utils.py

import numpy as np
import torch
import torch.nn.functional as F
from torch.autograd import Variable

# Graph-based Knowledge Tracing: Modeling Student Proficiency Using Graph Neural Network.
# For more information, please refer to https://dl.acm.org/doi/10.1145/3350546.3352513
# Author: jhljx
# Email: jhljx8918@gmail.com


def build_dense_graph(node_num):
    graph = 1. / (node_num - 1) * np.ones((node_num, node_num))
    np.fill_diagonal(graph, 0)
    graph = torch.from_numpy(graph).float()
    return graph


def sample_gumbel(shape, eps=1e-10):
    """
    NOTE: Stolen from https://github.com/ethanfetaya/NRI/blob/master/utils.py
    Sample from Gumbel(0, 1)
    based on
    https://github.com/ericjang/gumbel-softmax/blob/3c8584924603869e90ca74ac20a6a03d99a91ef9/Categorical%20VAE.ipynb ,
    """
    U = torch.rand(shape).float()
    return - torch.log(eps - torch.log(U + eps))


def gumbel_softmax_sample(logits, tau=1, eps=1e-10, dim=-1):
    """
    NOTE: Stolen from https://github.com/ethanfetaya/NRI/blob/master/utils.py
    Draw a sample from the Gumbel-Softmax distribution
    based on
    https://github.com/ericjang/gumbel-softmax/blob/3c8584924603869e90ca74ac20a6a03d99a91ef9/Categorical%20VAE.ipynb
    """
    gumbel_noise = sample_gumbel(logits.size(), eps=eps)
    if logits.is_cuda:
        gumbel_noise = gumbel_noise.cuda()
    y = logits + Variable(gumbel_noise)
    return F.softmax(y / tau, dim=dim)


def gumbel_softmax(logits, tau=1, hard=False, eps=1e-10, dim=-1):
    """
    NOTE: Stolen from https://github.com/ethanfetaya/NRI/blob/master/utils.py
    Sample from the Gumbel-Softmax distribution and optionally discretize.
    Args:
      logits: [batch_size, n_class] unnormalized log-probs
      tau: non-negative scalar temperature
      hard: if True, take argmax, but differentiate w.r.t. soft sample y
    Returns:
      [batch_size, n_class] sample from the Gumbel-Softmax distribution.
      If hard=True, then the returned sample will be one-hot, otherwise it will
      be a probability distribution that sums to 1 across classes
    Constraints:
    - this implementation only works on batch_size x num_features tensor for now
    based on
    https://github.com/ericjang/gumbel-softmax/blob/3c8584924603869e90ca74ac20a6a03d99a91ef9/Categorical%20VAE.ipynb
    """
    y_soft = gumbel_softmax_sample(logits, tau=tau, eps=eps, dim=dim)
    if hard:
        shape = logits.size()
        _, k = y_soft.data.max(-1)
        # this bit is based on
        # https://discuss.pytorch.org/t/stop-gradients-for-st-gumbel-softmax/530/5
        y_hard = torch.zeros(*shape)
        if y_soft.is_cuda:
            y_hard = y_hard.cuda()
        y_hard = y_hard.zero_().scatter_(-1, k.view(shape[:-1] + (1,)), 1.0)
        # this cool bit of code achieves two things:
        # - makes the output value exactly one-hot (since we add then
        #   subtract y_soft value)
        # - makes the gradient equal to y_soft gradient (since we strip
        #   all other gradients)
        y = Variable(y_hard - y_soft.data) + y_soft
    else:
        y = y_soft
    return y


def kl_categorical(preds, log_prior, concept_num, eps=1e-16):
    kl_div = preds * (torch.log(preds + eps) - log_prior)
    return kl_div.sum() / (concept_num * preds.size(0))


def kl_categorical_uniform(preds, concept_num, num_edge_types, add_const=False, eps=1e-16):
    kl_div = preds * torch.log(preds + eps)
    if add_const:
        const = np.log(num_edge_types)
        kl_div += const
    return kl_div.sum() / (concept_num * preds.size(0))


def nll_gaussian(preds, target, variance, add_const=False):
    # pred: [concept_num, embedding_dim]
    # target: [concept_num, embedding_dim]
    neg_log_p = ((preds - target) ** 2 / (2 * variance))
    if add_const:
        const = 0.5 * np.log(2 * np.pi * variance)
        neg_log_p += const
    return neg_log_p.mean()


# Calculate accuracy of prediction result and its corresponding label
# output: tensor, labels: tensor
def accuracy(output, labels):
    preds = output.max(1)[1].type_as(labels)
    correct = preds.eq(labels.reshape(-1)).double()
    correct = correct.sum()
    return correct / len(labels)