Completed notes of the course modulo 1

Pagina 1

E d i t e d b y : M a r c o V a r r o n e M I D A 1 C o u r s e N o t e s These notes have been made thanks to the effort of Polimi Data Scientists staff. Are you interested in Data Science activities? Follow PoliMi Data Scientists on Facebook ! Polimi Data Scientist is a community of students and Alumni of Politecnico di Milano. We organize events and activities related to Artificial Intelligence and Machine Learning, our aim is to create a strong and passionate community about Data Science at Politecnico di Milano. Do you want to learn more? Visit our website and join our Telegram Group ! ! Credits The following notes have been written by the Polimi Data Scientists student association by combining Prof. Bittanti’s lectures and notes with content from the Identificazione dei Modelli e Analisi dei Dati 1 2010-2011 notes by Stefano Invernizzi. They are meant as a support for the students following the course and they should not be considered as a replacement for the professor’s lectures or the book suggested in the course bibliography. 1 Contents I Prediction 4 1 The prediction problem 5 1.1 Symbolism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 The linear predictor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Random concepts 7 2.1 Random variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Random vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Stochastic (or random) process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Stationary process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4.1 White noise . . . . . . . . . . . . . . . . . .…