decision_boundary.py

# author: vlad niculae <[email protected]>
# license: mit

import torch
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.colors as colors

from entmax import sparsemax, entmax15
from entmax.losses import sparsemax_loss, entmax15_loss


# unify API for output layers: softmax, sparsemax, entmax.

def _extend_2d(z):
    z = z.unsqueeze(dim=-1)
    z = torch.cat((torch.zeros_like(z), z), dim=-1)
    return z


class SoftmaxOut(object):
    def __init__(self):
        self.loss_obj = torch.nn.BCEWithLogitsLoss()

    def loss(self, z, y_true):
        return self.loss_obj(z, y_true)

    def yhat(self, z):
        return torch.sigmoid(z)


class SparsemaxOut(object):

    def loss(self, z, y_true):
        return sparsemax_loss(_extend_2d(z), y_true.long()).mean()

    def yhat(self, z):
        return sparsemax(_extend_2d(z))[..., 1]


class Entmax15Out(object):

    def loss(self, z, y_true):
        return entmax15_loss(_extend_2d(z), y_true.long()).mean()

    def yhat(self, z):
        return entmax15(_extend_2d(z))[..., 1]


# evaluate a function over a mesh for making contour plots

class MeshEval(object):

    def __init__(self, xlim, ylim, n_points):

        self.n_points = n_points

        x_min, x_max = xlim
        y_min, y_max = ylim
        grid_x = np.linspace(x_min, x_max, n_points)
        grid_y = np.linspace(y_min, y_max, n_points)
        mesh_x, mesh_y = np.meshgrid(grid_x, grid_y)
        grid_pts = np.column_stack([mesh_x.ravel(), mesh_y.ravel()])

        self.mesh_x = mesh_x
        self.mesh_y = mesh_y
        self.grid_pts = torch.from_numpy(grid_pts).float()

    def __call__(self, net):
        z = (net(self.grid_pts)
             .reshape(self.n_points, self.n_points)
             .detach())
        return z


OUT_LAYERS = {
    'softmax': SoftmaxOut(),
    'sparsemax': SparsemaxOut(),
    'entmax15': Entmax15Out()
}


def train(net, X, y, out, n_epochs, callback):

    optim = torch.optim.SGD(params=net.parameters(), lr=0.05,
                            momentum=.9, nesterov=True)

    for it in range(n_epochs):
        optim.zero_grad()
        z = net(X).squeeze()
        loss = out.loss(z, y)
        callback(it, z.detach(), loss.item(), net)
        loss.backward()
        optim.step()


def main(out_name):

    # xor data
    hid = 100
    n_epochs = 300

    torch.manual_seed(42)

    def sample_X_y(batch_size):
        X = 2 * torch.rand(size=(batch_size, 2)) - 1
        y = (torch.prod(X, dim=1) > 0).float()
        return X, y

    X_train, y_train = sample_X_y(batch_size=300)

    net = torch.nn.Sequential(
        torch.nn.Linear(2, hid),
        torch.nn.ReLU(),
        torch.nn.Linear(hid, 1))

    its = []
    loss_vals = []
    acc_vals = []

    mesh_eval = MeshEval(xlim=(-1.5, 1.5),
                         ylim=(-1.5, 1.5),
                         n_points=50)

    out = OUT_LAYERS[out_name]

    def callback(it, y_pred, loss, net):
        accuracy = torch.mean(((y_pred > 0) == (y_train > 0)).double())
        its.append(it)
        loss_vals.append(loss)
        acc_vals.append(accuracy)

        print("Iter {:3d} Loss {:.3f} Acc {:.3f}".format(
            it,
            loss,
            accuracy
        ))

        mesh_z = mesh_eval(net)

        fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(14, 4), tight_layout=True)

        # plot decision function (z)
        max_val = np.abs(mesh_z).max()
        divnorm = colors.DivergingNorm(vmin=-max_val, vcenter=0, vmax=max_val)
        contour = ax1.contourf(mesh_eval.mesh_x,
                               mesh_eval.mesh_y,
                               mesh_z,
                               levels=np.linspace(-max_val, max_val, 30),
                               norm=divnorm,
                               cmap=plt.cm.PuOr)
        ax1.axvline(0, ls=":", color="k")
        ax1.axhline(0, ls=":", color="k")
        ax1.set_title('z')
        plt.colorbar(contour, ax=ax1)

        # plot positive class probability sigma(z)
        ax2.set_title('$\\sigma(z)$')
        divnorm = colors.DivergingNorm(vmin=0, vcenter=0.5, vmax=1)
        contour = ax2.contourf(mesh_eval.mesh_x,
                               mesh_eval.mesh_y,
                               out.yhat(mesh_z),
                               levels=np.linspace(0, 1, 30),
                               norm=divnorm,
                               cmap=plt.cm.PuOr)
        ax2.axvline(0, ls=":", color="k")
        ax2.axhline(0, ls=":", color="k")
        plt.colorbar(contour, ax=ax2)

        # plot training loss value
        ax3.plot(its, loss_vals)
        ax3.set_xlim(-1, n_epochs + 1)
        ax3.set_ylim(0, loss_vals[0])
        ax3.set_xlabel("iteration")
        ax3.set_title("loss")

        plt.suptitle(f"{out_name} Iter {it:03d} Accuracy {accuracy * 100:0.02f}")
        plt.savefig(f"{out_name}_{it:03d}.png")
        plt.close(fig)

    train(net, X_train, y_train, out, n_epochs, callback)


if __name__ == '__main__':
    main('softmax')
    main('sparsemax')
    main('entmax15')