Using template notation can be a powerful way to describe your model

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What is a sequence?

A sequence is a group of vertices that is repeated multiple times in the network. The vertices in one group can (optionally) depend on vertices in the previous group. They typically represent a concept larger than a vertex like an agent in an ABM, a time series or some observations that are associated.


Here are some examples that will walk you through the process of developing with Sequences.

Writing time series

This example shows you how you can write a simple time series model using Sequences

DoubleVertex two = new ConstantDoubleVertex(2);

// Define the labels of vertices we will use in our Sequence
VertexLabel x1Label = new VertexLabel("x1");
VertexLabel x2Label = new VertexLabel("x2");

// Define labels for the Proxy Vertices which stand in for a Vertex from the previous SequenceItem.
// They will be automatically wired up when you construct the Sequence.
// i.e. these are the 'inputs' to our SequenceItem
VertexLabel x1InputLabel = SequenceBuilder.proxyFor(x1Label);
VertexLabel x2InputLabel = SequenceBuilder.proxyFor(x2Label);

// Define a factory method that creates proxy vertices using the proxy vertex labels and then uses these
// to define the computation graph of the Sequence.
// Note we have labeled the output vertices of this SequenceItem
Consumer<SequenceItem> factory = sequenceItem -> {
    DoubleProxyVertex x1Input = new DoubleProxyVertex(x1InputLabel);
    DoubleProxyVertex x2Input = new DoubleProxyVertex(x2InputLabel);

    DoubleVertex x1Output = x1Input.multiply(two).setLabel(x1Label);
    DoubleVertex x2Output =;

    sequenceItem.addAll(x1Input, x2Input, x1Output, x2Output);

// Create the starting values of our sequence
DoubleVertex x1Start = new ConstantDoubleVertex(4).setLabel(x1Label);
DoubleVertex x2Start = new ConstantDoubleVertex(4).setLabel(x2Label);
VertexDictionary dictionary = SimpleVertexDictionary.of(x1Start, x2Start);

Sequence sequence = new SequenceBuilder<Integer>()

Note: by using the .withFactories method on the builder, rather than the .withFactory, it is possible to have factories which use proxy input vertices which are defined in other factories. i.e. your vertices can cross factories.

Observing many associated data points

This example shows you how you can repeat logic over many observed data points which are associated by having a dependency on a common global value. Here they are the intercept and weights of a linear regression model.

Let’s say you have a class MyData that looks like this:

public static class MyData {
    public double x;
    public double y;

    public MyData(String x, String y) {
        this.x = Double.parseDouble(x);
        this.y = Double.parseDouble(y);

This is an example of how you could pull in data from a csv file and run linear regression, using a sequence to build identical sections of the graph for each line of the csv.

 * Each sequence item contains a linear regression model:
 * VertexY = VertexX * VertexM + VertexB
 * @param dataFileName The input data file defines, for each sequence item:
 *                     - the value of the input, VertexX
 *                     - the value of the observed output, VertexY
public Sequence buildSequence(String dataFileName) {
    //Parse the csv data to MyData objects
    List<MyData> allMyData = ReadCsv.fromFile(dataFileName)

    DoubleVertex m = new GaussianVertex(0, 1);
    DoubleVertex b = new GaussianVertex(0, 1);
    VertexLabel xLabel = new VertexLabel("x");
    VertexLabel yLabel = new VertexLabel("y");

    //Build sequence from each line in the csv
    Sequence sequence = new SequenceBuilder<MyData>()
        .withFactory((item, csvMyData) -> {

            ConstantDoubleVertex x = new ConstantDoubleVertex(csvMyData.x).setLabel(xLabel);
            DoubleVertex y = m.multiply(x).plus(b).setLabel(yLabel);

            DoubleVertex yObserved = new GaussianVertex(y, 1);

            // this labels the x and y vertex for later use

    //now you have access to the "x" from any one of the sequence
    DoubleTensor valueForXAtCSVLine1 = sequence.asList()
        .get(1) // get sequence item 1 which is built from csv line 1
        .<DoubleVertex>get(xLabel) //get the vertex that we labelled "x" in that item
        .getValue(); //get the value from that vertex

    //Now run an inference algorithm on vertex m and vertex b and you have linear regression

    return sequence;