In this work, we aimed at forecasting the number of SARS-CoV-2 hospitalized patients at 14 days to help anticipate the bed requirements of a large scale hospital using public data and electronic health records data. Previous attempts led to mitigated performance in this high-dimension setting; we introduce a novel approach to time series forecasting by providing an alternative to conventional methods to deal with high number of potential features of interest (409 predictors). We integrate Reservoir Computing (RC) with feature selection using a genetic algorithm (GA) to gather optimal non-linear combinations of inputs to improve prediction in sample-efficient context. We illustrate that the RC-GA combination exhibits excellent performance in forecasting SARS-CoV-2 hospitalizations. This approach outperformed the use of RC alone and other conventional methods: LSTM, Transformers, Elastic-Net, XGBoost. Notably, this work marks the pioneering use of RC (along with GA) in the realm of short and high-dimensional time series, positioning it as a competitive and innovative approach in comparison to standard methods.

Proposed early in the 90ies, the detrended fluctuation analysis (DFA) can be used to estimate the Hurst exponent and has been proven relevant in various applications, from economics to biomedical. For the last years, variants have been proposed. They differ in the way to estimate the trend of the centered integrated signal. In this paper, we recall the main principles of some of these methods, provide explanations on the behaviours of the algorithms and analyze the relevance of new variants based on the Savitzky-Golay filter, also known as the LOESS approach, and the LOWESS. They bridge the gap between the DFA and the detrending moving average (DMA). We hence show that the LOESS-based method is a generalization of the DMA.

Machine Learning (ML) has now become an important and ubiquitous tool in science and engineering, with successful applications in many real-world domains. However, there are still areas in need of improvement, and problems that are still considered difficult with off-the-shelf methods. One such problem is Multi Target Regression (MTR), where the target variable is a multidimensional tuple instead of a scalar value. In this work, we propose a more difficult variant of this problem which we call Unlabeled MTR (uMTR), where the structure of the target space is not given as part of the training data. This version of the problem lies at the intersection of MTR and clustering, an unexplored problem type. Moreover, this work proposes a solution method for uMTR, a hybrid algorithm based on Genetic Programming and RANdom SAmple Consensus (RANSAC). Using a set of benchmark problems, we are able to show that this approach can effectively solve the uMTR problem.

Genetic programming (GP) is an evolutionary computation paradigm for automatic program induction. GP has produced impressive results but it still needs to overcome some practical limitations, particularly its high computational cost, overfitting and excessive code growth. Recently, many researchers have proposed fitness-case sampling methods to overcome some of these problems, with mixed results in several limited tests. This paper presents an extensive comparative study of four fitness-case sampling methods, namely: Interleaved Sampling, Random Interleaved Sampling, Lexicase Selection and Keep-Worst Interleaved Sampling. The algorithms are compared on 11 symbolic regression problems and 11 supervised classification problems, using 10 synthetic benchmarks and 12 real-world data-sets. They are evaluated based on test performance, overfitting and average program size, comparing them with a standard GP search. Comparisons are carried out using non-parametric multigroup tests and post hoc pairwise statistical tests. The experimental results suggest that fitness-case sampling methods are particularly useful for difficult real-world symbolic regression problems, improving performance, reducing overfitting and limiting code growth. On the other hand, it seems that fitness-case sampling cannot improve upon GP performance when considering supervised binary classification.

Since its introduction, Geometric Semantic Genetic Programming (GSGP) has aroused the interest of numerous researchers and several studies have demonstrated that GSGP is able to effectively optimize training data by means of small variation steps, that also have the effect of limiting overfitting. In order to speed up the search process, in this paper we propose a system that integrates a local search strategy into GSGP (called GSGP-LS). Furthermore, we present a hybrid approach, that combines GSGP and GSGP-LS, aimed at exploiting both the optimization speed of GSGP-LS and the ability to limit overfitting of GSGP. The experimental results we present, performed on a set of complex real-life applications, show that GSGP-LS achieves the best training fitness while converging very quickly, but severely overfits. On the other hand, GSGP converges slowly relative to the other methods, but is basically not affected by overfitting. The best overall results were achieved with the hybrid approach, allowing the search to converge quickly, while also exhibiting a noteworthy ability to limit overfitting. These results are encouraging, and suggest that future GSGP algorithms should focus on finding the correct balance between the greedy optimization of a local search strategy and the more robust geometric semantic operators.

In standard genetic programming (GP), a search is performed over a syntax space defined by the set of primitives, looking for the best expressions that minimize a cost function based on a training set. However, most GP systems lack a numerical optimization method to fine tune the implicit parameters of each candidate solution. Instead, GP relies on more exploratory search operators at the syntax level. This work proposes a memetic GP, tailored for binary classification problems. In the proposed method, each node in a GP tree is weighted by a real-valued parameter, which is then numerically optimized using a continuous transfer function and the Trust Region algorithm is used as a local search method. Experimental results show that potential classifiers produced by GP are improved by the local searcher, and hence the overall search is improved achieving significant performance gains, that are competitive with state-of-the-art methods on well-known benchmarks.

The objective of the present work is to develop a method able to automatically determine mental states of vigilance; i.e., a person's state of alertness. Such a task is relevant to diverse domains, where a person is expected or required to be in a particular state. For instance, pilots or medical staffs are expected to be in a highly alert state, and this method could help to detect possible problems. In this paper, an approach is developed to predict the state of alertness (“normal” or “relaxed”) from the study of electroencephalographic signals (EEG) collected with a limited number of electrodes. The EEG of 58 participants in the two alertness states (116 records) were collected via a cap with 58 electrodes. After a data validation step, 19 subjects were retained for further analysis. A genetic algorithm was used to select an optimal subset of electrodes. Common spatial pattern (CSP) coupled to linear discriminant analysis (LDA) was used to build a decision rule and thus predict the alertness of the participants. Different subset sizes were investigated and the best result was obtained by considering 9 electrodes (correct classification rate of 73.68%).

During the development of applied systems, an important problem that must be addressed is that of choosing the correct tools for a given domain or scenario. This general task has been addressed by the genetic programming (GP) community by attempting to determine the intrinsic difficulty that a problem poses for a GP search. This paper presents an approach to predict the performance of GP applied to data classification, one of the most common problems in computer science. The novelty of the proposal is to extract statistical descriptors and complexity descriptors of the problem data, and from these estimate the expected performance of a GP classifier. We derive two types of predictive models: linear regression models and symbolic regression models evolved with GP. The experimental results show that both approaches provide good estimates of classifier performance, using synthetic and real-world problems for validation. In conclusion, this paper shows that it is possible to accurately predict the expected performance of a GP classifier using a set of descriptors that characterize the problem data.

Local image features can provide the basis for robust and invariant recognition of objects and scenes. Therefore, compact and distinctive representations of local shape and appearance has become invaluable in modern computer vision. In this work, we study a local descriptor based on the Hölder exponent, a measure of signal regularity. The proposal is to find an optimal number of dimensions for the descriptor using a genetic algorithm (GA). To guide the GA search, fitness is computed based on the performance of the descriptor when applied to standard region matching problems. This criterion is quantified using the F-Measure, derived from recall and precision analysis. Results show that it is possible to reduce the size of the canonical Hölder descriptor without degrading the quality of its performance. In fact, the best descriptor found through the GA search is nearly 70% smaller and achieves similar performance on standard tests.

This paper presents a Genetic Programming (GP) approach to synthesize estimators for the pointwise Hölder exponent in 2D signals. It is known that irregularities and singularities are the most salient and informative parts of a signal. Hence, explicitly measuring these variations can be important in various domains of signal processing. The pointwise Hölder exponent provides a characterization of these types of features. However, current methods for estimation cannot be considered to be optimal in any sense. Therefore, the goal of this work is to automatically synthesize operators that provide an estimation for the Hölderian regularity in a 2D signal. This goal is posed as an optimization problem in which we attempt to minimize the error between a prescribed regularity and the estimated regularity given by an image operator. The search for optimal estimators is then carried out using a GP algorithm. Experiments confirm that the GP-operators produce a good estimation of the Hölder exponent in images of multifractional Brownian motions. In fact, the evolved estimators significantly outperform a traditional method by as much as one order of magnitude. These results provide further empirical evidence that GP can solve difficult problems of applied mathematics.

We consider the problem of interpolating a signal in Rdknown at a given resolution. In our approach, the signal is assumed to belong to a given (large) class of signals. This class is characterised by local regularity constraints, that can be described by a certain inter-scale behaviour of their wavelet coefficients. These constraints allow to predict the scale n coefficient from the ones at lower scales. We investigate some properties of this interpolation scheme. In particular, we give the Holder regularity of the refined signal, and present some asymptotic properties of the method. Finally, numerical experiments are presented. Both the theoretical and numerical results show that our regularity-based scheme allows to obtain good quality interpolated images

This work presents an approach for signal/image denoising in a semi-parametric frame. Our model is a wavelet-based one, which essentially assumes a minimal local regularity. This assumption translates into constraints on the multifractal spectrum of the signals. Such constraints are in turn used in a Bayesian framework to estimate the wavelet coefficients of the original signal from the noisy ones. Our scheme is well adapted to the processing of irregular signals, such as (multi-)fractal ones, and is potentially useful for the processing of e.g. turbulence, bio-medical or seismic data.

We present an approach for image denoising based on the analysis of the local Holder regularity. The method takes the point of view that denoising may be performed by increasing the Holder regularity at each point. Under the assumption that the noise is additive and white, our procedure is asymptotically minimax, provided the original signal belongs to a ball in some Besov space. Such a scheme is well adapted to the case where the image to be recovered is itself very irregular, e.g. nowhere differentiable with rapidly varying local regularity. The method is implemented through a wavelet analysis. We show an application to SAR image denoising where this technique yields good results compared to other algorithms.