public Classification MaximumAPosterioriInfer(ImageData test_input)
{
Vertex[,] site_nodes = new Vertex[test_input.XSites, test_input.YSites];
for(int i = 0; i < test_input.XSites; i++) for(int j = 0; j < test_input.YSites; j++)
{
site_nodes[i,j] = new Vertex();
}
Vertex source = new Vertex();
Vertex target = new Vertex();
for(int j = 0; j < test_input.YSites; j++)
{
for(int i = 0; i < test_input.XSites; i++)
{
Vertex t = site_nodes[i,j];
//Add the edge with capacity lambda_t from the source, or the edge with capacity -lambda_t to the target.
//Lambda_t is the log-likelihood ratio: log( p(y | x = 1) / p(y | x = 0) ).
//Using Bayes' law, we have
//Posterior Odds = P(x = 1 | y)/P(x = 0 | y) = Likelihood Ratio * Prior Odds = (P(y | x = 1) / P(y | x = 0))*(P(x=1)/P(x=0)) = e^(lambda_t)*1
//So lambda_t should be log(Posterior Odds) + log(Prior Odds) = log(P(x=1|y))-log(P(x=0|y)) + possibly 0?
//Now, P(x=1|y) is modeled as sigma(w^T * h(y)), so this should be
//log(sigma(w^T * h(y))) - log(1-sigma(w^T * h(y))).
//However, all these calculations were done at roughly 5:50 AM and I hadn't slept yet, so...
//I could totally be wrong.
//-Jesse Selover
double modeled_prob_of_one = MathWrapper.Sigma(W.DotProduct(Transformer.Transform(test_input[i,j])));
/*double prob_one = ((double)Ons_seen)/((double) Sites_seen);
double prob_zero = 1d - prob_one;
double lambda = MathWrapper.Log(modeled_prob_of_one) - MathWrapper.Log (1 - modeled_prob_of_one) + MathWrapper.Log (prob_one/prob_zero);*/
Edge.AddEdge(source,t,-MathWrapper.Log(modeled_prob_of_one),0);
Edge.AddEdge(t,target,-MathWrapper.Log(1-modeled_prob_of_one),0);
Console.WriteLine("Edge to target with strength {0}",-MathWrapper.Log(1-modeled_prob_of_one));
//Add an edge from the source with the modeled probability of 1, and an edge to the target with the modeled probability of 0.
//Console.WriteLine(ImageData.GetNewConnections(i,j).Count);
foreach(Tuple<int,int> other in test_input.GetNewConnections(i,j))
{
Vertex u = site_nodes[other.Item1,other.Item2];
//Add the edge with capacity Beta_{t,u} in both directions between t and u.
//DRFS (2006) says that the data dependent smoothing term is max(0,v^T * mu_{i,j}y)
DenseVector mu;
if(ImageData.IsEarlier(i,j,other.Item1,other.Item2))mu = Crosser.Cross(test_input[i,j],test_input[other.Item1,other.Item2]);
else mu = Crosser.Cross(test_input[other.Item1,other.Item2], test_input[i,j]);
double capacity = Math.Max(0,V.DotProduct(mu));
Console.WriteLine ("\tInternode edge with strength {0}",capacity);
Edge.AddEdge(t,u,capacity,capacity);
}
}
}
double flow_added = 0;
while(true)
{
flow_added = source.AddFlowTo(new List<Vertex>(), target, 400000000d);
if(flow_added <= 0.0000001d) break;
}; //Find the maximum flow
source.ResidualCapacityConnectedNodes(); //Find the source end of the minimum cut
Label[,] toReturn = new Label[test_input.XSites, test_input.YSites];
for(int i = 0; i < test_input.XSites; i++) for(int j = 0; j < test_input.YSites; j++)
{
if(site_nodes[i,j].tagged_as_one) toReturn[i,j] = Label.ON;
}
return new Classification(toReturn);
}
