Active Learning concerns methods to decide how to sample the most useful information in a specific domain; how can you select the best sample for an unknown model? Gathering data is very costly, we would like to create some principled manner to choose the best data point to…
The maximum entropy principle is one of the most important guiding motives in artificial artificial intelligence. Its roots emerge from a long tradition of probabilistic inference that goes back to Laplace and Occam's Razor, i.e. the principle of parsimony. Let's start with a…
This note extends the content Markov Processes in this specific context. One nice expansion, which treats the field a little bit more from the behavioural sciences perspectiv eis Intrinsic Motivation and Playfulness . Standard notions # Explore-exploit dilemma # We have seen…
While Active Learning looks for the most informative points to recover a true underlying function, Bayesian Optimization is just interested to find the maximum of that function. In Bayesian Optimization, we ask for the best way to find sequentially a set of points x 1 , … , x…
Andiamo a parlare di processi Markoviani. Dobbiamo avere bene a mente il contenuto di Markov Chains prima di approcciare questo capitolo. Markov property # Uno stato si può dire di godere della proprietà di Markov se, intuitivamente parlando, possiede già tutte le informazioni…
These algorithms are good for scaling state spaces, but not actions spaces. The Gradient Idea # Recall Temporal difference learning and Q-Learning, two model free policy evaluation techniques explored in Tabular Reinforcement Learning . A simple parametrization # The idea here…
We have a prior p ( model ) , we have a posterior p ( model ∣ data ) , a likelihood p ( data ∣ model ) and p ( data ) is called the evidence . Classical Linear regression # Let's start with a classical regression. In this setting we need to estimate a model that is generated…
DI Law of Large Numbers e Central limit theorem ne parliamo in Central Limit Theorem and Law of Large Numbers . Usually these methods are useful when you need to calculate following something similar to Bayes rule, but don't know how to calculate the denominator, often…
With variational inference we want to find a good approximation of the posterior distribution from which it is easy to sample. The objective is to approximate the posterior with a simpler one, because sometimes the prior or likelihood are difficult to compute. p ( θ ∣ x 1 : n …
There is huge literature on planning. We will attack this problem from the view of probabilistic artificial intelligence. In this case we focus on continuous, fully observed with non-linear transitions, an environment often used for robotics. It's called Model Predictive Control…