CIFAR-10. Note that when using LSTM and our model, only one generic model is trained and the neural network is not tuned for any city-specific patterns; nevertheless, we still observe significant improvement on SMAPE across all cities when compared to traditional approaches. Under finite sample scenario. output to arbitrary values. We can capture this uncertainty information with As for the dropout probability, the uncertainty estimation is relatively stable across a range of p, and so we choose the one that achieves the best performance on the validation set. is appropriate, leading to regularisation of the weights and. Sources: Notebook; Repository; I previously wrote about Bayesian neural networks and explained how uncertainty estimates can be obtained for network predictions. on adversarial examples has shown that Through our research, we found that a neural network forecasting model is able to outperform classical time series methods in use cases with long, interdependent time series. In a Bayesian neural network, instead of having fixed : Uses MC dropout in both the encoder and the prediction network, but without the inherent noise level. a Bernoulli distribution. We find that the uncertainty estimation step adds only a small amount of computation overhead and can be conducted within ten milliseconds per metric. provided in CIFAR-10 for validation. 4 N. Laptev, Yosinski, J., Li, L., and Smyl, S. “Time-series extreme event forecasting with neural networks at Uber,” in International Conference on Machine Learning, 2017. 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Inherent noise, on the other hand, captures the uncertainty in the data generation process and is irreducible. In the future, we intend to focus our research in this area on utilizing uncertainty information to conduct neural network debugging during high error periods. In addition, by further accounting for the inherent noise level, the empirical coverage of the final uncertainty estimation, Encoder + Prediction Network + Inherent Noise Level, nicely centers around 95 percent as desired. From there, we are able measure the distance between test cases and training samples in the embedded space. The learning curve for the model trained on the CIFAR-10 training set and evaluated on the CIFAR-10 test set. as a machine learning scientist or engineer at Uber! â What is Bayesian Neural Network? The key to estimating model uncertainty is the posterior distribution, . Nikolay Laptev is a scientist on Uber’s Intelligent Decision Systems team and a postdoctoral scholar at Stanford University. Approximate Variational Inference and as Then the model uncertainty can be approximated by the sample variance. Ideally, when given a new unlabeled data set, we could use this to find images that belong to classes that were not present during training. Then, a prediction network is trained to forecast the next one or more timestamps using the learned embedding as features. Fusion, 2008. However, for the nonlinear neural network, even if the pdf of the neural network weight is Gaussian, the pdf of the output can be nonâGaussian [Aires, 2004]. At test time, it is straightforward to revert these transformations to obtain predictions at the original scale. Risk Assess. from images that occur naturally in that class in the training set. This is particularly challenging in neural networks because of the non-conjugacy often caused by nonlinearities. The result 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. Given a set of N observations, and , Bayesian inference aims to find the posterior distribution over model parameters . The need for UQ is especially acute for neural models, which are becoming increasingly standard yet are challenging to interpret. Finally, we estimate the inherent noise level, . (, Note that this neural network was previously trained on a separate and much larger data set.). Kaggle National Data Science Bowl. If engineering the future of forecasting excites you, consider applying for. uncertainty in a deep convolutional neural network. softmax output, computed as the mean of the 50 stochastic forward passes. (SMAPE) of the four models evaluated against the testing set: Finally, we evaluate the quality of the uncertainty estimation by calibrating the empirical coverage of the predictive intervals. Immediately, we see that the variance is decomposed into two terms: , which reflects our ignorance regarding the specifications of model parameter, , referred to as the model uncertainty, and, An underlying assumption for the model uncertainty equation is that. The Bayesian neural networks can quantify the predictive uncertainty by treating the network parameters as random variables, and perform Bayesian inference on those uncertain parameters conditioned on limited observations. 0.0001$ and $p = 0.75$, after the $i$th weight update. to accurately capture the uncertainty information when dealing with image data. The implementation of a Bayesian neural network with Monte Carlo dropout is too crude of an approximation In Deep Neural Networks are Easily Fooled: High Confidence Predictions for shown below. Model uncertainty, also referred to as epistemic uncertainty, captures our ignorance of the model parameters and can be reduced as more samples are collected. Calibration classes of plankton, given a In the original MC dropout algorithm, this parameter is implicitly inferred from the prior over the smoothness of. Here, we take a principled approach by connecting the encoder-decoder network with a prediction network, and treat them as one large network during inference, as displayed in Algorithm 1 below: Algorithm 1, above, illustrates such an inference network using the MC dropout algorithm. : A naive model that uses the last day’s completed trips as the prediction for the next day. The simplest model is a standard deep neural network classiï¬er. 27(1), 137â146 (2013) CrossRef Google Scholar recognize when an image presented for classification contains a species that model’s predictions. to classes that were not present during training. This is especially important to keep in mind when Specifically, the LSTM cell states are extracted as learned fixed-dimensional embedding. . 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. In classification, the softmax likelihood is often used. 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. Unrecognizable Images, the authors explain 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. For the reasons given above, for any system to be practically useful, it has to. The winning team’s is generated by the same procedure, but this is not always the case. 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.4. 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. 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. In this calculation, the dropout probability is set to be 5 percent at each layer. One natural follow-up question is whether we can interpret the embedding features extracted by the encoder. practice, this mean that we can sample from the distribution by running several The number above each image is the maximum of the In particular, unlike in most data science competitions, the plankton species Quantifying the uncertainty in a deep convolutional neural network’s In the original MC dropout algorithm, this parameter is implicitly inferred from the prior over the smoothness of W. As a result, the model could end up with a drastically different estimation of the uncertainty level depending on the prespecified prior.13 This dependency is undesirable in anomaly detection because we want the uncertainty estimation to also have robust frequentist coverage, yet it is rarely the case that we would know the correct noise level. In this post, we consider the first point above, i.e., how we can quantify the GitHub. (Doctoral dissertation). another class to lead to a high-confidence output. model averaging. From there, we are able measure the distance between test cases and training samples in the embedded space. The intervals are constructed from the estimated predictive variance assuming. of this is that an image may lie within the region assigned to a class and so Two hyper-parameters need to be specified for inference: the dropout probability, p, and the number of iterations, B. Long overlooked by most researchers, model misspecification captures the scenario where testing samples come from a different population than the training set, which is often the case in time series anomaly detection. In an excellent blog A few hundred stochastic passes are executed to calculate the prediction uncertainty, which is updated every few minutes for each metric. The final inference algorithm in our BNN model combines inherent noise estimation with MC dropout and is presented in Algorithm 2, below: In the following section, we take our understanding of BNNs and apply it to Uber’s use case by introducing our time series prediction model. Next, within each sliding window, the first day is subtracted from all values so that trends are removed and the neural network is trained for the incremental value. As a result, the model could end up with a drastically different estimation of the uncertainty level depending on the prespecified prior. For special event uncertainty estimation, we found New Year’s Eve to be the most uncertain time. Hopefully we shall be able to shed some light on the situation and address some Front. 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.11,12. 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. Neurosci. This pattern is consistent with our previous neural network forecasts, where New Year’s Eve is usually the most difficult day to predict. The learning rate is initially set to $l = 0.01$, and We thus con- Confidence check 13:56. doi: 10.3389/fncom.2019.00056 solution is of particular paper, Here, the mean standard deviation (STD) ( = ) is estimated by â¦ Therefore, we propose that a complete measurement of prediction uncertainty should be composed of model uncertainty, model misspecification, and inherent noise level. Res. On Mixup Training: Improved Calibration and Predictive Uncertainty for Deep Neural Networks Sunil Thulasidasanâ¤â¤ , 1 2, Gopinath Chennupati , Jeff Bilmes , Tanmoy Bhattacharya 1, Sarah Michalak 1Los Alamos National Laboratory 2Department of Electrical and Computer Engineering, University of Washington Abstract Mixup [40] is a recently proposed method for training deep neural networks One important application of uncertainty estimation is to provide real-time anomaly detection and deploy alerts for potential outages and unusual behaviors. 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. Finally, an approximate α-level prediction interval is constructed by. ... but what Iâm trying to say is that isnât hard to obtain a distribution from a neural network, you just have to do things in a different way. 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. It is clear that the convolutional neural network has trouble with images that appear at least somewhat For the purpose of our model, we denote a neural network as function , where f captures the network architecture, and W is the collection of model parameters. Now that we have a deep convolutional network trained on the ten classes of The assessment of uncertainty prediction has become a necessity for most modeling studies within the hydrology community. Uncertainty estimation in deep learning remains a less trodden but increasingly important component of assessing forecast prediction truth in LSTM models. In other words, the neural network also predicts when it fails by assigning high uncertainty to its wrong predictions. All of the code used in the above experiment is available on Above questions are touching on different topics, all under the terminology of âuncertainty.â 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. distribution. This design is inspired from the success of video representation learning using a similar architecture.14. Next, we showcase our model’s performance on a moderately sized data set of daily trips processed by the Uber platform by evaluating the prediction accuracy and the quality of uncertainty estimation during both holidays and non-holidays. We measure the standard error across different repetitions, and find that a few hundreds of iterations will suffice to achieve a stable estimation. deep convolutional neural network to get uncertainty information from the that researchers wish to label are not fixed. 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. We run $T=50$ stochastic forward passes through the network and take In practice, we find that the uncertainty estimation is usually robust within a reasonable range of, Another way to frame this approach is that we must first fit a latent embedding space for all training time series using an. Similar concepts have gained attention in deep learning under the concept of adversarial examples in computer vision, but its implication in prediction uncertainty remains relatively unexplored. How to add uncertainty to your neural network. Understanding the uncertainty of a neural networkâs (NN) predictions is essential for many purposes. Although it may be tempting to interpret the values given by the final softmax After the encoder-decoder is pre-trained, it is treated as an intelligent feature-extraction blackbox. extend its classification capabilities to include this new class. The intervals are constructed from the estimated predictive variance assuming Gaussian distribution. neural networks is explored more in the literature. 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. In anomaly detection, for instance, it is expected that certain time series will have patterns that differ greatly from the trained model. GitHub. collecting high-quality images of plankton, a large training set is often In the scenario where external features are available, these can be concatenated to the embedding vector and passed together to the final prediction network. 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. We measure the standard error across different repetitions, and find that a few hundreds of iterations will suffice to achieve a stable estimation. With only ten classes in CIFAR-10, it is possible that the network does not need to learn highly 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). vision, I am trying to help plankton researchers accelerate the annotation of layer of a convolutional neural network as confidence scores, we need to be As for the number of iterations, , the standard error of the estimated prediction uncertainty is proportional to. 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. Citation: Wang G, Li W, Ourselin S and Vercauteren T (2019) Automatic Brain Tumor Segmentation Based on Cascaded Convolutional Neural Networks With Uncertainty Estimation. 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. There have been various research efforts on approximate inference in deep learning, which we follow to approximate model uncertainty using the Monte Carlo dropout (MC dropout) method.7,8, The algorithm proceeds as follows: given a new input , we compute the neural network output with stochastic dropouts at each layer; in other words, randomly drop out each hidden unit with certain probability p. The stochastic feedforward is repeated B times, and we obtain . . Bayesian neural networks by controlling the learning rate of each parameter as a function of its uncertainty. Classification with uncertainty using Expected Cross Entropy. From the embedded state, the decoder LSTM then constructs the following F timestamps , which are also guided via (as showcased in the bottom panel of Figure 1). ... principled and backpropagation-compatible algorithm for learning a probability distribution on the weights of a neural network, called Bayes by Backprop. Table 2, below, reports the empirical coverage of the 95 percent prediction band under three different scenarios: : Uses only model uncertainty estimated from MC dropout in the prediction network with no dropout layers in the encoder. Environ. In this work, a deep encoderâdecoder network is proposed to empower the UQ analysis of civil structures with spatially varying system properties. The key to estimating model uncertainty is the posterior distribution , also referred to as Bayesian inference. Intuitively, the more uncertain a parameter is, the We will be using pytorch for this tutorial along with several standard python packages. 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. 7,9,11, & [13] Y. Gal and Z. Ghahramani, “Dropout as a bayesian approximation: Representing model uncertainty in deep learning,” in international conference on machine learning, 2016, pp. Specifically, let, be an independent validation set. As for the dropout probability, the uncertainty estimation is relatively stable across a range of. 10 Y. Gal, J. Hron, and A. Kendall, “Concrete dropout,” arXiv preprint arXiv:1705.07832, 2017. 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. University of Cambridge (2016). In This design is inspired from the success of video representation learning using a similar architecture. weights, each weight is drawn from some distribution. GitHub. Footnotes Model uncertainty, also referred to as epistemic uncertainty, captures our ignorance of the model parameters and can be reduced as more samples are collected. Furthermore, they have successfully proposed novel adaptive neural network controllers for the robots with constraints [42] , where the â¦ MIT neural network knows when it can be trusted Shane McGlaun - Nov 23, 2020, 7:47am CST Deep learning neural networks are artificial intelligence systems that are â¦ We call them aleatoric and epistemic uncertainty. In particular, the variance quantifies the prediction uncertainty, which can be broken down using the law of total variance: . predictions as described in the blog post mentioned above would allow us to At Uber, we track millions of metrics each day to monitor the status of various services across the company. Figure 1 illustrates how posterior distributions evolve for certain and uncertain weight distributions while learning two consecutive tasks. 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). 1 S. Hochreiter and J. Schmidhuber, “Long short-term memory,” Neural Comput., 1997. 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. The uncertainty estimation is to the relevant species may change as they are influenced by seasonal and environmental disturbance quantifies... Is available on GitHub short-term memory, ” arXiv preprint arXiv:1705.07832, 2017 output, computed as the mean the... Of intrinsic highâdimensional mapping Uber, we estimate the inherent noise, provides an asymptotically unbiased estimation on the hand... Likelihood is often used over weights p ( WjD ) to predict generation process is... Must address is how to combine this uncertainty with model uncertainty is upper. ÂEpistemic uncertaintyâ, that is generated by the encoder and the variance Ï² is posterior! Is whether we can sample from the last-day forecast multiplied by the variance... 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Model trained on a separate and much larger data set. ), provides an asymptotically unbiased estimation on validation!