Tree cumulants and the geometry of binary tree models

In this paper we investigate undirected discrete graphical tree models when all the variables in the system are binary, where leaves represent the observable variables and where all the inner nodes are unobserved. A novel approach based on the theory of partially ordered sets allows us to obtain a convenient parametrization of this model class. The construction of the proposed coordinate system mirrors the combinatorial definition of cumulants. A simple product-like form of the resulting parametrization gives insight into identifiability issues associated with this model class. In particular, we provide necessary and sufficient conditions for such a model to be identified up to the switching of labels of the inner nodes. When these conditions hold, we give explicit formulas for the parameters of the model. Whenever the model fails to be identified, we use the new parametrization to describe the geometry of the unidentified parameter space. We illustrate these results using a simple example.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ338 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Integrating AI into UAVs

This research project explores the application of Deep Learning (DL) techniques, specifically Convolutional Neural Networks (CNNs), to develop a smoke detection algorithm for deployment on mobile platforms, such as drones and self-driving vehicles. The project focuses on enhancing the decision-making capabilities of these platforms in emergency response situations. The methodology involves three phases: algorithm development, algorithm implementation, and testing and optimization. The developed CNN model, based on ResNet50 architecture, is trained on a dataset of fire, smoke, and neutral images obtained from the web. The algorithm is implemented on the Jetson Nano platform to provide responsive support for first responders. The study contributes to the intersection of artificial intelligence and autonomous systems, aiming to improve early detection capabilities for critical scenarios