# Enhancing Logistic Regression Using Neural Networks for Classification in Actuarial Learning
## 1 Introduction  
The past decade has seen an emergence of a range of new technologies and big data analytics which have begun to reshape the landscape of predictive modeling in many enterprises. The highly data-driven insurance sector not only has to cover the risks which usually fall within its remit but it also needs to continuously adapt and evolve to cover new risks which may result from a combination of traditional data with new data collected from various sources called \"_big data_\" which consist of structured, unstructured and semi-structured data. Examples include, but are not limited to, analyzing information from telematics and usage-based insurance for computing insurance premiums, consumer analytics focusing on preferences for certain insurance products, insurance fraud detection, catastrophe modeling, automatic diagnosis of disease from images, crop insurance and weather monitoring and variable annuity products. Therefore, it can be clearly understood why machine learning (ML) approaches are increasingly being considered in actuarial literature research, as can be seen in [1; 2; 3; 4]. The ML methods which have been used so far for efficiently addressing alternative regression and classification problems in insurance include, for example, XGBoost, random forest (RF), decision trees (DTs), naive Bayes, K-nearest neighbor (K-NN) model, AdaBoost (AB) model, stochastic gradient boosting (SGB) model, support vector machine (SVM) model and NNs. Additionally, a very interesting and novel research direction, which follows in this study, is the combined actuarial neural network (CANN) approach of [5; 6]. Under this approach, every classical actuarial model can be embedded in an NN. In particular, the CANN approach can be interpreted as an NN boosting of the classical actuarial regressionmodel. Therefore, the CANN models can be used to address all kinds of regression and classification tasks with the latter being the main research focus of this study. For more details regarding the use of ML methods in insurance, as can be seen, for instance, in Refs. [7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37]. The aim of this paper was to present alternative ways in which the predictive performance of the classical logistic regression model can be enhanced using neural networks (noting that the methods which are explored herein can be used for any binary response model). The neural network boosting of logistic regression allows us to explore missing interactions of nonlinear type that cannot be captured by generalized linear models such as logistic regression. Following the fundamental approach in the ML process, the generic algorithms which we employ for all the classification models we develop split the input data into a learning or training dataset and a test dataset. Subsequently, the proposed models are fitted on the learning dataset and evaluated on the test dataset in order to demonstrate their ability to make more accurate predictions than the logistic regression, which is used as a benchmark. We compare their predictive performance and investigate whether they generalize well to external data, which in this case, are unseen insurance policies concerning a particular classification task. This procedure is in line with the concept of the so-called \"_algorithmic modelling culture_\" according to [38]. In particular, the main contributions we make are as follows:  
* We bring the statistical and ML algorithmic cultures concerning binary classification problems into a more integrated relationship by describing how the logistic regression model can be fitted or \"trained\" by either maximizing its log-likelihood or by minimizing the deviance loss, i.e., the difference between the log-likelihood of the \"optimal\" model and the learned model.