the cost of alternative methods based on minimizing the entropy of the Pareto set. The reason for this is that it is easier to approximate the required computations in MESMOC+. Moreover, MESMOC+'s acquisition function is expressed as the sum of one acquisition per each black-box (objective or constraint). Thus, it can be used in a decoupled evaluation setting in which one chooses not only the next input location to evaluate, but also which black-box to evaluate there. We compare MESMOC+ with related methods in synthetic and real optimization problems. These experiments show that the entropy estimation provided by MESMOC+ is more accurate than that of previous methods. This leads to better optimization results. MESMOC+ is also competitive with other information-based methods for constrained multi-objective Bayesian optimization, but it is significantly faster.

Santiago González-Carvajal, Eduardo C. Garrido-Merchán

The BERT model has arisen as a popular state-of-the-art machine learning model in the recent years that is able to cope with multiple NLP tasks such as supervised text classification without human supervision. Its flexibility to cope with any type of corpus delivering great results has make this approach very popular not only in academia but also in the industry. Although, there are lots of different approaches that have been used throughout the years with success. In this work, we first present BERT and include a little review on classical NLP approaches. Then, we empirically test with a suite of experiments dealing different scenarios the behaviour of BERT against the traditional TF-IDF vocabulary fed to machine learning algorithms. Our purpose of this work is to add empirical evidence to support or refuse the use of BERT as a default on NLP tasks. Experiments show the superiority of BERT and its independence of features of the NLP problem such as the language of the text adding empirical evidence to use BERT as a default technique to be used in NLP problems.

Eduardo C. Garrido-Merchán, Daniel Hernández-Lobato

Real-world problems often involve the optimization of several objectives under multiple constraints. An example is the hyper-parameter tuning problem of machine learning algorithms. In particular, the minimization of the estimation of the generalization error of a deep neural network and at the same time the minimization of its prediction time. We may also consider as a constraint that the deep neural network must be implemented in a chip with an area below some size. Here, both the objectives and the constraint are black boxes, i.e., functions whose analytical expressions are unknown and are expensive to evaluate. Bayesian optimization (BO) methodologies have given state-of-the-art results for the optimization of black-boxes. Nevertheless, most BO methods are sequential and evaluate the objectives and the constraints at just one input location, iteratively. Sometimes, however, we may have resources to evaluate several configurations in parallel. Notwithstanding, no parallel BO method has been proposed to deal with the optimization of multiple objectives under several constraints. If the expensive evaluations can be carried out in parallel (as when a cluster of computers is available), sequential evaluations result in a waste of resources. This article introduces PPESMOC, Parallel Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraints, an information-based batch method for the simultaneous optimization of multiple expensive-to-evaluate black-box functions under the presence of several constraints. Iteratively, PPESMOC selects a batch of input locations at which to evaluate the black-boxes so as to maximally reduce the entropy of the Pareto set of the optimization problem. We present empirical evidence in the form of synthetic, benchmark and real-world experiments that illustrate the effectiveness of PPESMOC.

Eduardo C. Garrido-Merchán, Cristina Puente, Rafael Palacios

Society is experimenting changes in information consumption, as new information channels such as social networks let people share news that do not necessarily be trust worthy. Sometimes, these sources of information produce fake news deliberately with doubtful purposes and the consumers of that information share it to other users thinking that the information is accurate. This transmission of information represents an issue in our society, as can influence negatively the opinion of people about certain figures, groups or ideas. Hence, it is desirable to design a system that is able to detect and classify information as fake and categorize a source of information as trust worthy or not. Current systems experiment difficulties performing this task, as it is complicated to design an automatic procedure that can classify this information independent on the context. In this work, we propose a mechanism to detect fake news through a classifier based on weighted causal graphs. These graphs are specific hybrid models that are built through causal relations retrieved from texts and consider the uncertainty of causal relations. We take advantage of this representation to use the probability distributions of this graph and built a fake news classifier based on the entropy and KL divergence of learned and new information. We believe that the problem of fake news is accurately tackled by this model due to its hybrid nature between a symbolic and quantitative methodology. We describe the methodology of this classifier and add empirical evidence of the usefulness of our proposed approach in the form of synthetic experiments and a real experiment involving lung cancer.

Eduardo C. Garrido-Merchán, C. Puente, A. Sobrino et al.

Causality has traditionally been a scientific way to generate knowledge by relating causes to effects. From an imaginery point of view, causal graphs are a helpful tool for representing and infering new causal information. In previous works, we have generated automatically causal graphs associated to a given concept by analyzing sets of documents and extracting and representing the found causal information in that visual way. The retrieved information shows that causality is frequently imperfect rather than exact, feature gathered by the graph. In this work we will attempt to go a step further modelling the uncertainty in the graph through probabilistic improving the management of the imprecision in the quoted graph.

Carlos Villacampa-Calvo, Bryan Zaldivar, Eduardo C. Garrido-Merchán et al.

It is a common practice in the machine learning community to assume that the observed data are noise-free in the input attributes. Nevertheless, scenarios with input noise are common in real problems, as measurements are never perfectly accurate. If this input noise is not taken into account, a supervised machine learning method is expected to perform sub-optimally. In this paper, we focus on multi-class classification problems and use Gaussian processes (GPs) as the underlying classifier. Motivated by a data set coming from the astrophysics domain, we hypothesize that the observed data may contain noise in the inputs. Therefore, we devise several multi-class GP classifiers that can account for input noise. Such classifiers can be efficiently trained using variational inference to approximate the posterior distribution of the latent variables of the model. Moreover, in some situations, the amount of noise can be known before-hand. If this is the case, it can be readily introduced in the proposed methods. This prior information is expected to lead to better performance results. We have evaluated the proposed methods by carrying out several experiments, involving synthetic and real data. These include several data sets from the UCI repository, the MNIST data set and a data set coming from astrophysics. The results obtained show that, although the classification error is similar across methods, the predictive distribution of the proposed methods is better, in terms of the test log-likelihood, than the predictive distribution of a classifier based on GPs that ignores input noise.

Eduardo C. Garrido-Merchán, Alejandro Albarca-Molina

Cooking typically involves a plethora of decisions about ingredients and tools that need to be chosen in order to write a good cooking recipe. Cooking can be modelled in an optimization framework, as it involves a search space of ingredients, kitchen tools, cooking times or temperatures. If we model as an objective function the quality of the recipe, several problems arise. No analytical expression can model all the recipes, so no gradients are available. The objective function is subjective, in other words, it contains noise. Moreover, evaluations are expensive both in time and human resources. Bayesian Optimization (BO) emerges as an ideal methodology to tackle problems with these characteristics. In this paper, we propose a methodology to suggest recipe recommendations based on a Machine Learning (ML) model that fits real and simulated data and BO. We provide empirical evidence with two experiments that support the adequacy of the methodology.

Irene Córdoba, Eduardo C. Garrido-Merchán, Daniel Hernández-Lobato et al.

The PC algorithm is a popular method for learning the structure of Gaussian Bayesian networks. It carries out statistical tests to determine absent edges in the network. It is hence governed by two parameters: (i) The type of test, and (ii) its significance level. These parameters are usually set to values recommended by an expert. Nevertheless, such an approach can suffer from human bias, leading to suboptimal reconstruction results. In this paper we consider a more principled approach for choosing these parameters in an automatic way. For this we optimize a reconstruction score evaluated on a set of different Gaussian Bayesian networks. This objective is expensive to evaluate and lacks a closed-form expression, which means that Bayesian optimization (BO) is a natural choice. BO methods use a model to guide the search and are hence able to exploit smoothness properties of the objective surface. We show that the parameters found by a BO method outperform those found by a random search strategy and the expert recommendation. Importantly, we have found that an often overlooked statistical test provides the best over-all reconstruction results.

Eduardo C. Garrido-Merchán, Daniel Hernández-Lobato

Bayesian Optimization (BO) methods are useful for optimizing functions that are expen- sive to evaluate, lack an analytical expression and whose evaluations can be contaminated by noise. These methods rely on a probabilistic model of the objective function, typically a Gaussian process (GP), upon which an acquisition function is built. The acquisition function guides the optimization process and measures the expected utility of performing an evaluation of the objective at a new point. GPs assume continous input variables. When this is not the case, for example when some of the input variables take categorical or integer values, one has to introduce extra approximations. Consider a suggested input location taking values in the real line. Before doing the evaluation of the objective, a common approach is to use a one hot encoding approximation for categorical variables, or to round to the closest integer, in the case of integer-valued variables. We show that this can lead to problems in the optimization process and describe a more principled approach to account for input variables that are categorical or integer-valued. We illustrate in both synthetic and a real experiments the utility of our approach, which significantly improves the results of standard BO methods using Gaussian processes on problems with categorical or integer-valued variables.

Eduardo C. Garrido-Merchán, Daniel Hernández-Lobato

Bayesian optimization (BO) methods are useful for optimizing functions that are expensive to evaluate, lack an analytical expression and whose evaluations can be contaminated by noise. These methods rely on a probabilistic model of the objective function, typically a Gaussian process (GP), upon which an acquisition function is built. This function guides the optimization process and measures the expected utility of performing an evaluation of the objective at a new point. GPs assume continous input variables. When this is not the case, such as when some of the input variables take integer values, one has to introduce extra approximations. A common approach is to round the suggested variable value to the closest integer before doing the evaluation of the objective. We show that this can lead to problems in the optimization process and describe a more principled approach to account for input variables that are integer-valued. We illustrate in both synthetic and a real experiments the utility of our approach, which significantly improves the results of standard BO methods on problems involving integer-valued variables.

Eduardo C. Garrido-Merchán, Daniel Hernández-Lobato

This work presents PESMOC, Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraints, an information-based strategy for the simultaneous optimization of multiple expensive-to-evaluate black-box functions under the presence of several constraints. PESMOC can hence be used to solve a wide range of optimization problems. Iteratively, PESMOC chooses an input location on which to evaluate the objective functions and the constraints so as to maximally reduce the entropy of the Pareto set of the corresponding optimization problem. The constraints considered in PESMOC are assumed to have similar properties to those of the objective functions in typical Bayesian optimization problems. That is, they do not have a known expression (which prevents gradient computation), their evaluation is considered to be very expensive, and the resulting observations may be corrupted by noise. These constraints arise in a plethora of expensive black-box optimization problems. We carry out synthetic experiments to illustrate the effectiveness of PESMOC, where we sample both the objectives and the constraints from a Gaussian process prior. The results obtained show that PESMOC is able to provide better recommendations with a smaller number of evaluations than a strategy based on random search.