dropout. (LSTM) technique has become a popular time series modeling framework due to its end-to-end modeling, ease of incorporating exogenous variables, and automatic feature extraction abilities. deep convolutional neural networks to annotate plankton data sets in practice. (Doctoral dissertation). Classification with uncertainty using Expected Cross Entropy. Understanding the uncertainty of a neural network’s (NN) predictions is essential for many purposes. At test time, the quality of encoding each sample will provide insight into how close it is to the training set. With highly imbalanced data, we aim to reduce the false positive rate as much as possible to avoid unnecessary on-call duties, while making sure the false negative rate is properly controlled so that real outages will be captured. In order to provide real-time anomaly detection at Uber’s scale, each predictive interval must be calculated within a few milliseconds during the inference stage. A Bayesian Neural Network (BNN) assumes a likelihood of the form y= f(x;W) + , where fis a neural network parametrized by Wand is a normally distributed noise variable. We tackle this challenge by seeking to capture the uncertainty when predicting unseen samples with very different patterns from the training data set and aim to account for this source of uncertainty by training an encoder that extracts the representative features from a time series. The need for UQ is especially acute for neural models, which are becoming increasingly standard yet are challenging to interpret. In the following section, we further interpret these results. OpenCV (for image I/O), and We will be using pytorch for this tutorial along with several standard python packages. in that it captures uncertainty about which neural network. Using the MC dropout technique and model misspecification distribution, we developed a simple way to provide uncertainty estimation for a BNN forecast at scale while providing 95 percent uncertainty coverage. Hopefully we shall be able to shed some light on the situation and address some uncertainty in a deep convolutional neural network. In Figure 2, below, we visualizes the true values and our predictions during the testing period in San Francisco as an example: Through our SMAPE tests, we observed that accurate predictions are achieved for both normal days and holidays (e.g., days with high rider traffic). Although it may be tempting to interpret the values given by the final softmax visually similar to images from classes that it saw during training. . In terms of the actual classification of plankton images, CIFAR-100's apple misclassified as CIFAR-10's automobile class with $p > 0.9$. This paper addresses uncertainty analysis on a novel hybrid double feedforward neural network (HDFNN) model for generating the sediment load prediction interval (PI). While beneficial in other ways, our new model did not offer insights into prediction uncertainty, which helps determine how much we can trust the forecast. adaptively by treating it as part of the model parameter, but this approach requires modifying the training phase. Based on the naive last-day prediction, a quantile random forest is further trained to estimate the holiday lifts (i.e., the ratio to adjust the forecast during holidays). Where is my neural network uncertain or what is my neural network uncertain about? , containing 128, 64, and 16 hidden units, respectively. In recent years, the Long Short Term Memory (LSTM) technique has become a popular time series modeling framework due to its end-to-end modeling, ease of incorporating exogenous variables, and automatic feature extraction abilities. From there, we are able measure the distance between test cases and training samples in the embedded space. network. In an excellent blog In the following sections, we propose a principled solution to incorporate this uncertainty using an encoder-decoder framework. Immediately, we see that the variance is decomposed into two terms:  , which reflects our ignorance regarding the specifications of model parameter W, referred to as the model uncertainty, and , which represents the inherent noise. Another way to frame this approach is that we must first fit a latent embedding space for all training time series using an encoder-decoder framework. namely a batch size of 128, weight decay of 0.0005, and dropout applied in all We also discuss how Uber has successfully applied this model to large-scale time series anomaly detection, enabling us to better accommodate rider demand during high-traffic intervals. By adding MC dropout layers in the neural network, the estimated predictive intervals achieved 100 percent recall rate and a 80.95 percent precision rate. Recently, BNNs have garnered increasing attention as a framework to provide uncertainty estimation for deep learning models, and in in early 2017, Uber began examining how we can use them for time series prediction of extreme events. Such a model how-ever doesnt capture epistemic uncertainty. 0.0001$ and $p = 0.75$, after the $i$th weight update. Uncertainty Estimation Using a Single Deep Deterministic Neural Network sensitive to changes in the input, such that we can reliably detect out of distribution data and avoid mapping out of distribution data to in distribution feature representations — an effect we call feature collapse. 3 O. P. Ogunmolu, X. Gu, S. B. Jiang, and N. R. Gans, “Nonlinear systems identification using deep dynamic neural networks,” CoRR, 2016. One natural follow-up question is whether we can interpret the embedding features extracted by the encoder. How to add uncertainty to your neural network. Finally, an approximate α-level prediction interval is constructed by  , where  is the upper  quantile of a standard normal. By utilizing a large amount of data across numerous dimensions, an LSTM approach can model complex nonlinear feature interactions, which is critical for forecasting extreme events. practice, this mean that we can sample from the distribution by running several Citation: Wang G, Li W, Ourselin S and Vercauteren T (2019) Automatic Brain Tumor Segmentation Based on Cascaded Convolutional Neural Networks With Uncertainty Estimation. Variational open set neural networks We consider three different models for which we investi-gate open set detection based on both prediction uncertainty as well as the EVT based approach. Under the BNN framework, prediction uncertainty can be categorized into three types: model uncertainty, model misspecification, and inherent noise. Using uncertainty information, we adjusted the confidence bands of an internal anomaly detection model to improve precision during high uncertainty events, resulting in a four percent accuracy improvement, a large increase given the number of metrics we track at Uber. softmax output, computed as the mean of the 50 stochastic forward passes. This robust architecture is depicted in Figure 1, below: Prior to fitting the prediction model, we first conduct pre-training to fit an encoder that can extract useful and representative embeddings from a time series. large data sets. Our encoder-decoder framework is constructed with two-layer LSTM cells containing 128 and 32 hidden states, respectively, and the prediction network is composed of three fully connected layers with tanh activation, containing 128, 64, and 16 hidden units, respectively. Uncertainty quantification (UQ) is an important component of molecular property prediction, particularly for drug discovery applications where model predictions direct experimental design and where unanticipated imprecision wastes valuable time and resources. Before we detail our use case, we discuss how we capture prediction uncertainty in BBN frameworks and its three types (model uncertainty, inherent noise, and model misspecification). We further specify the data generating distribution as  . Note that  are independent from . as a machine learning scientist or engineer at Uber! The complete inference algorithm is presented in Figure 1, where the prediction uncertainty contains two terms: (i) the inherent noise level, estimated on a held-out validation set, and (ii) the model and misspecification uncertainties, estimated by the sample variance of a number of stochastic feedforward passes where MC dropout is applied to both the encoder and the prediction network. output to arbitrary values. Ideally, Some possibilities are mentioned below. Table 2, below, reports the empirical coverage of the 95 percent prediction band under three different scenarios: By comparing the Prediction Network and Encoder + Prediction Network scenarios, it is clear that introducing MC dropout to the encoder network drastically improves the empirical coverage—from 78 percent to 90 percent—by capturing potential model misspecification. We measure the standard error across different repetitions, and find that a few hundreds of iterations will suffice to achieve a stable estimation. how the region corresponding to a particular class may be much larger than the Then, we estimate, is an unbiased estimation of the true model, we have, with respect to the training data, which decreases as the training sample size increases, and the bias approaches 0 as the training size N approaches. With only ten classes in CIFAR-10, it is possible that the network does not need to learn highly Neurosci. The best validation loss is 0.547969 and the corresponding As a result, the model could end up with a drastically different estimation of the uncertainty level depending on the prespecified prior. 05/20/2015 ∙ by Charles Blundell, et al. careful not to read too much into this. K. S. Kasiviswanathan, K. P. Sudheer, Uncertainty Analysis on Neural Network Based Hydrological Models Using Probabilistic Point Estimate Method, Proceedings of the International Conference on Soft Computing for Problem Solving (SocProS 2011) December 20-22, 2011, 10.1007/978-81-322-0487-9_36, (377-384), (2012). Bayes by Backprop is an algorithm for training Bayesian neural networks (what is a Bayesian neural network, you ask? model averaging. In order to construct the next few time steps from the embedding, it must contain the most representative and meaningful aspects from the input time series. We extract the cell states of the two LSTM layers, and project as a 2D space for visualization using Principal Component Analysis (PCA), as displayed in Figure 4, below: As evidenced by our visualizations, the strongest pattern we observed is day of the week, where weekdays and weekends from different clusters, with Fridays usually sitting in between. This loss function. of these problems as the topic of modeling uncertainty in deep convolutional If engineering the future of forecasting excites you, consider applying for. paper, 5 in the paper. made with low uncertainty requires further investigation. In this article, we introduce a new end-to-end. At Uber, we track millions of metrics each day to monitor the status of various services across the company. 1 S. Hochreiter and J. Schmidhuber, “Long short-term memory,” Neural Comput., 1997. a Bayesian neural network, where dropout is used in all weight layers to represent weights drawn from As a result, the random dropout in the encoder intelligently perturbs the input in the embedding space, which accounts for potential model misspecification and is further propagated through the prediction network. In a BNN, a prior is introduced for the weight parameters, and the model aims to fit the optimal posterior distribution. This dependency is undesirable in anomaly detection because we want the uncertainty estimation to also have robust, In this scenario, we propose a simple but adaptive approach by estimating the noise level via the residual sum of squares, evaluated on an independent held-out validation set. post, Yarin Gal explains how we can use dropout in a a Bernoulli distribution. Therefore, we propose that a complete measurement of prediction uncertainty should be composed of model uncertainty, model misspecification, and inherent noise level. There are two main challenges we need to address in this application, scalability, and performance, detailed below: In Figure 5, below, we illustrate the precision and recall of this framework on an example data set containing 100 metrics randomly selected with manual annotation available, where 17 of them are true anomalies: Figure 5 depicts four different metrics representative of this framework: (a) a normal metric with large fluctuation, where the observation falls within the predictive interval; (b) a normal metric with small fluctuation following an unusual inflation; (c) an anomalous metric with a single spike that falls outside the predictive interval; and (d) an anomalous metric with two consecutive spikes, also captured by our model. This includes any uncertainty present in the underlying input data, as well as in the model’s final decision. 10 Y. Gal, J. Hron, and A. Kendall, “Concrete dropout,” arXiv preprint arXiv:1705.07832, 2017. We compared the prediction accuracy among four different models: Table 1, below, reports the symmetric mean absolute percentage error (SMAPE) of the four models evaluated against the testing set: In the figure above, we see that using a QRF to adjust for holiday lifts is only slightly better than the naive prediction. Basically, there are two groups of uncertainties and the variance σ² is the sum of both . Above questions are touching on different topics, all under the terminology of “uncertainty.” This post will try to answer the questions above by scratching the surface of the following topics: calibration, uncertainty within a model, Bayesian neural network. Additionally, because of the difficulties involved in Inherent noise, on the other hand, captures the uncertainty in the data generation process and is irreducible. Finally, we estimate the inherent noise level, . At test time, it is straightforward to revert these transformations to obtain predictions at the original scale. Two hyper-parameters need to be specified for inference: the dropout probability, p, and the number of iterations, B. In the scenario where external features are available, these can be concatenated to the embedding vector and passed together to the final prediction network. Neural Network with Output Uncertainty U~ L( U| T, à) Let’s commit to a parametric distribution: U~ è ( U| ä, ê) We will model äas a Neural Network: ä( T, à) We either model êas a scalar parameter under the assumption of homoskestic uncertainty or as a Neural Network: ê( T, à) for heteroskedastic uncertainty … In this article, we introduce a new end-to-end Bayesian neural network (BNN) architecture that more accurately forecasts time series predictions and uncertainty estimations at scale. (as showcased in the bottom panel of Figure 1). In Deep Neural Networks are Easily Fooled: High Confidence Predictions for Kaggle National Data Science Bowl. Algorithm 1, above, illustrates such an inference network using the MC dropout algorithm. Front. The results, while a little Figure 3, below, shows the estimated predictive uncertainty on six U.S. holidays during our testing period: Our research indicates that New Year’s Eve has significantly higher uncertainty than all other holidays. Unrecognizable Images, the authors explain This uncertainty can … ∙ 0 ∙ share . Introducing Base Web, Uber’s New Design System for Building Websites in... Streamific, the Ingestion Service for Hadoop Big Data at Uber Engineering, An Uber Engineer Discusses Cash for India Growth and Beyond. forward passes through the network. This design is inspired from the success of video representation learning using a similar architecture. The following three sections address how Uber handles BNN model uncertainty and its three categories when calculating our time series predictions. For the purpose of this article, we illustrate our BNN model’s performance using the daily completed trips over four years across eight representative cities in U.S. and Canada, including Atlanta, Boston, Chicago, Los Angeles, New York City, San Francisco, Toronto, and Washington, D.C. We use three years of data as the training set, the following four months as the validation set, and the final eight months as the testing set. Footnotes The assessment of uncertainty prediction has become a necessity for most modeling studies within the hydrology community. MC dropout models “epistemic uncertainty”, that is, uncertainty in the parameters. Therefore, we propose that a complete measurement of prediction uncertainty should be composed of model uncertainty, model misspecification, and inherent noise level. This design is inspired from the success of video representation learning using a similar architecture.14. CIFAR-10. We train the model on the 50000 training images and used the 10000 test images An underlying assumption for the model uncertainty equation is that  is generated by the same procedure, but this is not always the case. Here, variational dropout for recurrent neural networks is applied to the LSTM layers in the encoder, and regular dropout is applied to the prediction network. Why these misclassifications are on adversarial examples has shown that Therefore,  provides an asymptotically unbiased estimation on the inherent noise level if the model is unbiased. 8 Y. Gal and Z. Ghahramani, “A theoretically grounded application of dropout in recurrent neural networks,” in Advances in Neural Information Processing Systems 29, 2016. These two sources have been previously recognized with successful application in. 13:56. doi: 10.3389/fncom.2019.00056 Dropout network Gal, Yarin. For the purpose of this article, we illustrate our BNN model’s performance using the daily completed trips over four years across eight representative cities in U.S. and Canada, including Atlanta, Boston, Chicago, Los Angeles, New York City, San Francisco, Toronto, and Washington, D.C. We use three years of data as the training set, the following four months as the validation set, and the final eight months as the testing set. The derivative of forward function is evaluated at w MLP. We call them aleatoric and epistemic uncertainty. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters and data. This research has been accepted as a publication under the title “Deep and Confident Prediction for Time Series at Uber” and will be presented at the IEEE International Conference on Data Mining (ICDM) in New Orleans on November 18, 2017. 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