# A Federated Generalized Linear Model for Privacy-Preserving Analysis
## 1 Introduction  
### Federated Learning  
In the past few years, there has been a surge in the amount of potential data available for gathering [1]. Machine learning (ML) and artificial intelligence (AI) have leveraged this and have allowed the development of numerous analytic tools across many different industries, such as healthcare, banking, and manufacturing, among many others [2, 3, 4, 5].  
Due to the inherent complex nature of systems and processes, data are usually fragmented in silos across parties. For example, parties could have collected different data features for the same group of individuals (i.e., vertically partitioned data). Alternatively, parties could have gathered the same features but for a different group of individuals (i.e., horizontally partitioned data) [6]--the latter being the focus of this work.  
In the traditional way of working, data fragmentation is solved by pooling the data from all parties into a single location. In other words, each party generates a copy of its data. Then, these copies are brought together and centralized by a trusted party, which then proceeds with analyzing the data and obtaining a global model. Unfortunately, this centralized approach is undesirable due to several operational, organizational, and political challenges. For example, once a copy of the data is created and is shared outside its point of origin, is very hard to keep control of it. Sometimes, the costs of integrating huge amounts of data scattered across different parties can make centralization infeasible [7]. More importantly, there are increasing privacy and security concerns and requirements that make merging the data in a single point infeasible. Users are more and more concerned that their private data are being used for commercial or political purposes without their consent [8]. Moreover, regulatory bodies all around the world have started implementing laws that regulate responsible data management and use, such as the California ConsumerPrivacy Act (CCPA, 2020) in California, USA and the General Data Protection Regulation (GDPR, 2018) in Europe, among many others ([PERSON] et al., 2018; [PERSON] et al., 2019; [PERSON] et al., 2019).  
Federated learning (FL) has emerged as an alternative paradigm to overcome these shortcomings ([PERSON] et al., 2018). In this approach, the process of generating the global model is distributed among the parties. Instead of sharing their data, the involved parties perform computations on them, generating aggregated statistics (often encrypted) that are then shared to generate the global model. This keeps the original data undisclosed and safe at their original location, greatly reducing the risk of leaking privacy-sensitive information while generating global models that are very close (if not practically identical) to their centralized counterparts ([PERSON] et al., 2018).  
Several ML/AI algorithms have been implemented as their corresponding federated counterparts for analyzing horizontally partitioned data ([PERSON] et al., 2018), such as decision trees ([PERSON] et al., 2018), support vector machines ([PERSON] et al., 2018), hierarchical training ([PERSON] et al., 2018), gradient boosting decision trees ([PERSON] et al., 2018; [PERSON] et al., 2019), logistic regression ([PERSON] et al., 2018), Cox Proportional Hazard model ([PERSON] et al., 2018), and neural networks ([PERSON] et al., 2018; [PERSON] et al., 2018), among others. However, in spite of their versatility (Section 1.2), the implementation of generalized linear models (GLMs) has received little attention.