Fabrício Olivetti de França

F. O. de Franca, M. Virgolin, M. Kommenda et al. · cambridge, meta-ai

Symbolic regression searches for analytic expressions that accurately describe studied phenomena. The main attraction of this approach is that it returns an interpretable model that can be insightful to users. Historically, the majority of algorithms for symbolic regression have been based on evolutionary algorithms. However, there has been a recent surge of new proposals that instead utilize approaches such as enumeration algorithms, mixed linear integer programming, neural networks, and Bayesian optimization. In order to assess how well these new approaches behave on a set of common challenges often faced in real-world data, we hosted a competition at the 2022 Genetic and Evolutionary Computation Conference consisting of different synthetic and real-world datasets which were blind to entrants. For the real-world track, we assessed interpretability in a realistic way by using a domain expert to judge the trustworthiness of candidate models.We present an in-depth analysis of the results obtained in this competition, discuss current challenges of symbolic regression algorithms and highlight possible improvements for future competitions.

Gabriel Kronberger, Fabricio Olivetti de Franca, Harry Desmond et al.

We analyse the search behaviour of genetic programming for symbolic regression in practically relevant but limited settings, allowing exhaustive enumeration of all solutions. This enables us to quantify the success probability of finding the best possible expressions, and to compare the search efficiency of genetic programming to random search in the space of semantically unique expressions. This analysis is made possible by improved algorithms for equality saturation, which we use to improve the Exhaustive Symbolic Regression algorithm; this produces the set of semantically unique expression structures, orders of magnitude smaller than the full symbolic regression search space. We compare the efficiency of random search in the set of unique expressions and genetic programming. For our experiments we use two real-world datasets where symbolic regression has been used to produce well-fitting univariate expressions: the Nikuradse dataset of flow in rough pipes and the Radial Acceleration Relation of galaxy dynamics. The results show that genetic programming in such limited settings explores only a small fraction of all unique expressions, and evaluates expressions repeatedly that are congruent to already visited expressions.

Fabricio Olivetti de Franca

Symbolic Regression searches for a function form that approximates a dataset often using Genetic Programming. Since there is usually no restriction to what form the function can have, Genetic Programming may return a hard to understand model due to non-linear function chaining or long expressions. A novel representation called Interaction-Transformation was recently proposed to alleviate this problem. In this representation, the function form is restricted to an affine combination of terms generated as the application of a single univariate function to the interaction of selected variables. This representation obtained competing solutions on standard benchmarks. Despite the initial success, a broader set of benchmarking functions revealed the limitations of the constrained representation. In this paper we propose an extension to this representation, called Transformation-Interaction-Rational representation that defines a new function form as the rational of two Interaction-Transformation functions. Additionally, the target variable can also be transformed with an univariate function. The main goal is to improve the approximation power while still constraining the overall complexity of the expression. We tested this representation with a standard Genetic Programming with crossover and mutation. The results show a great improvement when compared to its predecessor and a state-of-the-art performance for a large benchmark.

Fabricio Olivetti de Franca, Gabriel Kronberger

Symbolic regression is a nonlinear regression method which is commonly performed by an evolutionary computation method such as genetic programming. Quantification of uncertainty of regression models is important for the interpretation of models and for decision making. The linear approximation and so-called likelihood profiles are well-known possibilities for the calculation of confidence and prediction intervals for nonlinear regression models. These simple and effective techniques have been completely ignored so far in the genetic programming literature. In this work we describe the calculation of likelihood profiles in details and also provide some illustrative examples with models created with three different symbolic regression algorithms on two different datasets. The examples highlight the importance of the likelihood profiles to understand the limitations of symbolic regression models and to help the user taking an informed post-prediction decision.

Gabriel Kronberger, Fabricio Olivetti de Franca, Deaglan J. Bartlett et al.

Symbolic regression with genetic programming (GPSR) may suffer from overfitting and structural bloat, especially when noise is present. In this paper we evaluate description length (DL) and fractional Bayes factor (FBF) criteria as principled, data-efficient alternatives to heuristics for selecting compact expressions that generalise well. We implement DL using a Fisher-information-based parameter encoding and compare it to AIC and BIC across multiple datasets, including noisy synthetic benchmarks and real-world regression problems. We study three search/selection strategies: (i) multi-objective search for accuracy and program length followed by DL/FBF selection; (ii) multi-objective search using DL directly as an objective; and (iii) single-objective optimisation with DL/FBF as the fitness. Across datasets we find that DL/FBF post-selection improves test performance compared to AIC/BIC baseline and that BIC in combination with the same function complexity penalty from DL/FBF produces similar results. In contrast, using DL/FBF directly as a fitness function in single-objective GPSR frequently induces premature convergence to overly simple models. We conclude with practical guidance for using DL/FBF as robust model-selection tools in genetic programming workflows.

Ali Soltani, Gabriel Kronberger, Fabricio Olivetti de Franca et al.

Effective model selection is critical in symbolic regression (SR) to identify mathematical expressions that balance accuracy and complexity, and have low expected error on unseen data. Many modern implementations of genetic programming (GP) for SR generate a set of Pareto optimal candidate solutions, but reliable automatic selection of solutions that generalize well remains an open issue. Current literature offers various information-theoretic and Bayesian approaches, yet comprehensive comparisons of their performance across different data regimes are limited. This study presents a systematic empirical comparison of widely used selection criteria: the Akaike information criterion (AIC), the corrected AIC (AICc), the Bayesian information criterion (BIC), minimum description length (MDL), as well as Efron's bootstrap estimate for the in-sample prediction error on seven synthetic datasets with Gaussian noise. We rank candidate expressions generated by perturbing ground-truth functions to assess generalization error and selection probability of the ground-truth expression. Our findings reveal that MDL consistently identifies models with the lowest test error and the shortest length across most datasets. While no single criterion dominates all results, MDL and BIC produced the highest probability of selecting the ground-truth expressions.

Matheus Campos Fernandes, Fabrício Olivetti de França, Emilio Francesquini

Program synthesis is the process of generating a computer program following a set of specifications, which can be a high-level description of the problem and/or a set of input-output examples. The synthesis can be modeled as a search problem in which the search space is the set of all the programs valid under a grammar. As the search space is vast, brute force is usually not viable and search heuristics, such as genetic programming, also have difficulty navigating it without any guidance. In this paper we present HOTGP, a new genetic programming algorithm that synthesizes pure, typed, and functional programs. HOTGP leverages the knowledge provided by the rich data-types associated with the specification and the built-in grammar to constrain the search space and improve the performance of the synthesis. The grammar is based on Haskell's standard base library (the synthesized code can be directly compiled using any standard Haskell compiler) and includes support for higher-order functions, $λ$-functions, and parametric polymorphism. Experimental results show that, when compared to $6$ state-of-the-art algorithms using a standard set of benchmarks, HOTGP is competitive and capable of synthesizing the correct programs more frequently than any other of the evaluated algorithms.

William La Cava, Patryk Orzechowski, Bogdan Burlacu et al.

Many promising approaches to symbolic regression have been presented in recent years, yet progress in the field continues to suffer from a lack of uniform, robust, and transparent benchmarking standards. In this paper, we address this shortcoming by introducing an open-source, reproducible benchmarking platform for symbolic regression. We assess 14 symbolic regression methods and 7 machine learning methods on a set of 252 diverse regression problems. Our assessment includes both real-world datasets with no known model form as well as ground-truth benchmark problems, including physics equations and systems of ordinary differential equations. For the real-world datasets, we benchmark the ability of each method to learn models with low error and low complexity relative to state-of-the-art machine learning methods. For the synthetic problems, we assess each method's ability to find exact solutions in the presence of varying levels of noise. Under these controlled experiments, we conclude that the best performing methods for real-world regression combine genetic algorithms with parameter estimation and/or semantic search drivers. When tasked with recovering exact equations in the presence of noise, we find that deep learning and genetic algorithm-based approaches perform similarly. We provide a detailed guide to reproducing this experiment and contributing new methods, and encourage other researchers to collaborate with us on a common and living symbolic regression benchmark.

Fabricio Olivetti de Franca, Gabriel Kronberger

In Symbolic Regression (SR), Genetic Programming (GP) is a popular search algorithm that delivers state-of-the-art results in term of accuracy. Its success relies on the concept of neutrality, which induces large plateaus that the search can safely navigate to more promising regions. Navigating these plateaus, while necessary, requires the computation of redundant expressions, up to 60% of the total number of evaluation, as noted in a recent study. The equality graph (e-graph) structure can compactly store and group equivalent expressions enabling us to verify if a given expression and their variations were already visited by the search, thus enabling us to avoid unnecessary computation. We propose a new search algorithm for symbolic regression called SymRegg that revolves around the e-graph structure following simple steps: perturb solutions sampled from a selection of expressions stored in the e-graph, if it generates an unvisited expression, insert it into the e-graph and generates its equivalent forms. We show that SymRegg is capable of improving the efficiency of the search, maintaining consistently accurate results across different datasets while requiring a choice of a minimalist set of hyperparameters.

Guilherme Seidyo Imai Aldeia, Fabricio Olivetti de Franca

In some situations, the interpretability of the machine learning models plays a role as important as the model accuracy. Interpretability comes from the need to trust the prediction model, verify some of its properties, or even enforce them to improve fairness. Many model-agnostic explanatory methods exists to provide explanations for black-box models. In the regression task, the practitioner can use white-boxes or gray-boxes models to achieve more interpretable results, which is the case of symbolic regression. When using an explanatory method, and since interpretability lacks a rigorous definition, there is a need to evaluate and compare the quality and different explainers. This paper proposes a benchmark scheme to evaluate explanatory methods to explain regression models, mainly symbolic regression models. Experiments were performed using 100 physics equations with different interpretable and non-interpretable regression methods and popular explanation methods, evaluating the performance of the explainers performance with several explanation measures. In addition, we further analyzed four benchmarks from the GP community. The results have shown that Symbolic Regression models can be an interesting alternative to white-box and black-box models that is capable of returning accurate models with appropriate explanations. Regarding the explainers, we observed that Partial Effects and SHAP were the most robust explanation models, with Integrated Gradients being unstable only with tree-based models. This benchmark is publicly available for further experiments.

Fabricio Olivetti de Franca, Gabriel Kronberger

The search for symbolic regression models with genetic programming (GP) has a tendency of revisiting expressions in their original or equivalent forms. Repeatedly evaluating equivalent expressions is inefficient, as it does not immediately lead to better solutions. However, evolutionary algorithms require diversity and should allow the accumulation of inactive building blocks that can play an important role at a later point. The equality graph is a data structure capable of compactly storing expressions and their equivalent forms allowing an efficient verification of whether an expression has been visited in any of their stored equivalent forms. We exploit the e-graph to adapt the subtree operators to reduce the chances of revisiting expressions. Our adaptation, called eggp, stores every visited expression in the e-graph, allowing us to filter out from the available selection of subtrees all the combinations that would create already visited expressions. Results show that, for small expressions, this approach improves the performance of a simple GP algorithm to compete with PySR and Operon without increasing computational cost. As a highlight, eggp was capable of reliably delivering short and at the same time accurate models for a selected set of benchmarks from SRBench and a set of real-world datasets.

Fabricio Olivetti de Franca

The Transformation-Interaction-Rational is a representation for symbolic regression that limits the search space of functions to the ratio of two nonlinear functions each one defined as the linear regression of transformed variables. This representation has the main objective to bias the search towards simpler expressions while keeping the approximation power of standard approaches. The performance of using Genetic Programming with this representation was substantially better than with its predecessor (Interaction-Transformation) and ranked close to the state-of-the-art on a contemporary Symbolic Regression benchmark. On a closer look at these results, we observed that the performance could be further improved with an additional selective pressure for smaller expressions when the dataset contains just a few data points. The introduction of a penalization term applied to the fitness measure improved the results on these smaller datasets. One problem with this approach is that it introduces two additional hyperparameters: i) a criteria to when the penalization should be activated and, ii) the amount of penalization to the fitness function. In this paper, we extend Transformation-Interaction-Rational to support multi-objective optimization, specifically the NSGA-II algorithm, and apply that to the same benchmark. A detailed analysis of the results show that the use of multi-objective optimization benefits the overall performance on a subset of the benchmarks while keeping the results similar to the single-objective approach on the remainder of the datasets. Specifically to the small datasets, we observe a small (and statistically insignificant) improvement of the results suggesting that further strategies must be explored.

Guilherme S. Imai Aldeia, Hengzhe Zhang, Geoffrey Bomarito et al.

Symbolic Regression (SR) is a powerful technique for discovering interpretable mathematical expressions. However, benchmarking SR methods remains challenging due to the diversity of algorithms, datasets, and evaluation criteria. In this work, we present an updated version of SRBench. Our benchmark expands the previous one by nearly doubling the number of evaluated methods, refining evaluation metrics, and using improved visualizations of the results to understand the performances. Additionally, we analyze trade-offs between model complexity, accuracy, and energy consumption. Our results show that no single algorithm dominates across all datasets. We propose a call for action from SR community in maintaining and evolving SRBench as a living benchmark that reflects the state-of-the-art in symbolic regression, by standardizing hyperparameter tuning, execution constraints, and computational resource allocation. We also propose deprecation criteria to maintain the benchmark's relevance and discuss best practices for improving SR algorithms, such as adaptive hyperparameter tuning and energy-efficient implementations.

Etienne Russeil, Fabrício Olivetti de França, Konstantin Malanchev et al.

Symbolic regression (SR) searches for analytical expressions representing the relationship between a set of explanatory and response variables. Current SR methods assume a single dataset extracted from a single experiment. Nevertheless, frequently, the researcher is confronted with multiple sets of results obtained from experiments conducted with different setups. Traditional SR methods may fail to find the underlying expression since the parameters of each experiment can be different. In this work we present Multi-View Symbolic Regression (MvSR), which takes into account multiple datasets simultaneously, mimicking experimental environments, and outputs a general parametric solution. This approach fits the evaluated expression to each independent dataset and returns a parametric family of functions f(x; theta) simultaneously capable of accurately fitting all datasets. We demonstrate the effectiveness of MvSR using data generated from known expressions, as well as real-world data from astronomy, chemistry and economy, for which an a priori analytical expression is not available. Results show that MvSR obtains the correct expression more frequently and is robust to hyperparameters change. In real-world data, it is able to grasp the group behavior, recovering known expressions from the literature as well as promising alternatives, thus enabling the use of SR to a large range of experimental scenarios.

Julia Reuter, Fabricio Olivetti de Franca

Symbolic regression (SR) is a class of methods that systematically explore the space of mathematical functions to discover models that accurately capture the underlying relationships in a dataset. Despite recent advances in the field, a lack of support for uncertainty quantification (UQ) limits its adoption in real-world decision processes. In regression analysis, UQ provides important information about the model reliability, which can both help to avoid overfitting by accounting for uncertainty in the data, and provide insights for decision-making. This survey is the first to clearly address this issue, with the objective of introducing essential UQ concepts and reviewing the current literature on UQ in SR, which can be broadly organized into three research directions: frequentist, Bayesian, and model selection. Despite its importance, UQ in SR is still underexplored, which motivates further research into reliable UQ methods for SR.

Fabricio Olivetti de Franca, Gabriel Kronberger

Regression analysis is used for prediction and to understand the effect of independent variables on dependent variables. Symbolic regression (SR) automates the search for non-linear regression models, delivering a set of hypotheses that balances accuracy with the possibility to understand the phenomena. Many SR implementations return a Pareto front allowing the choice of the best trade-off. However, this hides alternatives that are close to non-domination, limiting these choices. Equality graphs (e-graphs) allow to represent large sets of expressions compactly by efficiently handling duplicated parts occurring in multiple expressions. E-graphs allow to store and query all SR solution candidates visited in one or multiple GP runs efficiently and open the possibility to analyse much larger sets of SR solution candidates. We introduce rEGGression, a tool using e-graphs to enable the exploration of a large set of symbolic expressions which provides querying, filtering, and pattern matching features creating an interactive experience to gain insights about SR models. The main highlight is its focus in the exploration of the building blocks found during the search that can help the experts to find insights about the studied phenomena.This is possible by exploiting the pattern matching capability of the e-graph data structure.

Guilherme Seidyo Imai Aldeia, Fabricio Olivetti de Franca, William G. La Cava

Symbolic regression (SR) searches for parametric models that accurately fit a dataset, prioritizing simplicity and interpretability. Despite this secondary objective, studies point out that the models are often overly complex due to redundant operations, introns, and bloat that arise during the iterative process, and can hinder the search with repeated exploration of bloated segments. Applying a fast heuristic algebraic simplification may not fully simplify the expression and exact methods can be infeasible depending on size or complexity of the expressions. We propose a novel agnostic simplification and bloat control for SR employing an efficient memoization with locality-sensitive hashing (LHS). The idea is that expressions and their sub-expressions traversed during the iterative simplification process are stored in a dictionary using LHS, enabling efficient retrieval of similar structures. We iterate through the expression, replacing subtrees with others of same hash if they result in a smaller expression. Empirical results shows that applying this simplification during evolution performs equal or better than without simplification in minimization of error, significantly reducing the number of nonlinear functions. This technique can learn simplification rules that work in general or for a specific problem, and improves convergence while reducing model complexity.

Etienne Russeil, Fabrício Olivetti de França, Konstantin Malanchev et al.

Describing the world behavior through mathematical functions help scientists to achieve a better understanding of the inner mechanisms of different phenomena. Traditionally, this is done by deriving new equations from first principles and careful observations. A modern alternative is to automate part of this process with symbolic regression (SR). The SR algorithms search for a function that adequately fits the observed data while trying to enforce sparsity, in the hopes of generating an interpretable equation. A particularly interesting extension to these algorithms is the Multi-view Symbolic Regression (MvSR). It searches for a parametric function capable of describing multiple datasets generated by the same phenomena, which helps to mitigate the common problems of overfitting and data scarcity. Recently, multiple implementations added support to MvSR with small differences between them. In this paper, we test and compare MvSR as supported in Operon, PySR, phy-SO, and eggp, in different real-world datasets. We show that they all often achieve good accuracy while proposing solutions with only few free parameters. However, we find that certain features enable a more frequent generation of better models. We conclude by providing guidelines for future MvSR developments.

Roman Kalkreuth, Fabricio Olivetti de França, Julian Dierkes et al.

Over the years, genetic programming (GP) has evolved, with many proposed variations, especially in how they represent a solution. Being essentially a program synthesis algorithm, it is capable of tackling multiple problem domains. Current benchmarking initiatives are fragmented, as the different representations are not compared with each other and their performance is not measured across the different domains. In this work, we propose a unified framework, dubbed TinyverseGP (inspired by tinyGP), which provides support to multiple representations and problem domains, including symbolic regression, logic synthesis and policy search.

Christian Haider, Fabricio Olivetti de França, Bogdan Burlacu et al.

We describe and analyze algorithms for shape-constrained symbolic regression, which allows the inclusion of prior knowledge about the shape of the regression function. This is relevant in many areas of engineering -- in particular whenever a data-driven model obtained from measurements must have certain properties (e.g. positivity, monotonicity or convexity/concavity). We implement shape constraints using a soft-penalty approach which uses multi-objective algorithms to minimize constraint violations and training error. We use the non-dominated sorting genetic algorithm (NSGA-II) as well as the multi-objective evolutionary algorithm based on decomposition (MOEA/D). We use a set of models from physics textbooks to test the algorithms and compare against earlier results with single-objective algorithms. The results show that all algorithms are able to find models which conform to all shape constraints. Using shape constraints helps to improve extrapolation behavior of the models.

Gabriel Kronberger, Fabricio Olivetti de França, Bogdan Burlacu et al.

We investigate the addition of constraints on the function image and its derivatives for the incorporation of prior knowledge in symbolic regression. The approach is called shape-constrained symbolic regression and allows us to enforce e.g. monotonicity of the function over selected inputs. The aim is to find models which conform to expected behaviour and which have improved extrapolation capabilities. We demonstrate the feasibility of the idea and propose and compare two evolutionary algorithms for shape-constrained symbolic regression: i) an extension of tree-based genetic programming which discards infeasible solutions in the selection step, and ii) a two population evolutionary algorithm that separates the feasible from the infeasible solutions. In both algorithms we use interval arithmetic to approximate bounds for models and their partial derivatives. The algorithms are tested on a set of 19 synthetic and four real-world regression problems. Both algorithms are able to identify models which conform to shape constraints which is not the case for the unmodified symbolic regression algorithms. However, the predictive accuracy of models with constraints is worse on the training set and the test set. Shape-constrained polynomial regression produces the best results for the test set but also significantly larger models.

Terry Ruas, Charles Henrique Porto Ferreira, William Grosky et al.

The relationship between words in a sentence often tells us more about the underlying semantic content of a document than its actual words, individually. In this work, we propose two novel algorithms, called Flexible Lexical Chain II and Fixed Lexical Chain II. These algorithms combine the semantic relations derived from lexical chains, prior knowledge from lexical databases, and the robustness of the distributional hypothesis in word embeddings as building blocks forming a single system. In short, our approach has three main contributions: (i) a set of techniques that fully integrate word embeddings and lexical chains; (ii) a more robust semantic representation that considers the latent relation between words in a document; and (iii) lightweight word embeddings models that can be extended to any natural language task. We intend to assess the knowledge of pre-trained models to evaluate their robustness in the document classification task. The proposed techniques are tested against seven word embeddings algorithms using five different machine learning classifiers over six scenarios in the document classification task. Our results show the integration between lexical chains and word embeddings representations sustain state-of-the-art results, even against more complex systems.

Fabricio Olivetti de Franca, Denis Fantinato, Karine Miras et al.

This paper describes a competition proposal for evolving Intelligent Agents for the game-playing framework called EvoMan. The framework is based on the boss fights of the game called Mega Man II developed by Capcom. For this particular competition, the main goal is to beat all of the eight bosses using a generalist strategy. In other words, the competitors should train the agent to beat a set of the bosses and then the agent will be evaluated by its performance against all eight bosses. At the end of this paper, the competitors are provided with baseline results so that they can have an intuition on how good their results are.

Fabricio Olivetti de Franca, Guilherme Seidyo Imai Aldeia

The Interaction-Transformation (IT) is a new representation for Symbolic Regression that restricts the search space into simpler, but expressive, function forms. This representation has the advantage of creating a smoother search space unlike the space generated by Expression Trees, the common representation used in Genetic Programming. This paper introduces an Evolutionary Algorithm capable of evolving a population of IT expressions supported only by the mutation operator. The results show that this representation is capable of finding better approximations to real-world data sets when compared to traditional approaches and a state-of-the-art Genetic Programming algorithm.

Charles Henrique Porto Ferreira, Debora Maria Rossi de Medeiros, Fabricio Olivetti de França

Text Mining is a field that aims at extracting information from textual data. One of the challenges of such field of study comes from the pre-processing stage in which a vector (and structured) representation should be extracted from unstructured data. The common extraction creates large and sparse vectors representing the importance of each term to a document. As such, this usually leads to the curse-of-dimensionality that plagues most machine learning algorithms. To cope with this issue, in this paper we propose a new supervised feature extraction and reduction algorithm, named DCDistance, that creates features based on the distance between a document to a representative of each class label. As such, the proposed technique can reduce the features set in more than 99% of the original set. Additionally, this algorithm was also capable of improving the classification accuracy over a set of benchmark datasets when compared to traditional and state-of-the-art features selection algorithms.

Fabricio Olivetti de Franca

Symbolic Regression tries to find a mathematical expression that describes the relationship of a set of explanatory variables to a measured variable. The main objective is to find a model that minimizes the error and, optionally, that also minimizes the expression size. A smaller expression can be seen as an interpretable model considered a reliable decision model. This is often performed with Genetic Programming which represents their solution as expression trees. The shortcoming of this algorithm lies on this representation that defines a rugged search space and contains expressions of any size and difficulty. These pose as a challenge to find the optimal solution under computational constraints. This paper introduces a new data structure, called Interaction-Transformation (IT), that constrains the search space in order to exclude a region of larger and more complicated expressions. In order to test this data structure, it was also introduced an heuristic called SymTree. The obtained results show evidence that SymTree are capable of obtaining the optimal solution whenever the target function is within the search space of the IT data structure and competitive results when it is not. Overall, the algorithm found a good compromise between accuracy and simplicity for all the generated models.

Karine da Silva Miras de Araújo, Fabrício Olivetti de França

One of the common artificial intelligence applications in electronic games consists of making an artificial agent learn how to execute some determined task successfully in a game environment. One way to perform this task is through machine learning algorithms capable of learning the sequence of actions required to win in a given game environment. There are several supervised learning techniques able to learn the correct answer for a problem through examples. However, when learning how to play electronic games, the correct answer might only be known by the end of the game, after all the actions were already taken. Thus, not being possible to measure the accuracy of each individual action to be taken at each time step. A way for dealing with this problem is through Neuroevolution, a method which trains Artificial Neural Networks using evolutionary algorithms. In this article, we introduce a framework for testing optimization algorithms with artificial agent controllers in electronic games, called EvoMan, which is inspired in the action-platformer game Mega Man II. The environment can be configured to run in different experiment modes, as single evolution, coevolution and others. To demonstrate some challenges regarding the proposed platform, as initial experiments we applied Neuroevolution using Genetic Algorithms and the NEAT algorithm, in the context of competitively coevolving two distinct agents in this game.

André L. V. Coelho, Fabrício O. de França

Perceptrons are neuronal devices capable of fully discriminating linearly separable classes. Although straightforward to implement and train, their applicability is usually hindered by non-trivial requirements imposed by real-world classification problems. Therefore, several approaches, such as kernel perceptrons, have been conceived to counteract such difficulties. In this paper, we investigate an enhanced perceptron model based on the notion of contrastive biclusters. From this perspective, a good discriminative bicluster comprises a subset of data instances belonging to one class that show high coherence across a subset of features and high differentiation from nearest instances of the other class under the same features (referred to as its contrastive bicluster). Upon each local subspace associated with a pair of contrastive biclusters a perceptron is trained and the model with highest area under the receiver operating characteristic curve (AUC) value is selected as the final classifier. Experiments conducted on a range of data sets, including those related to a difficult biosignal classification problem, show that the proposed variant can be indeed very useful, prevailing in most of the cases upon standard and kernel perceptrons in terms of accuracy and AUC measures.

Fabricio Olivetti de França

Many real-life data are described by categorical attributes without a pre-classification. A common data mining method used to extract information from this type of data is clustering. This method group together the samples from the data that are more similar than all other samples. But, categorical data pose a challenge when extracting information because: the calculation of two objects similarity is usually done by measuring the number of common features, but ignore a possible importance weighting; if the data may be divided differently according to different subsets of the features, the algorithm may find clusters with different meanings from each other, difficulting the post analysis. Data Co-Clustering of categorical data is the technique that tries to find subsets of samples that share a subset of features in common. By doing so, not only a sample may belong to more than one cluster but, the feature selection of each cluster describe its own characteristics. In this paper a novel Co-Clustering technique for categorical data is proposed by using Locality Sensitive Hashing technique in order to preprocess a list of Co-Clusters seeds based on a previous research. Results indicate this technique is capable of finding high quality Co-Clusters in many different categorical data sets and scales linearly with the data set size.

Fabricio Olivetti de Franca, Guilherme Palermo Coelho

Most community detection algorithms from the literature work as optimization tools that minimize a given \textit{fitness function}, while assuming that each node belongs to a single community. Since there is no hard concept of what a community is, most proposed fitness functions focus on a particular definition. As such, these functions do not always lead to partitions that correspond to those observed in practice. This paper proposes a new flexible fitness function that allows the identification of communities with distinct characteristics. Such flexibility was evaluated through the adoption of an immune-inspired optimization algorithm, named cob-aiNet[C], to identify both disjoint and overlapping communities in a set of benchmark networks. The results have shown that the obtained partitions are much closer to the ground-truth than those obtained by the optimization of the modularity function.

Fabricio Olivetti de Franca

Most multimodal optimization algorithms use the so called \textit{niching methods}~\cite{mahfoud1995niching} in order to promote diversity during optimization, while others, like \textit{Artificial Immune Systems}~\cite{de2010conceptual} try to find multiple solutions as its main objective. One of such algorithms, called \textit{dopt-aiNet}~\cite{de2005artificial}, introduced the Line Distance that measures the distance between two solutions regarding their basis of attraction. In this short abstract I propose the use of the Line Distance measure as the main objective-function in order to locate multiple optima at once in a population.

Fabricio Olivetti de Franca

Minhashing is a technique used to estimate the Jaccard Index between two sets by exploiting the probability of collision in a random permutation. In order to speed up the computation, a random permutation can be approximated by using an universal hash function such as the $h_{a,b}$ function proposed by Carter and Wegman. A better estimate of the Jaccard Index can be achieved by using many of these hash functions, created at random. In this paper a new iterative procedure to generate a set of $h_{a,b}$ functions is devised that eliminates the need for a list of random values and avoid the multiplication operation during the calculation. The properties of the generated hash functions remains that of an universal hash function family. This is possible due to the random nature of features occurrence on sparse datasets. Results show that the uniformity of hashing the features is maintaned while obtaining a speed up of up to $1.38$ compared to the traditional approach.