Gaussians are one of the most important family of probability distributions. They arise naturally in the law of large numbers and have some nice properties that we will briefly present and prove here in this note. They are also quite common for Gaussian Processes and the…
Robbins-Moro Algorithm # The Algorithm # the algorithm is very simple we do the following until convergence: set some learning rates that satisfy the Robbins Moro Conditions, choose a w 0 then update in the following way: w n + 1 = w n − α n Δ w n For example with α 0…
As we will briefly see, Kernels will have an important role in many machine learning applications. In this note we will get to know what are Kernels and why are they useful. Intuitively they measure the similarity between two input points. So if they are close the kernel should…
Gaussian processes can be viewed through a Bayesian lens of the function space: rather than sampling over individual data points, we are now sampling over entire functions. They extend the idea of bayesian linear regression by introducing an infinite number of feature functions…
Introduzione alle catene di Markov # La proprietà di Markov # Una sequenza di variabili aleatorie X 1 , X 2 , X 3 , … gode della proprietà di Markov se vale: P ( X n ∣ X n − 1 , X n − 2 , … , X 1 ) = P ( X n ∣ X n − 1 ) Ossia posso scordarmi tutta la storia…
Here is a historical treatment on the topic: https://jwmi.github.io/ASM/6-KalmanFilter.pdf . Kalman Filters are defined as follows: We start with a variable X 0 ∼ N ( μ , Σ ) , then we have a motion model and a sensor model : { X t + 1 = F X t + ε t Y t = H X t + η t…
This note will mainly attempt to summarize the introduction of some intuitive notions of probability used in common sense human reasoning. Most of what is said here is available here (Jaynes 2003) . Three intuitive notions of probability # Jaynes presents some forms of inference…
The main difference between reinforcement learning and other machine learning, pattern inference methods is that reinforcement learning takes the concept of actions into its core: models developed in this field can be actively developed to have an effect in its environment,…