/// <summary>
/// Slowest possible way to calculate a derivative for a model: exhaustive definitional calculation, using the super
/// slow logLikelihood function from this test suite.
/// </summary>
/// <param name="model">the model the get the derivative for</param>
/// <param name="weights">the weights to get the derivative at</param>
/// <returns>the derivative of the log likelihood with respect to the weights</returns>
private ConcatVector DefinitionOfDerivative(GraphicalModel model, ConcatVector weights)
{
double epsilon = 1.0e-7;
ConcatVector goldGradient = new ConcatVector(ConcatVecComponents);
for (int i = 0; i < ConcatVecComponents; i++)
{
double[] component = new double[ConcatVecComponentLength];
for (int j = 0; j < ConcatVecComponentLength; j++)
{
// Create a unit vector pointing in the direction of this element of this component
ConcatVector unitVectorIJ = new ConcatVector(ConcatVecComponents);
unitVectorIJ.SetSparseComponent(i, j, 1.0);
// Create a +eps weight vector
ConcatVector weightsPlusEpsilon = weights.DeepClone();
weightsPlusEpsilon.AddVectorInPlace(unitVectorIJ, epsilon);
// Create a -eps weight vector
ConcatVector weightsMinusEpsilon = weights.DeepClone();
weightsMinusEpsilon.AddVectorInPlace(unitVectorIJ, -epsilon);
// Use the definition (f(x+eps) - f(x-eps))/(2*eps)
component[j] = (LogLikelihood(model, weightsPlusEpsilon) - LogLikelihood(model, weightsMinusEpsilon)) / (2 * epsilon);
// If we encounter an impossible assignment, logLikelihood will return negative infinity, which will
// screw with the definitional calculation
if (double.IsNaN(component[j]))
{
component[j] = 0.0;
}
}
goldGradient.SetDenseComponent(i, component);
}
return(goldGradient);
}
public virtual void TestGetSummaryForInstance(GraphicalModel[] dataset, ConcatVector weights)
{
LogLikelihoodDifferentiableFunction fn = new LogLikelihoodDifferentiableFunction();
foreach (GraphicalModel model in dataset)
{
double goldLogLikelihood = LogLikelihood(model, (ConcatVector)weights);
ConcatVector goldGradient = DefinitionOfDerivative(model, (ConcatVector)weights);
ConcatVector gradient = new ConcatVector(0);
double logLikelihood = fn.GetSummaryForInstance(model, (ConcatVector)weights, gradient);
NUnit.Framework.Assert.AreEqual(logLikelihood, Math.Max(1.0e-3, goldLogLikelihood * 1.0e-2), goldLogLikelihood);
// Our check for gradient similarity involves distance between endpoints of vectors, instead of elementwise
// similarity, b/c it can be controlled as a percentage
ConcatVector difference = goldGradient.DeepClone();
difference.AddVectorInPlace(gradient, -1);
double distance = Math.Sqrt(difference.DotProduct(difference));
// The tolerance here is pretty large, since the gold gradient is computed approximately
// 5% still tells us whether everything is working or not though
if (distance > 5.0e-2)
{
System.Console.Error.WriteLine("Definitional and calculated gradient differ!");
System.Console.Error.WriteLine("Definition approx: " + goldGradient);
System.Console.Error.WriteLine("Calculated: " + gradient);
}
NUnit.Framework.Assert.AreEqual(distance, 5.0e-2, 0.0);
}
}
// this magic number was arrived at with relation to the CoNLL benchmark, and tinkering
public override bool UpdateWeights(ConcatVector weights, ConcatVector gradient, double logLikelihood, AbstractBatchOptimizer.OptimizationState optimizationState, bool quiet)
{
BacktrackingAdaGradOptimizer.AdaGradOptimizationState s = (BacktrackingAdaGradOptimizer.AdaGradOptimizationState)optimizationState;
double logLikelihoodChange = logLikelihood - s.lastLogLikelihood;
if (logLikelihoodChange == 0)
{
if (!quiet)
{
log.Info("\tlogLikelihood improvement = 0: quitting");
}
return(true);
}
else
{
// Check if we should backtrack
if (logLikelihoodChange < 0)
{
// If we should, move the weights back by half, and cut the lastDerivative by half
s.lastDerivative.MapInPlace(null);
weights.AddVectorInPlace(s.lastDerivative, -1.0);
if (!quiet)
{
log.Info("\tBACKTRACK...");
}
// if the lastDerivative norm falls below a threshold, it means we've converged
if (s.lastDerivative.DotProduct(s.lastDerivative) < 1.0e-10)
{
if (!quiet)
{
log.Info("\tBacktracking derivative norm " + s.lastDerivative.DotProduct(s.lastDerivative) + " < 1.0e-9: quitting");
}
return(true);
}
}
else
{
// Apply AdaGrad
ConcatVector squared = gradient.DeepClone();
squared.MapInPlace(null);
s.adagradAccumulator.AddVectorInPlace(squared, 1.0);
ConcatVector sqrt = s.adagradAccumulator.DeepClone();
sqrt.MapInPlace(null);
gradient.ElementwiseProductInPlace(sqrt);
weights.AddVectorInPlace(gradient, 1.0);
// Setup for backtracking, in case necessary
s.lastDerivative = gradient;
s.lastLogLikelihood = logLikelihood;
if (!quiet)
{
log.Info("\tLL: " + logLikelihood);
}
}
}
return(false);
}
internal static long CloneBenchmark(ConcatVector vector)
{
long before = Runtime.CurrentTimeMillis();
for (int i = 0; i < 10000000; i++)
{
vector.DeepClone();
}
return(Runtime.CurrentTimeMillis() - before);
}
public TrainingWorker(AbstractBatchOptimizer _enclosing, T[] dataset, AbstractDifferentiableFunction <T> fn, ConcatVector initialWeights, double l2regularization, double convergenceDerivativeNorm, bool quiet)
{
this._enclosing = _enclosing;
this.optimizationState = this._enclosing.GetFreshOptimizationState(initialWeights);
this.weights = initialWeights.DeepClone();
this.dataset = dataset;
this.fn = fn;
this.l2regularization = l2regularization;
this.convergenceDerivativeNorm = convergenceDerivativeNorm;
this.quiet = quiet;
}
public virtual void TestOptimizeLogLikelihood(AbstractBatchOptimizer optimizer, GraphicalModel[] dataset, ConcatVector initialWeights, double l2regularization)
{
AbstractDifferentiableFunction <GraphicalModel> ll = new LogLikelihoodDifferentiableFunction();
ConcatVector finalWeights = optimizer.Optimize((GraphicalModel[])dataset, ll, (ConcatVector)initialWeights, (double)l2regularization, 1.0e-9, true);
System.Console.Error.WriteLine("Finished optimizing");
double logLikelihood = GetValueSum((GraphicalModel[])dataset, finalWeights, ll, (double)l2regularization);
// Check in a whole bunch of random directions really nearby that there is no nearby point with a higher log
// likelihood
Random r = new Random(42);
for (int i = 0; i < 1000; i++)
{
int size = finalWeights.GetNumberOfComponents();
ConcatVector randomDirection = new ConcatVector(size);
for (int j = 0; j < size; j++)
{
double[] dense = new double[finalWeights.IsComponentSparse(j) ? finalWeights.GetSparseIndex(j) + 1 : finalWeights.GetDenseComponent(j).Length];
for (int k = 0; k < dense.Length; k++)
{
dense[k] = (r.NextDouble() - 0.5) * 1.0e-3;
}
randomDirection.SetDenseComponent(j, dense);
}
ConcatVector randomPerturbation = finalWeights.DeepClone();
randomPerturbation.AddVectorInPlace(randomDirection, 1.0);
double randomPerturbedLogLikelihood = GetValueSum((GraphicalModel[])dataset, randomPerturbation, ll, (double)l2regularization);
// Check that we're within a very small margin of error (around 3 decimal places) of the randomly
// discovered value
if (logLikelihood < randomPerturbedLogLikelihood - (1.0e-3 * Math.Max(1.0, Math.Abs(logLikelihood))))
{
System.Console.Error.WriteLine("Thought optimal point was: " + logLikelihood);
System.Console.Error.WriteLine("Discovered better point: " + randomPerturbedLogLikelihood);
}
NUnit.Framework.Assert.IsTrue(logLikelihood >= randomPerturbedLogLikelihood - (1.0e-3 * Math.Max(1.0, Math.Abs(logLikelihood))));
}
}
/// <summary>Create an Inference object for a given set of weights, and a model.</summary>
/// <remarks>
/// Create an Inference object for a given set of weights, and a model.
/// <p>
/// The object is around to facilitate cacheing as an eventual optimization, when models are changing in minor ways
/// and inference is required several times. Work is done lazily, so is left until actual inference is requested.
/// </remarks>
/// <param name="model">the model to be computed over, subject to change in the future</param>
/// <param name="weights">
/// the weights to dot product with model features to get log-linear factors, is cloned internally so
/// that no changes to the weights vector will be reflected by the CliqueTree. If you want to change
/// the weights, you must create a new CliqueTree.
/// </param>
public CliqueTree(GraphicalModel model, ConcatVector weights)
{
// This is the metadata key for the model to store an observed value for a variable, as an int
this.model = model;
this.weights = weights.DeepClone();
}