Machine learning models increase their representational power by increasing the number of parameters in the model. The number of parameters in the model can be increased by introducing hidden nodes, higher-order interaction effects or by introducing new features into the model. In this talk, we will introduce the concepts in incidence algebra and information geometry to develop novel machine learning models to include higher-order interactions effects into the model. Incidence algebra provides a natural formulation for combinatorics by expressing it as a generative function and information geometry provides many theoretical guarantees in the model by projecting the problem onto a dually flat Riemannian structure for optimization. Combining the two techniques together formulates the information geometric formulation of the binary log-linear model. We first discuss how to apply these techniques to formulate the higher-order Boltzmann machine (HBM) to compare the different behaviours when using hidden nodes and higher-order feature interactions to increase the representational power of the model. We the present techniques to include higher-order interaction terms in Blind Source Separation (BSS) and to design efficient approach to estimate higher order intensity functions in Poisson process. Zoom Link: https://uni-sydney.zoom.us/j/97639217433 About Simon: Simon Luo is a Postdoctoral Research Fellow in the School of Mathematics and Statistics at The University of Sydney. He received a Bachelors of Engineering (Aeronautical) and Bachelors of Science (Computer Science) in 2015 at The University of Sydney. Simon has recently submitted his PhD at The University of Sydney where he has made contributions in transfer learning, Bayesian non-parametric models, probabilistic graphical models and information geometry. His work has been published several top-tier venues such as AAAI and PAKDD and have been awarded the "Reviewers’ Choice Award" at INTERACT’17 and "The Brian Shackel Award" which is the most prestigious award in the field (awarded once every 2 years) for "the most outstanding contribution with international impact in the field of human interaction with computers and information technology". Simon was supervised by Lamiae and Prof F. Ramos (Faculty of Engineering and NVIDIA).