Deep Learning the Bayesian way :

Moving Towards safer AI

ayush0016

Uncertainty

What and Why ?

Aleatoric Uncertainty

A measure of what can not be understood from data.

Occlusions, lack of visual features, over/under exposed areas (glare & shading).

what and why ?

Epistemic Uncertainty

Measure of what model doesn’t know due to lack of training data.

what and why ?

Bayesian Deep Learning

A field at the intersection between Deep learning and Bayesian probability theory

Deep Neural Networks

Bayesian Neural Network

Bayes Theorem

Approximation Techniques

Variational Inference
MC Dropout

Variational Inference

Variational inference is a Bayesian approach to estimate posteriors using an arbitrary distribution

Monte Carlo Dropout

Bayesian interpretation of the regularization technique known as “dropout”

Dropout

What and Why ?

Regularization technique to prevent "overfitting"

Training Phase : for each iteration, ignore (zero out) a random fraction, p, of nodes (and corresponding activations).

Testing Phase : Use all activations, but reduce them by a factor p (to account for the missing activations during training).

MC Dropout Key Idea

Dropout could be used to perform variational inference where the variational distribution is from a Bernoulli distribution (where the states are “on” and “off”).

Bernoulli distribution


class LeNet_dropout(nn.Module):
    def __init__(self):
        super(LeNet_dropout, self).__init__()
        self.conv1 = nn.Conv2d(1, 10, kernel_size=5)
        self.conv2 = nn.Conv2d(10, 20, kernel_size=5)
        self.fc1 = nn.Linear(320, 50)
        self.fc2 = nn.Linear(50, 10)

    def forward(self, x):
        x = F.relu(F.max_pool2d(F.dropout(self.conv1(x), training=True), 2))
        x = F.relu(F.max_pool2d(F.dropout(self.conv2(x), training=True), 2))
        x = x.view(-1, 320)
        x = F.relu(self.fc1(x))
        x = F.dropout(x, training=True)
        x = self.fc2(x)
        return x


def train(model, opt, epoch):
    model.train()
    lr = args.lr * (0.1 ** (epoch // 10))
    opt.param_groups[0]['lr'] = lr
    for batch_idx, (data, target) in enumerate(train_loader):
        if args.cuda:
            data, target = data.cuda(), target.cuda()
        data, target = Variable(data), Variable(target)
        opt.zero_grad()
        output = model(data)
        loss = F.nll_loss(F.log_softmax(output), target)
        loss.backward()
        opt.step()
        if batch_idx % args.log_interval == 0:
            print('Train Epoch: {} [{}/{} ({:.0f}%)] lr: {}\tLoss: {:.6f}'
                  .format(epoch, batch_idx * len(data),
                          len(train_loader.dataset),
                          100. * batch_idx / len(train_loader),
                          lr, loss.data[0]))


def mcdropout_test(model):
    model.train()
    test_loss = 0
    correct = 0
    T = 100
    for data, target in test_loader:
        if args.cuda:
            data, target = data.cuda(), target.cuda()
        data, target = Variable(data, volatile=True), Variable(target)
        output_list = []
        for i in xrange(T):
            output_list.append(torch.unsqueeze(model(data), 0))
        output_mean = torch.cat(output_list, 0).mean(0)
        test_loss += F.nll_loss(F.log_softmax(output_mean), target, size_average=False).data[0]  # sum up batch loss
        pred = output_mean.data.max(1, keepdim=True)[1]  # get the index of the max log-probability
        correct += pred.eq(target.data.view_as(pred)).cpu().sum()

    test_loss /= len(test_loader.dataset)
    print('\nMC Dropout Test set: Average loss: {:.4f}, Accuracy: {}/{} ({:.2f}%)\n'.format(
        test_loss, correct, len(test_loader.dataset),
        100. * correct / len(test_loader.dataset)))

Thank You !

Questions ?

https://github.com/ayush1997/bdl

https://slides.com/ayush1997/ml-3/

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