Luiz Otávio V. B. Oliveira

Samantha Biegel, Rafah El-Khatib, Luiz Otavio Vilas Boas Oliveira et al.

The availability of labelled data is one of the main limitations in machine learning. We can alleviate this using weak supervision: a framework that uses expert-defined rules $\boldsymbolλ$ to estimate probabilistic labels $p(y|\boldsymbolλ)$ for the entire data set. These rules, however, are dependent on what experts know about the problem, and hence may be inaccurate or may fail to capture important parts of the problem-space. To mitigate this, we propose Active WeaSuL: an approach that incorporates active learning into weak supervision. In Active WeaSuL, experts do not only define rules, but they also iteratively provide the true label for a small set of points where the weak supervision model is most likely to be mistaken, which are then used to better estimate the probabilistic labels. In this way, the weak labels provide a warm start, which active learning then improves upon. We make two contributions: 1) a modification of the weak supervision loss function, such that the expert-labelled data inform and improve the combination of weak labels; and 2) the maxKL divergence sampling strategy, which determines for which data points expert labelling is most beneficial. Our experiments show that when the budget for labelling data is limited (e.g. $\leq 60$ data points), Active WeaSuL outperforms weak supervision, active learning, and competing strategies, with only a handful of labelled data points. This makes Active WeaSuL ideal for situations where obtaining labelled data is difficult.

Luiz Otavio Vilas Boas Oliveira, Joao Francisco Barreto da Silva Martins, Luis Fernando Miranda et al.

The definition of a concise and effective testbed for Genetic Programming (GP) is a recurrent matter in the research community. This paper takes a new step in this direction, proposing a different approach to measure the quality of the symbolic regression benchmarks quantitatively. The proposed approach is based on meta-learning and uses a set of dataset meta-features---such as the number of examples or output skewness---to describe the datasets. Our idea is to correlate these meta-features with the errors obtained by a GP method. These meta-features define a space of benchmarks that should, ideally, have datasets (points) covering different regions of the space. An initial analysis of 63 datasets showed that current benchmarks are concentrated in a small region of this benchmark space. We also found out that number of instances and output skewness are the most relevant meta-features to GP output error. Both conclusions can help define which datasets should compose an effective testbed for symbolic regression methods.

Joao Francisco B. S. Martins, Luiz Otavio V. B. Oliveira, Luis F. Miranda et al.

Advances in Geometric Semantic Genetic Programming (GSGP) have shown that this variant of Genetic Programming (GP) reaches better results than its predecessor for supervised machine learning problems, particularly in the task of symbolic regression. However, by construction, the geometric semantic crossover operator generates individuals that grow exponentially with the number of generations, resulting in solutions with limited use. This paper presents a new method for individual simplification named GSGP with Reduced trees (GSGP-Red). GSGP-Red works by expanding the functions generated by the geometric semantic operators. The resulting expanded function is guaranteed to be a linear combination that, in a second step, has its repeated structures and respective coefficients aggregated. Experiments in 12 real-world datasets show that it is not only possible to create smaller and completely equivalent individuals in competitive computational time, but also to reduce the number of nodes composing them by 58 orders of magnitude, on average.

Luis F. Miranda, Luiz Otavio V. B. Oliveira, Joao Francisco B. S. Martins et al.

Noise is a consequence of acquiring and pre-processing data from the environment, and shows fluctuations from different sources---e.g., from sensors, signal processing technology or even human error. As a machine learning technique, Genetic Programming (GP) is not immune to this problem, which the field has frequently addressed. Recently, Geometric Semantic Genetic Programming (GSGP), a semantic-aware branch of GP, has shown robustness and high generalization capability. Researchers believe these characteristics may be associated with a lower sensibility to noisy data. However, there is no systematic study on this matter. This paper performs a deep analysis of the GSGP performance over the presence of noise. Using 15 synthetic datasets where noise can be controlled, we added different ratios of noise to the data and compared the results obtained with those of a canonical GP. The results show that, as we increase the percentage of noisy instances, the generalization performance degradation is more pronounced in GSGP than GP. However, in general, GSGP is more robust to noise than GP in the presence of up to 10% of noise, and presents no statistical difference for values higher than that in the test bed.