Bayesian networks

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Bayesian networks

What are Bayesian networks?

A Bayesian network is a kind of Probabilistic Graphical Model that makes use of Bayesian inference to carry out probability computations. 

They are probabilistic because they are created from probability distributions. They also employ the laws of probability for prediction and anomaly detection, reasoning, diagnostics, decision-making under uncertainty, and time series prediction.

Bayesian networks are also called Belief networks, Causal networks, and Bayes nets. You can use them to build models from data and/or expert opinions. They are used for modeling and reasoning with uncertain beliefs.

By representing conditional dependence by edges in a directed graph, they seek to model conditional dependence, thus modeling causation as well.

The relationships help you conduct inference on random variables in the graph by using of factors. The networks are directed acyclic graphs and every one of their edges corresponds to a conditional dependency, while every node corresponds to a unique random variable.

These networks satisfy the local Markov property which allows you to simplify the joint distribution to a smaller form. It helps you minimize the amount of computation needed in bigger networks.

Bayesian networks
Source: Towards Data Science

What do Bayesian networks predict?

A Bayesian network learned from data, built from expert opinion, or  a combination of both can be used to perform prediction, diagnostics, anomaly detection, decision automation (decision graphs), automatic extraction of insights, and many more tasks.

The task of prediction is about calculating a probability distribution over one or more variables whose values that you would like to know, wiht information or evidence that you have about some other variables.

The variables that Bayesian networks predict are known as output variables and the variables whose information we are using to make the predictions are referred to as Input variables. In statistics, the input variables are referred to as predictor, explanatory, or independent variables, while output variables are usuallty known as response or dependent variables.

When the Bayesian network is built from data, the task of predicting outputs is called supervised learning.

Bayesian networks are even able to make predictions when there is missing data due to their probabilistic foundations. The data could be missing for several reasons. Maybe you do not currently know the value of an input cause of a sensor being broken or not responding or someone not answering a question. The input value could also be misisng because an anomaly analysis has pointed out that the value from a defective sensor is clearly wrong, and therefore you wish to exclude that value. There usually is no need to fill in missing data via imputation or other methods, but Bayesian networks themselves can be used for the purpose of filling in missing data.

Bayesian networks can also be used to predict multiple outputs simultaneously. They are not limited to only predicting a single output. The outputs received can be discrete, continuous or a mixture of both.

It is also possible to use Bayesian networks to predict the joint probability over multiple outputs (discrete and or continuous). This is important when simply predicting two variables separately is not enough, whether you are using separate models or even when they are in the same model.

What is the difference between Markov networks and Bayesian networks?

Bayesian networks, aka belief networks, Bayes(ian) models or probabilistic directed acyclic graphical models, are probabilistic graphical models that represent sets of random variables and their conditional dependencies through the means of directed acyclic graphs (DAGs).

A Markov network, Markov random field (MRF), undirected graphical model is a set of random variables that has a Markov property described by an undirected graph. Basically, a  random field can be considered to be a Markov random field if it satisfies Markov properties.

A Markov network or Markov random field (MRF) would be rather similar to a Bayesian network in its representation of dependencies. The main differences between Markov networks and Bayesian networks are that Bayesian networks are directed and acyclic, whereas Markov networks are undirected and could be cyclic. 

This means that a Markov network can represent certain dependencies that a Bayesian network just can’t represent. (like cyclic dependencies). But the Markov network cannot represent some dependencies that a Bayesian network can (like induced dependencies).

What are the important components of Bayesian networks?

The two important components of Bayesian networks are the qualitative component, i.e. the Directed Acyclic Graph (DAG), and the quantitative component, i.e., the conditional probabilities.

How to create a Bayesian network?

To create a Bayesian network, you need to identify and define three things.

First, you need to define the variables that exist in the problem that you want to be solved and identify the main variable. 

After that, you need to define the conditional relationships between all the variables, i.e., the structure of the network.

Next, you need to figure out the probability distributions for each variable, i.e., the probability rules for the relationships between variables.

These steps can be carried out with data or expert opinions. They can even be done using both.

What are Bayesian networks used for?

Bayesian networks have a number of applications. Here are their most prominent uses:

1. Medical diagnosis

They can be used to figure out the probable disease that a patient is suffering from, based on the symptoms that are identified. A doctor can note the symptoms that are observed and enter them into the program which would compute the probabilities of multiple diseases based on the symptoms that were identified.

2. Testing hypotheses

Bayesian networks help us understand causal relationships. They help us understand whether the effect of a new feature is desirable. 

3. Environmental modeling

These networks can be used to model animal population trends. Environmental stressors have a lot of attention paid to them here.

4. Forecasting traffic 

Bayesian networks can be used to forecast traffic flows and learn from them.

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