About regression loss for steering prediction

[godspeed1989]

Thanks for your great work.
In your paper:

To train DroNet for steering prediction, did you just use MSE for supervision?

Can you paste the part of code to calculate training loss and evaluation metrics?
The release code just contains SoftmaxHeteroscedasticLoss for classification in CIFAR.

[mattiasegu]

Hi @godspeed1989

I am glad to know that you appreciate our work!

The loss to train our network is literally torch.nn.functional.mse(outputs,targets), plus L2 regularization on model weights.
To evaluate the network, we use RMSE, EVA and NLL.

EVA:

def explained_variance_1d(ypred,y):
    """
    Var[ypred - y] / var[y].
    https://www.quora.com/What-is-the-meaning-proportion-of-variance-explained-in-linear-regression
    """
    assert y.ndim == 1 and ypred.ndim == 1
    vary = np.var(y)
    return np.nan if vary==0 else 1 - np.var(y-ypred)/vary

def compute_explained_variance(predictions, real_values):
    """
    Computes the explained variance of prediction for each
    steering and the average of them
    """
    assert np.all(predictions.shape == real_values.shape)
    ex_variance = explained_variance_1d(predictions, real_values)
    print("EVA = {}".format(ex_variance))
    return ex_variance

RMSE:

def compute_rmse(predictions, real_values):
    assert np.all(predictions.shape == real_values.shape)
    mse = np.mean(np.square(predictions - real_values))
    rmse = np.sqrt(mse)
    print("RMSE = {}".format(rmse))
    return rmse

Log-Likelihood:

def log_likelihood(y_pred, y_true, sigma):
    y_true = torch.Tensor(y_true)
    y_pred= torch.Tensor(y_pred)
    sigma = torch.Tensor(sigma)
    
    dist = torch.distributions.normal.Normal(loc=y_pred, scale=sigma)
    ll = torch.mean(dist.log_prob(y_true))
    ll = np.asscalar(ll.numpy())
    return ll

I hope these functions can be helpful!
Cheers

[godspeed1989]

Hi @mattiasegu
Thanks for your reply.
One more question ;)
I am still confusing about how we can estimate aleatoric uncertainty (i.e., output var) without a specific supervision.
The output var is used in SoftmaxHeteroscedasticLoss.

In my mind, the steering prediction is a regression problem.
From ADF's original paper Lightweight Probabilistic Deep Networks, there is a probabilistic analog for regression by minimizing negative log likelihood:

So, why can't we add this as a part of the learning target?