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Construction & inference (Time series) in C#

// --------------------------------------------------------------------------------------------------------------------
// <copyright file="DbnExample.cs" company="Bayes Server">
// Copyright (C) Bayes Server. All rights reserved.
// </copyright>
// --------------------------------------------------------------------------------------------------------------------

namespace BayesServer.HelpSamples
{
using System;

using BayesServer.Inference.RelevanceTree;

public static class DbnExample
{
public static void Main()
{
// In this example we programatically create a Dynamic Bayesian network (time series).
// Note that you can automatically define nodes from data using
// classes in BayesServer.Data.Discovery,
// and you can automatically learn the parameters using classes in
// BayesServer.Learning.Parameters,
// however here we build a Bayesian network from scratch.

var network = new Network("DBN");

var cluster1 = new State("Cluster1");
var cluster2 = new State("Cluster2");
var cluster3 = new State("Cluster3");
var varTransition = new Variable("Transition", cluster1, cluster2, cluster3);
var nodeTransition = new Node(varTransition);

// make the node temporal, so that it appears in each time slice
nodeTransition.TemporalType = TemporalType.Temporal;

var varObs1 = new Variable("Obs1", VariableValueType.Continuous);
var varObs2 = new Variable("Obs2", VariableValueType.Continuous);
var varObs3 = new Variable("Obs3", VariableValueType.Continuous);
var varObs4 = new Variable("Obs4", VariableValueType.Continuous);

// observation node is a multi variable node, consisting of 4 continuous variables
var nodeObservation = new Node("Observation", new Variable[] { varObs1, varObs2, varObs3, varObs4 });
nodeObservation.TemporalType = TemporalType.Temporal;

network.Nodes.Add(nodeTransition);
network.Nodes.Add(nodeObservation);

// link the transition node to the observation node within each time slice
network.Links.Add(new Link(nodeTransition, nodeObservation));

// add a temporal link of order 1. This links the transition node to itself in the next time slice
network.Links.Add(new Link(nodeTransition, nodeTransition, 1));

// at this point the structural specification is complete

// now complete the distributions

// because the transition node has an incoming temporal link of order 1 (from itself), we must specify
// two distributions, the first of which is specified for time = 0

var cluster1Time0 = new StateContext(cluster1, 0);
var cluster2Time0 = new StateContext(cluster2, 0);
var cluster3Time0 = new StateContext(cluster3, 0);

var prior = nodeTransition.NewDistribution(0).Table;
prior[cluster1Time0] = 0.2;
prior[cluster2Time0] = 0.3;
prior[cluster3Time0] = 0.5;

// NewDistribution does not assign the new distribution, so it still must be assigned
nodeTransition.Distribution = prior;

// the second is specified for time >= 1
var transition = nodeTransition.NewDistribution(1).Table;

// when specifying temporal distributions, variables which belong to temporal nodes must have times associated
// NOTE: Each time is specified relative to the current point in time which is defined as zero,
// therefore the time for variables at the previous time step is -1

var cluster1TimeM1 = new StateContext(cluster1, -1);
var cluster2TimeM1 = new StateContext(cluster2, -1);
var cluster3TimeM1 = new StateContext(cluster3, -1);

transition[cluster1TimeM1, cluster1Time0] = 0.2;
transition[cluster1TimeM1, cluster2Time0] = 0.3;
transition[cluster1TimeM1, cluster3Time0] = 0.5;
transition[cluster2TimeM1, cluster1Time0] = 0.4;
transition[cluster2TimeM1, cluster2Time0] = 0.4;
transition[cluster2TimeM1, cluster3Time0] = 0.2;
transition[cluster3TimeM1, cluster1Time0] = 0.9;
transition[cluster3TimeM1, cluster2Time0] = 0.09;
transition[cluster3TimeM1, cluster3Time0] = 0.01;

// an alternative would be to set values using TableIterator.CopyFrom

//new TableIterator(transition, new Variable[] { varTransition, varTransition }, new int?[] { -1, 0 }).CopyFrom(new double[]
// {
// 0.2, 0.3, 0.5, 0.4, 0.4, 0.2, 0.9, 0.09, 0.01
// });

nodeTransition.Distributions[1] = transition;

// Node observation does not have any incoming temporal links, so
// only requires a distribution specified at time >=0
// Calling NewDistribution without specifying a time assumes time zero.
var gaussian = (CLGaussian)nodeObservation.NewDistribution();

// set the Gaussian parameters corresponding to the state "Cluster1" of variable "transition"

var varObs1Time0 = new VariableContext(varObs1, 0, HeadTail.Head);
var varObs2Time0 = new VariableContext(varObs2, 0, HeadTail.Head);
var varObs3Time0 = new VariableContext(varObs3, 0, HeadTail.Head);
var varObs4Time0 = new VariableContext(varObs4, 0, HeadTail.Head);

gaussian.SetMean(varObs1Time0, 3.2, cluster1Time0);
gaussian.SetMean(varObs2Time0, 2.4, cluster1Time0);
gaussian.SetMean(varObs3Time0, -1.7, cluster1Time0);
gaussian.SetMean(varObs4Time0, 6.2, cluster1Time0);

gaussian.SetVariance(varObs1Time0, 2.3, cluster1Time0);
gaussian.SetVariance(varObs2Time0, 2.1, cluster1Time0);
gaussian.SetVariance(varObs3Time0, 3.2, cluster1Time0);
gaussian.SetVariance(varObs4Time0, 1.4, cluster1Time0);

gaussian.SetCovariance(varObs1Time0, varObs2Time0, -0.3, cluster1Time0);
gaussian.SetCovariance(varObs1Time0, varObs3Time0, 0.5, cluster1Time0);
gaussian.SetCovariance(varObs1Time0, varObs4Time0, 0.35, cluster1Time0);
gaussian.SetCovariance(varObs2Time0, varObs3Time0, 0.12, cluster1Time0);
gaussian.SetCovariance(varObs2Time0, varObs4Time0, 0.1, cluster1Time0);
gaussian.SetCovariance(varObs3Time0, varObs4Time0, 0.23, cluster1Time0);

// set the Gaussian parameters corresponding to the state "Cluster2" of variable "transition"
gaussian.SetMean(varObs1Time0, 3.0, cluster2Time0);
gaussian.SetMean(varObs2Time0, 2.8, cluster2Time0);
gaussian.SetMean(varObs3Time0, -2.5, cluster2Time0);
gaussian.SetMean(varObs4Time0, 6.9, cluster2Time0);

gaussian.SetVariance(varObs1Time0, 2.1, cluster2Time0);
gaussian.SetVariance(varObs2Time0, 2.2, cluster2Time0);
gaussian.SetVariance(varObs3Time0, 3.3, cluster2Time0);
gaussian.SetVariance(varObs4Time0, 1.5, cluster2Time0);

gaussian.SetCovariance(varObs1Time0, varObs2Time0, - 0.4, cluster2Time0);
gaussian.SetCovariance(varObs1Time0, varObs3Time0, 0.5, cluster2Time0);
gaussian.SetCovariance(varObs1Time0, varObs4Time0, 0.45, cluster2Time0);
gaussian.SetCovariance(varObs2Time0, varObs3Time0, 0.22, cluster2Time0);
gaussian.SetCovariance(varObs2Time0, varObs4Time0, 0.15, cluster2Time0);
gaussian.SetCovariance(varObs3Time0, varObs4Time0, 0.24, cluster2Time0);

// set the Gaussian parameters corresponding to the state "Cluster3" of variable "transition"

gaussian.SetMean(varObs1Time0, 3.8, cluster3Time0);
gaussian.SetMean(varObs2Time0, 2.0, cluster3Time0);
gaussian.SetMean(varObs3Time0, -1.9, cluster3Time0);
gaussian.SetMean(varObs4Time0, 6.25, cluster3Time0);

gaussian.SetVariance(varObs1Time0, 2.34, cluster3Time0);
gaussian.SetVariance(varObs2Time0, 2.11, cluster3Time0);
gaussian.SetVariance(varObs3Time0, 3.22, cluster3Time0);
gaussian.SetVariance(varObs4Time0, 1.43, cluster3Time0);

gaussian.SetCovariance(varObs1Time0, varObs2Time0, -0.31, cluster3Time0);
gaussian.SetCovariance(varObs1Time0, varObs3Time0, 0.52, cluster3Time0);
gaussian.SetCovariance(varObs1Time0, varObs4Time0, 0.353, cluster3Time0);
gaussian.SetCovariance(varObs2Time0, varObs3Time0, 0.124, cluster3Time0);
gaussian.SetCovariance(varObs2Time0, varObs4Time0, 0.15, cluster3Time0);
gaussian.SetCovariance(varObs3Time0, varObs4Time0, 0.236, cluster3Time0);

nodeObservation.Distribution = gaussian;

// optional check to validate network
network.Validate(new ValidationOptions());


// at this point the network has been fully specified

// we will now perform some queries on the network

var inference = new RelevanceTreeInference(network);
var queryOptions = new RelevanceTreeQueryOptions();
var queryOutput = new RelevanceTreeQueryOutput();

// set some temporal evidence

inference.Evidence.Set(varObs1, new double?[] { 2.2, 2.4, 2.6, 2.9}, 0, 0, 4);
inference.Evidence.Set(varObs2, new double?[] { null, 4.0, 4.1, 4.88}, 0, 0, 4);
inference.Evidence.Set(varObs3, new double?[] {-2.5, -2.3, null, -4.0 }, 0, 0, 4);
inference.Evidence.Set(varObs4, new double?[] { 4.0, 6.5, 4.9, 4.4}, 0, 0, 4);

queryOptions.LogLikelihood = true; // only ask for this if you really need it

// predict the observation variables one time step in the future
var predictTime = 4;

var gaussianFuture = new CLGaussian[nodeObservation.Variables.Count];

for(int i = 0; i < gaussianFuture.Length; i++)
{
gaussianFuture[i] = new CLGaussian(nodeObservation.Variables[i], predictTime);
inference.QueryDistributions.Add(gaussianFuture[i]);
}

// we will also demonstrate querying a joint distribution

var jointFuture = new CLGaussian(new Variable[] { varObs1, varObs2 }, predictTime);
inference.QueryDistributions.Add(jointFuture);


inference.Query(queryOptions, queryOutput); // note that this can raise an exception (see help for details)

Console.WriteLine("LogLikelihood: " + queryOutput.LogLikelihood.Value);
Console.WriteLine();

for (int h = 0; h < gaussianFuture.Length; h++)
{
var variableH = nodeObservation.Variables[h];
Console.WriteLine("Mean({0}(t=4)|evidence)={1}", variableH.Name, gaussianFuture[h].GetMean(variableH, predictTime));
}

Console.WriteLine();
Console.WriteLine("{0},{1}|evidence:", varObs1.Name, varObs2.Name);
Console.WriteLine(jointFuture.GetMean(varObs1, predictTime) + "\t" + jointFuture.GetMean(varObs2, predictTime));
Console.WriteLine(jointFuture.GetVariance(varObs1, predictTime) + "\t" + jointFuture.GetCovariance(varObs1, predictTime, varObs2, predictTime));
Console.WriteLine(jointFuture.GetCovariance(varObs2, predictTime, varObs1, predictTime) + "\t" + jointFuture.GetVariance(varObs2, predictTime));

// Expected output...

// LogLikelihood: -26.3688322999762

// P(Obs1(t=4)|evidence)=3.33914912825023
// P(Obs2(t=4)|evidence)=2.38039739886759
// P(Obs3(t=4)|evidence)=-1.98416436694525
// P(Obs4(t=4)|evidence)=6.40822262492584

// P(Obs1,Obs2|evidence)=
// 3.33914912825023 2.38039739886759
// 2.36608725717058 -0.427500059391733
// -0.427500059391733 2.22592296205311

}
}
}