How to define a model

Loading...

En provenance du cours de National Research University Higher School of Economics

Bayesian Methods for Machine Learning

140 notes

National Research University Higher School of Economics

Bayesian Methods for Machine Learning

140 notes

Cours 3 sur 7 dans Specialization Advanced Machine Learning

Bayesian methods are used in lots of fields: from game development to drug discovery. They give superpowers to many machine learning algorithms: handling missing data, extracting much more information from small datasets. Bayesian methods also allow us to estimate uncertainty in predictions, which is a really desirable feature for fields like medicine. When Bayesian methods are applied to deep learning, it turns out that they allow you to compress your models 100 folds, and automatically tune hyperparametrs, saving your time and money. In six weeks we will discuss the basics of Bayesian methods: from how to define a probabilistic model to how to make predictions from it. We will see how one can fully automate this workflow and how to speed it up using some advanced techniques. We will also see applications of Bayesian methods to deep learning and how to generate new images with it. We will see how new drugs that cure severe diseases be found with Bayesian methods.

À partir de la leçon

Introduction to Bayesian methods & Conjugate priors

Welcome to first week of our course! Today we will discuss what bayesian methods are and what are probabilistic models. We will see how they can be used to model real-life situations and how to make conclusions from them. We will also learn about conjugate priors — a class of models where all math becomes really simple.

Think bayesian & Statistics review7:26

Bayesian approach to statistics5:25

How to define a model3:22

Example: thief & alarm11:10

Linear regression10:49

Rencontrer les enseignants

Daniil Polykovskiy
Researcher
HSE Faculty of Computer Science
Alexander Novikov
Researcher
HSE Faculty of Computer Science

>>In this video, we'll see how to define a probabilistic model.

The most convenient way to do this is called the Bayesian Network. It is a graph.

Its nodes are in variables and edges are direct impact.

For example, here we have two invariables,

rain and the fact that the grass is wet.

And these edge shows as if there is rain,

if it's raining, then the grass will be wet for sure.

We can see a more complex graph.

For example, here we added another invariable called sprinkler,

and the grass maybe wet either because the sprinkler is working or because it is raining.

Also the sprinkler will not work if there is rain.

From the graph, we can write down the probabilistic model.

The probabilistic model is a joint probability over all random variables.

It can be written using the following formula.

The joint probability over all variables equals to the product for each variable,

is probability given all the parents.

On this graph, for example,

the parents of the node grass are sprinkler and the rain.

Let's try to write down the probabilistic model for this graph.

So the joint probability of sprinkler,

rain, and the grass equals to the product of two terms.

The first one is the probability of grass is worse given the sprinkler and the rain.

Those are the parents of this node.

Next, multiplier is the probability of the sprinkler given the rain.

The rain is the only parent of this node.

And finally, we write down the probability of the rain.

Since this node doesn't have any parents,

we just write down the probability of the rain.

And this is our final model.

We can see a bit more complex ones.

For example, you all know the Naive Bayes classifier.

It's graphical model looks as follows.

We have a class,

C that directly impacts the values of the features,

that is for different classes.

The distribution of the features may be different.

And the joint distribution can be written using the following formula.

It is the probability of the class times the product over all features,

the probability of the current feature given the class.

However, this notation is a bit interesting since we have a lot of equal sub-graphs.

A bit more convenient way to write down this graph is called a plate notation.

It is written as follows.

So we have a random variable that corresponds to the class,

that directly impacts the features.

And this works around this random variable with a number of

repetitions such that we have to repeat this sub-graph

that is contained inside this box and times.

And so this is exactly Kuhn's graphical model,

the one we saw on the previous slide.

Explorer notre catalogue

Rejoignez-nous gratuitement et obtenez des recommendations, des mises à jour et des offres personnalisées.

Coursera propose un accès universel à la meilleure formation au monde, en partenariat avec des universités et des organisations du plus haut niveau, pour proposer des cours en ligne.

© 2018 Coursera Inc. Tous droits réservés.

Télécharger dans l'App Store

Disponible sur Google Play