Mohammad Nazmul Haque

Pablo Moscato, Hugh Craig, Gabriel Egan et al.

The date of the first performance of a play of Shakespeare's time must usually be guessed with reference to multiple indirect external sources, or to some aspect of the content or style of the play. Identifying these dates is important to literary history and to accounts of developing authorial styles, such as Shakespeare's. In this study, we took a set of Shakespeare-era plays (181 plays from the period 1585--1610), added the best-guess dates for them from a standard reference work as metadata, and calculated a set of probabilities of individual words in these samples. We applied 11 regression methods to predict the dates of the plays at an 80/20 training/test split. We withdrew one play at a time, used the best-guess date metadata with the probabilities and weightings to infer its date, and thus built a model of date-probabilities interaction. We introduced a memetic algorithm-based Continued Fraction Regression (CFR) which delivered models using a small number of variables, leading to an interpretable model and reduced dimensionality. An in-depth analysis of the most commonly occurring 20 words in the CFR models in 100 independent runs helps explain the trends in linguistic and stylistic terms. The analysis with the subset of words revealed an interesting correlation of signature words with the Shakespeare-era play's genre.

Pablo Moscato, Mohammad Nazmul Haque, Kevin Huang et al.

In the field of Artificial Intelligence (AI) and Machine Learning (ML), the approximation of unknown target functions $y=f(\mathbf{x})$ using limited instances $S={(\mathbf{x^{(i)}},y^{(i)})}$, where $\mathbf{x^{(i)}} \in D$ and $D$ represents the domain of interest, is a common objective. We refer to $S$ as the training set and aim to identify a low-complexity mathematical model that can effectively approximate this target function for new instances $\mathbf{x}$. Consequently, the model's generalization ability is evaluated on a separate set $T=\{\mathbf{x^{(j)}}\} \subset D$, where $T \neq S$, frequently with $T \cap S = \emptyset$, to assess its performance beyond the training set. However, certain applications require accurate approximation not only within the original domain $D$ but also in an extended domain $D'$ that encompasses $D$. This becomes particularly relevant in scenarios involving the design of new structures, where minimizing errors in approximations is crucial. For example, when developing new materials through data-driven approaches, the AI/ML system can provide valuable insights to guide the design process by serving as a surrogate function. Consequently, the learned model can be employed to facilitate the design of new laboratory experiments. In this paper, we propose a method for multivariate regression based on iterative fitting of a continued fraction, incorporating additive spline models. We compare the performance of our method with established techniques, including AdaBoost, Kernel Ridge, Linear Regression, Lasso Lars, Linear Support Vector Regression, Multi-Layer Perceptrons, Random Forests, Stochastic Gradient Descent, and XGBoost. To evaluate these methods, we focus on an important problem in the field: predicting the critical temperature of superconductors based on physical-chemical characteristics.

Pablo Moscato, Haoyuan Sun, Mohammad Nazmul Haque

We present an approach for regression problems that employs analytic continued fractions as a novel representation. Comparative computational results using a memetic algorithm are reported in this work. Our experiments included fifteen other different machine learning approaches including five genetic programming methods for symbolic regression and ten machine learning methods. The comparison on training and test generalization was performed using 94 datasets of the Penn State Machine Learning Benchmark. The statistical tests showed that the generalization results using analytic continued fractions provides a powerful and interesting new alternative in the quest for compact and interpretable mathematical models for artificial intelligence.