---
description: What is the DAG for our use case ? What does it mean ?
---

# Building the Image Generation Directed Graph

In the previous section, we took a look at how to probabilistic-ally reason with causal DAGs and inference algorithms. In this section, we take a look at our image generation use case.&#x20;

![Game character Image Generation DAG](https://1424433991-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MFBM73ocV8YCzRKuMr4%2F-MFnAFJOxbQojQzQE3AE%2F-MFnD04LAyZLdsi2_bK6%2Ffinal_dag_rect.png?alt=media\&token=00eadb1b-5140-494b-b0d0-53d8706ab5b5)

Each image is a situation with 2 characters where there is an instigator also known as the **Actor** and a character reacting to the instigation named the **Reactor**. All the nodes in the DAG are Discrete random variables except the image.

| Node Abbr |        Node        |          Values         |                    Explanation                    |
| --------- | :----------------: | :---------------------: | :-----------------------------------------------: |
| AC        |   Actor Character  |       Satyr, Golem      |           The Actor can be any character          |
| RC        |  Reactor Character |       Satyr, Golem      |          The Reactor can be any character         |
| AT        |     Actor Type     |   Type1, Type2, Type3   |        There are 3 types for each character       |
| RT        |    Reactor Type    |   Type1, Type2, Type3   |        There are 3 types for each character       |
| AD        |    Actor Defense   |        Low, High        |          Defense of the actor. Unobserved         |
| AS        |   Actor Strength   |        Low, High        |         Strength of the actor. Unobserved         |
| AA        |    Actor Attack    |        Low, High        |  Attacking capabilities of the actor. Unobserved. |
| RD        |   Reactor Defense  |        Low, High        |         Defense of the reactor. Unobserved        |
| RS        |  Reactor Strength  |        Low, High        |        Strength of the reactor. Unobserved.       |
| RA        |   Reactor Attack   |        Low, High        | Attacking capabilities of the reactor. Unobserved |
| AACT      |   Actor's Action   |   Attack, Walk, Taunt   |              The Action of the actor.             |
| RRCT      | Reactor's Reaction | Die, Hurt, Idle, Attack |            The Reaction of the reactor            |
| IMG       |        Image       |            NA           |                  Generated Image                  |

![Sample Image](https://1424433991-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MFBM73ocV8YCzRKuMr4%2F-MFj2fiz_2qYU9n2fg3l%2F-MFj2kfUXTLHl5KVIcWq%2Fcombination142.png?alt=media\&token=2d290de1-8f09-43d3-9ba9-6567ef8deacc)



The joint probability can be written by factorizing the DAG.

> P(AC,RC,AT,RT,AD,AS,AA,RD,RS,RA,AACT, RRCT, IMG) = P(AC) \* P(RC) \* P(AT|AC) \* P(RT|RC) \* P(AD | AC, AT) \* P(AS|AC,AT) \* P(AA|AC,AT) \* P(RD|RC,RT) \* P(RS|RC,RT) \* P(RA|RC,RT) \* P(AACT| AD,AS,AA) \* P(RRCT|RA,RS,RD,AACT) \* P(IMG|AACT,RRCT,AT,RT,AC,RC)

{% hint style="info" %}
P(IMG|AACT,RRCT,AT,RT,AC,RC) is learnt by a neural network. The decoder of the learned network generates an image
{% endhint %}

Like in the previous section, we need to specify certain prior conditional probabilities to make the sampling easy for us. Instead of computing intervention/condition distributions using inference algorithms at run time, we use probability propagation methods to compute conditional probabilities for the queries that we are interested in. This is done to simplify the problem and avoid unnecessary troubles during inference.&#x20;

{% hint style="warning" %}
Need to figure out a way to do inference at run time, instead of pre-computing them.
{% endhint %}

&#x20;The next section deals with how to compute these probabilities using R packages **gRain** and **bnlearn.**
