➕Probabilistic-Artificial-Intelligence

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, while other methods are mainly used to summarize interesting data or generating sort of reports. Reinforcement learning (RL) is an interdisciplinary area of machine learning and optimal control concerned with how an intelligent agent ought to take actions in a dynamic environment in order to maximize the cumulative reward....

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. $$ p(\theta \mid x_{1:n}, y_{1:n}) = \frac{1}{z} p(y_{1:n} \mid \theta, x_{1:n}) p(\theta \mid x_{1:n}) \approx q(\theta \mid \lambda) $$ For Bayesian Linear Regression we had high dimensional Gaussians which made the inference closed form, in general this is not true, so we need some kinds of approximation....

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 that are not possible in classical first order or propositional logic, yet they are frequent in human common sense reasoning. Let’s present some rules and some examples along them:...

aussians are one of the most important 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 Expectation Maximization algorithm. The best thing if you want to learn this part actually well is section 2.3 of (Bishop 2006), so go there my friend :)...

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 for the input XXX. In geostatistics, Gaussian processes are referred to as kriging regressions, and many other models, such as Kalman Filters or radial basis function networks, can be understood as special cases of Gaussian processes....