/// <summary>
/// Given (symbolic) log-domain potentials, construct the graph for forward inference in a chain CRF.
/// </summary>
/// <param name="obs_potentials">(n_steps, n_classes) Axes correspond to time and the value of the discrete label variable
/// This is the energy assigned to a configuration (so higher energy = lower probability).</param>
/// <param name="chain_potentials">(n_classes, n_classes, n_classes) Axes correspond to left label state, right label state, and the global label.
/// Corresponds to the energy of a given pair of labels adjacent to one another (higher energy = lower probability).</param>
/// <param name="viterbi">Perform MAP inference with the Viterbi algorithm rather than marginalizing the step-specific
/// label variables, Instead, use the single most likely configuration.</param>
/// <returns>(1-dimensional) The energy assigned for a given global label.
/// This can be turned into a log probability by subtracting logsumexp(energy).</returns>
public static Tensor <float> Forward(Tensor <float> obs_potentials, Tensor <float> chain_potentials, bool viterbi = false)
{
Func <Tensor <float>, Tensor <float>, Tensor <float> > inner_function = (obs, prior_result /*, chain_potentials*/) =>
{
prior_result = prior_result.DimShuffle(0, 'x', 1);
obs = obs.DimShuffle('x', 0, 'x');
if (viterbi)
{
return(T.Max((-prior_result - obs - chain_potentials), axis: 0));
}
else
{
return(LogSumExp(-prior_result - obs - chain_potentials, axis: 0));
}
};
Debug.Assert(obs_potentials.NDim == 2);
Debug.Assert(chain_potentials.NDim == 3);
var initial = (obs_potentials[0].DimShuffle(0, 'x') * T.OnesLike(chain_potentials[0]));
var scanned = T.Scan(
fn: inner_function,
outputsInfo: initial,
sequences: new[] { obs_potentials[XSlicer.From(1)] }
//non_sequences: chain_potentials
);
if (viterbi)
{
return(-(T.Max(scanned[-1], axis: 0)));
}
else
{
return(-LogSumExp(scanned[-1], axis: 0));
}
}
public void TestShapeOfSlice()
{
var v = T.Shared(0.2f * NN.Random.Uniform(-1.0f, 1.0f, 13).As <float>(), "v");
AssertArray.WriteTheSame(new[] { 3 }, v[XSlicer.Range(5, 8)].Shape);
AssertArray.WriteTheSame(new[] { 3 }, v[XSlicer.Range(8, 5, -1)].Shape);
AssertArray.WriteTheSame(new[] { 4 }, v[XSlicer.Range(3, 11, 2)].Shape);
var M = T.Shared(0.2f * NN.Random.Uniform(-1.0f, 1.0f, 8, 22).As <float>(), "M");
AssertArray.WriteTheSame(new[] { 5, 17 }, M[XSlicer.Range(6, 1, -1), XSlicer.From(5)].Shape);
}
public void TestRecursive()
{
// http://deeplearning.net/software/theano/tutorial/loop.html
// define tensor variables
var X = T.Vector <float>("X");
var W = T.Matrix <float>("W");
var b_sym = T.Matrix <float>("b_sym");
var U = T.Matrix <float>("U");
var Y = T.Matrix <float>("Y");
var V = T.Matrix <float>("V");
var P = T.Matrix <float>("P");
var results = T.Scan((yy, pp, xx_tm1) => T.Tanh(T.Dot(xx_tm1, W) + T.Dot(yy, U) + T.Dot(pp, V)),
sequences: new[] { Y, P[XSlicer.Step(-1)] },
outputsInfo: X);
var compute_seq = T.Function(inputs: new[] { X, W, Y, U, P, V }, output: results);
// test values
var x = NN.Zeros <float>(2);
x.Item[1] = 1;
var w = NN.Ones <float>(2, 2);
var y = NN.Ones <float>(5, 2);
y.Item[0] = -3;
var u = NN.Ones <float>(2, 2);
var p = NN.Ones <float>(5, 2);
p.Item[0] = 3;
var v = NN.Ones <float>(2, 2);
var result = compute_seq(new[] { x, w, y, u, p, v }); // Array<float>[5] => theano returns Array<float>[5][1]
// comparison with numpy
var x_res = NN.Zeros <float>(5, 2);
x_res[0] = NN.Tanh(x.Dot(w) + y[0].Dot(u) + p[4].Dot(v));
for (int i = 1; i < 5; i++)
{
x_res[i] = NN.Tanh(x_res[i - 1].Dot(w) + y[i].Dot(u) + p[4 - i].Dot(v));
}
AssertArray.AreAlmostEqual(x_res, result);
}