Comparing Ridge and Logistic Regression with Neural Networks

This research paper presents a comparative analysis of neural networks, logistic regression, and Ridge methods, aiming to assess their respective advantages and limitations. The study involves conducting four analyses on two distinct datasets: two for classification tasks utilizing the MNIST dataset and two for regression tasks based on data derived from the Franke function. The classification analyses employ the widely used MNIST dataset, where the algorithms are trained to classify handwritten digits accurately. In contrast, the regression analyses utilize the Franke function dataset, which generates a two-dimensional surface with smoothly varying peaks and valleys, serving as a benchmark for evaluating the performance of regression models. The findings reveal that neural networks, despite their potential to produce results comparable to more established techniques, present certain challenges in terms of setup and optimization. The complexity of the neural network models used in this study further contributes to the difficulty in interpreting the generated results. These intricacies highlight the need for careful consideration and expertise when employing neural networks for classification and regression tasks. By providing additional information on the concepts of classification and regression, as well as clarifying the datasets used (MNIST and Franke function), we offer a more comprehensive overview of neural networks, logistic regression, and Ridge.