graph_simulator

Fast library to simulate data from directed acyclic graphs (DAGs).

Dependencies between vertices in the graph are specified in a human-readable YAML file. For example, the simple graph \( X \rightarrow Y \) is specified by the YAML code below:

X:
  kernel:
    type: "uniform"
    sample_domain: [0, 1]
    terms: null
  dependencies: null

Y:
  kernel:
    type: "linear"
    sample_domain: [1, 1.5]
    noise: 0.1
    terms:
      - intercept: 1
        indicators: null
        value: 0.5
        variable:
          1: "X"
  dependencies:
    1: ["X"]

Here, X does not have any parents, as specified by dependencies: null, and it is uniformly distributed with support \( {0, 1} \). In contrast, \( Y_t \) has a parent \( X_{t-1} \) (graphically we write \( X_{t-1} \rightarrow Y_t \)), which is specified by 1: ["X"] under dependencies — interpreted as “X of lag 1”.

In the kernel section, we see that Y depends on its parents linearly (type: "linear"), but takes a random value with probability 0.1 in \( {1, 1.5} \), as indicated by noise: 0.1 and sample_domain: [1, 1.5].

The linear dependency is specified in the terms subsection. In this case, there is a single term composed of an intercept of value 1 (intercept: 1) plus a value of 0.5 (value: 0.5) times the value of “X at lag 1” (1: "X" under variable). Terms may, in addition, depend on indicator functions that can render the whole term zero.

Thus, in the above example, we may write the functional form of \( Y_t \) as:

Y_t =
\begin{cases}
  1 + 0.5 \cdot X_{t-1}, & \text{with probability } 0.9 \\\\
  \text{Unif}(\{1, 1.5\}), & \text{with probability } 0.1
\end{cases}

Supported kernels:

• uniform
• linear
• poisson
• binomial
• mixed
• constant