Deep Learning is a consolidated, state-of-the-art Machine Learning tool to fit a function (y=f(x) ) when provided with large data sets of examples ( (x_i, y_i) ). However, in regression tasks, the straightforward application of Deep Learning models provides a point estimate of the target. In addition, the model does not take into account the uncertainty of a prediction. This represents a great limitation for tasks where communicating an erroneous prediction carries a risk. In this paper we tackle a real-world problem of forecasting impending financial expenses and incomings of customers, while displaying predictable monetary amounts on a mobile app. In this context, we investigate if we would obtain an advantage by applying Deep Learning models with a Heteroscedastic model of the variance of a network’s output. Experimentally, we achieve a higher accuracy than non-trivial baselines. More importantly, we introduce a mechanism to discard low-confidence predictions, which means that they will not be visible to users. This should help enhance the user experience of our product.
In the case of using Deep Learning for classification, it is common to use a Softmax activation function in the last layer @cite_6 . This yields a non-calibrated probability score which can be used heuristically as the confidence score or calibrated to a true probability @cite_10 . However, in the case of regression, the output variables are not class labels and it is not possible to obtain such scores. On the other hand, @cite_13 introduces the idea of combining different kinds of Aleatoric and Epistemic uncertainties. Nevertheless, as we saw in Table , the use of Epistemic uncertainty for our problem worsens the accuracy and the general performance of the model.
@cite_13 @cite_10 @cite_6
2950517871 2952053192 183625566
There are two major types of uncertainty one can model. Aleatoric uncertainty captures noise inherent in the observations. On the other hand, epistemic uncertainty accounts for uncertainty in the model -- uncertainty which can be explained away given enough data. Traditionally it has been difficult to model epistemic uncertainty in computer vision, but with new Bayesian deep learning tools this is now possible. We study the benefits of modeling epistemic vs. aleatoric uncertainty in Bayesian deep learning models for vision tasks. For this we present a Bayesian deep learning framework combining input-dependent aleatoric uncertainty together with epistemic uncertainty. We study models under the framework with per-pixel semantic segmentation and depth regression tasks. Further, our explicit uncertainty formulation leads to new loss functions for these tasks, which can be interpreted as learned attenuation. This makes the loss more robust to noisy data, also giving new state-of-the-art results on segmentation and depth regression benchmarks. We consider the two related problems of detecting if an example is misclassified or out-of-distribution. We present a simple baseline that utilizes probabilities from softmax distributions. Correctly classified examples tend to have greater maximum softmax probabilities than erroneously classified and out-of-distribution examples, allowing for their detection. We assess performance by defining several tasks in computer vision, natural language processing, and automatic speech recognition, showing the effectiveness of this baseline across all. We then show the baseline can sometimes be surpassed, demonstrating the room for future research on these underexplored detection tasks. We are concerned with feed-forward non-linear networks (multi-layer perceptrons, or MLPs) with multiple outputs. We wish to treat the outputs of the network as probabilities of alternatives (e.g. pattern classes), conditioned on the inputs. We look for appropriate output non-linearities and for appropriate criteria for adaptation of the parameters of the network (e.g. weights). We explain two modifications: probability scoring, which is an alternative to squared error minimisation, and a normalised exponential (softmax) multi-input generalisation of the logistic non-linearity. The two modifications together result in quite simple arithmetic, and hardware implementation is not difficult either. The use of radial units (squared distance instead of dot product) immediately before the softmax output stage produces a network which computes posterior distributions over class labels based on an assumption of Gaussian within-class distributions. However the training, which uses cross-class information, can result in better performance at class discrimination than the usual within-class training method, unless the within-class distribution assumptions are actually correct.