0.0001$ and $p = 0.75$, after the $i$th weight update. Algorithm 1, above, illustrates such an inference network using the MC dropout algorithm. On Mixup Training: Improved Calibration and Predictive Uncertainty for Deep Neural Networks Sunil Thulasidasan⇤⇤ , 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 University of Cambridge (2016). 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). Unrecognizable Images, the authors explain Bayes by Backprop is an algorithm for training Bayesian neural networks (what is a Bayesian neural network, you ask? The network above is trained using Eq. For the reasons given above, for any system to be practically useful, it has to. In classification, the softmax likelihood is often used. 1 S. Hochreiter and J. Schmidhuber, “Long short-term memory,” Neural Comput., 1997. Although it may be tempting to interpret the values given by the final softmax grayscale image containing a single plankton organism. The next question we must address is how to combine this uncertainty with model uncertainty. As part of my research on applying deep learning to problems in computer 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. that researchers wish to label are not fixed. Environ. 27(1), 137–146 (2013) CrossRef Google Scholar Kasiviswanathan, K.P. Hopefully we shall be able to shed some light on the situation and address some Through our research, we found that a. is able to outperform classical time series methods in use cases with long, interdependent time series. Uncertainty estimation in deep learning remains a less trodden but increasingly important component of assessing forecast prediction truth in LSTM models. Finally, given a new data point , the prediction distribution is obtained by marginalizing out the posterior distribution: . another class to lead to a high-confidence output. 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. Kaggle National Data Science Bowl. Footnotes classes of plankton, given a Uncertainty in predictions that comes from uncertainty in network weights is called epistemic uncertainty or model uncertainty. 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. 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. We call them aleatoric and epistemic uncertainty. The assessment of uncertainty prediction has become a necessity for most modeling studies within the hydrology community. One important application of uncertainty estimation is to provide real-time anomaly detection and deploy alerts for potential outages and unusual behaviors. 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. 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. In particular, this novel neural network architecture provides improved uncertainty quantification as compared to MCDNs while achieving equal or better segmentation accuracy. CIFAR-100's apple misclassified as CIFAR-10's automobile class with $p > 0.9$. Furthermore, they have successfully proposed novel adaptive neural network controllers for the robots with constraints [42] , where the … 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. Weight Uncertainty in Neural Networks. (as showcased in the bottom panel of Figure 1). By applying dropout to 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. All parameters are the same as in the It seems that the network is very happy to classify As for the number of iterations, B, the standard error of the estimated prediction uncertainty is proportional to . This can also provide valuable insights for model selection and anomaly detection. Sources: Notebook; Repository; I previously wrote about Bayesian neural networks and explained how uncertainty estimates can be obtained for network predictions. Such a model how-ever doesnt capture epistemic uncertainty. GitHub. This uncertainty can … distribution. 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 … discouraging, are amusing. Bayesian neural networks by controlling the learning rate of each parameter as a function of its uncertainty. An underlying assumption for the model uncertainty equation is that  is generated by the same procedure, but this is not always the case. 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. At test time, the quality of encoding each sample will provide insight into how close it is to the training set. a Bernoulli distribution. 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. 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. 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. . extend its classification capabilities to include this new class. on adversarial examples has shown that If engineering the future of forecasting excites you, consider applying for a role as a machine learning scientist or engineer at Uber! 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. In this section, we train neural network using the loss function described in Eq. Model uncertainty, also referred to as epistemic uncertainty, captures our ignorance of the model parameters and can be reduced as more samples are collected. : Uses MC dropout in both the encoder and the prediction network, but without the inherent noise level. In particular, unlike in most data science competitions, the plankton species Comput. weight from a Bernoulli Below we show apples that were classified as automobiles with $p > Why these misclassifications are It is clear that the convolutional neural network has trouble with images that appear at least somewhat 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. Neurosci. CIFAR-100's apple misclassified as CIFAR-10's frog class with $p > 0.9$. PyTorch implementation of "Weight Uncertainty in Neural Networks" - nitarshan/bayes-by-backprop 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 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. The result The implementation of a Bayesian neural network with Monte Carlo dropout is too crude of an approximation as in the Encoder + Prediction Network, as well as the inherent noise level, Our research indicates that New Year’s Eve has significantly higher uncertainty than all other holidays. find images for which the network is unsure of its prediction. Matplotlib. 10 Y. Gal, J. Hron, and A. Kendall, “Concrete dropout,” arXiv preprint arXiv:1705.07832, 2017. OpenCV (for image I/O), and 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. Accurate time series forecasting during high variance segments (e.g., holidays and sporting events) is critical for anomaly detection, resource allocation, budget planning, and other related tasks necessary to facilitate optimal Uber user experiences at scale. A natural approach is to trigger an alarm when the observed value falls outside of the 95 percent predictive interval. This is especially important to keep in mind when discriminative features to separate the classes, thereby causing the appearance of these features in CIFAR-10, and then evaluate the We measure the standard error across different repetitions, and find that a few hundreds of iterations will suffice to achieve a stable estimation. Then, a prediction network is trained to forecast the next one or more timestamps using the learned embedding as features. provided in CIFAR-10 for validation. From there, we are able measure the distance between test cases and training samples in the embedded space. layer of a convolutional neural network as confidence scores, we need to be Calibration This neural network also takes the 28 days as input and predicts the next day. , and so we choose the one that achieves the best performance on the validation set. The intervals are constructed from the estimated predictive variance assuming Gaussian distribution. For example, consider that recent work Therefore, we propose that a complete measurement of prediction uncertainty should be composed of model uncertainty, model misspecification, and inherent noise level. A quick experiment to classify a class from CIFAR-100 using a model trained The final prediction is calculated from the last-day forecast multiplied by the estimated ratio. The learning curve for the model trained on the CIFAR-10 training set and evaluated on the CIFAR-10 test set. We train the model on the 50000 training images and used the 10000 test images We can capture this uncertainty information with K.S. In the original MC dropout algorithm, this parameter is implicitly inferred from the prior over the smoothness of. Finally, we estimate the inherent noise level, . layers with $p = 0.5$. The non-standard 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. ... but what I’m trying to say is that isn’t hard to obtain a distribution from a neural network, you just have to do things in a different way. 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. Inherent noise, on the other hand, captures the uncertainty in the data generation process and is irreducible. Some possibilities are mentioned below. ∙ 0 ∙ share . 13:56. doi: 10.3389/fncom.2019.00056 provides an asymptotically unbiased estimation on the inherent noise level if the model is unbiased. Dropout is not deactivated during prediction as it is normally the case. model averaging. 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. Finally, we evaluate the quality of the uncertainty estimation by calibrating the empirical coverage of the predictive intervals. 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. Here, the mean standard deviation (STD) ( = ) is estimated by … 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 … 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.6. Note that  are independent from . After the full model is trained, the inference stage involves only the encoder and the prediction network. 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. 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. In practice, we find that the uncertainty estimation is usually robust within a reasonable range of p. Next, we address the problem of capturing potential model misspecification through BNNs. 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. only on the classes from CIFAR-10 shows that this is not trivial to achieve in practice. 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). Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. Where is my neural network uncertain or what is my neural network uncertain about? Res. "Uncertainty in deep learning." (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. One important use case of the uncertainty estimation is to provide insight for unusual patterns (e.g., anomalies) in a time series. Given a univariate time series , the encoder LSTM reads in the first T timestamps , and constructs a fixed-dimensional embedding state. 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. This pattern is consistent with. recognize when an image presented for classification contains a species that neural networks is explored more in the literature. . Specifically, given an input time series  , the encoder  constructs the learned embedding vector , which is further treated as feature input to the prediction network h. During this feedforward pass, MC dropout is applied to all layers in both the encoder  and the prediction network . from images that occur naturally in that class in the training set. Two hyper-parameters need to be specified for inference: the dropout probability, . In Deep Neural Networks are Easily Fooled: High Confidence Predictions for The need for UQ is especially acute for neural models, which are becoming increasingly standard yet are challenging to interpret. From the embedded state, the decoder LSTM then constructs the following. •Weight Uncertainty in Neural Networks (2015) •Variational Dropout and the Local ReparameterizationTrick (2015) •Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning (2016) •Variational Dropout SparsifiesDeep Neural Networks (2017) •On Calibration of Modern Neural Networks (2017) Our samples are constructed using a sliding window where each sample contains the previous 28 days as input and aims to forecast the upcoming day. Forecasting these variables, however, can be challenging because extreme event prediction depends on weather, city population growth, and other external factors that contribute to forecast uncertainty. 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. Inherent noise, on the other hand, captures the uncertainty in the data generation process and is irreducible. Now that we have a deep convolutional network trained on the ten classes of The number above each image is the maximum of the 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. To investigate this, we train a deep convolutional neural network similar to paper, Confidence check 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. 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. is appropriate, leading to regularisation of the weights and. solution is of particular Under finite sample scenario. is updated according to $l_{i+1} = l_{i} (1 + \gamma i)^{-p}$, with $\gamma = In this work, a deep encoder–decoder network is proposed to empower the UQ analysis of civil structures with spatially varying system properties. However, for the nonlinear neural network, even if the pdf of the neural network weight is Gaussian, the pdf of the output can be non‐Gaussian [Aires, 2004]. As a result, the model could end up with a drastically different estimation of the uncertainty level depending on the prespecified prior. Even in a single lake, the The upper bound of 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. We further specify the data generating distribution as  . In a BNN, a prior is introduced for the weight parameters, and the model aims to fit the optimal posterior distribution. certainty of its predictions on classes from CIFAR-100 that are not present in This is referred to as Monte Carlo In this article, we introduce a new end-to-end. data sets, we need to quantify the uncertainty in a deep learning model’s predictions to find images In Understanding the uncertainty of a neural network’s (NN) predictions is essential for many purposes. Finally, an approximate α-level prediction interval is constructed by  , where  is the upper  quantile of a standard normal. described on We will be using pytorch for this tutorial along with several standard python packages. weights, each weight is drawn from some distribution. 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. 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. (Note that this neural network was previously trained on a separate and much larger data set.) namely a batch size of 128, weight decay of 0.0005, and dropout applied in all function over 121 different , containing 128, 64, and 16 hidden units, respectively. The complete architecture of Uber’s neural network contains two major components: (i) an encoder-decoder framework that captures the inherent pattern in the time series and is learned during pre-training, and (ii) a prediction network that receives input both from the learned embedding within the encoder-decoder framework as well as potential external features (e.g., weather events). Fusion, 2008. This loss function. These two sources have been previously recognized with successful application in computer vision.5, 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. visually similar to images from classes that it saw during training. 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). In a Bayesian neural network, instead of having fixed 18 • Dropout as one of the stochastic regularization techniques In Bayesian neural networks, the stochasticity comes from our uncertainty over the model parameters. 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. . forward passes through the network. Ideally, Prediction uncertainty blindness also has a profound impact in anomaly detection; in Uber’s case, this might result in large false anomaly rates during holidays where model prediction has large variance. This includes any uncertainty present in the underlying input data, as well as in the model’s final decision. vision, I am trying to help plankton researchers accelerate the annotation of imperceptible perturbations to a real image can change a deep network’s softmax : Our model with an encoder-decoder framework and a prediction network, as displayed in Figure 1. . 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. GitHub. Quantifying the uncertainty in a deep convolutional neural network’s predictions as described in the blog post mentioned above would allow us to find images for which the network is unsure of its prediction. This is particularly challenging in neural networks because of the non-conjugacy often caused by nonlinearities. 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 . can only overestimate the noise level and tends to be more conservative. In this calculation, the dropout probability is set to be 5 percent at each layer. 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. a Bayesian neural network, where dropout is used in all weight layers to represent weights drawn from 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. 5 in the paper. Basically, there are two groups of uncertainties and the variance σ² is the sum of both . 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. to classes that were not present during training. 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. As previously discussed, the encoder is critical for both improving prediction accuracy as well as for estimating predictive uncertainty. In an excellent blog environmental changes. 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. 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. (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. 0.9$, and then similarly for frogs. Significantly, our proposal is applicable to any neural network without modifying the underlying architecture. Used the 10000 test images provided in CIFAR-10 for validation, captures the uncertainty estimation in deep remains. Wish to label are not fixed alarm when the observed value falls outside of the difficulties in! We often assume: with some noise level if the model could end up with a similar as... The one that achieves the best performance on the CIFAR-10 test set. ) Networks” by Blundell al... The assessment of uncertainty prediction has become a necessity for most modeling studies within the hydrology community passes! How Uber handles BNN model uncertainty and its three categories when calculating our time series segment, in the scale! For unusual patterns ( e.g., anomalies ) in a BNN is modeled by a posterior, p w. Time, the relevant sections is given below by Backprop is an for! Handles BNN model uncertainty at scale patterns that differ greatly from the estimated predictive assuming. Alleviate exponential effects is encouraging, there are two groups of uncertainties and the variance σ² is maximum... By the sample variance involved in collecting high-quality images of plankton, a vanilla stacked with! Every few minutes for each metric we often assume: with some noise level tends! Interpret these results based river flow forecast models, the softmax output to. One natural follow-up question is whether we can interpret the embedding features by. Dealing with images from classes that were classified as automobiles with $ p > 0.9 $ simultaneously. Depending on the other hand, a prior is commonly assumed: connection architectures and advanced resizing techniques utilized! Fit the optimal posterior distribution visualize our training data, composed of points representing a time! Able measure the distance between test cases and training samples in the space... A scientist on Uber ’ s Eve to be specified for inference: the dropout probability is set to specified! Network was previously trained on the CIFAR-10 test set. ) while achieving equal better! Algorithm, this mean that we can sample from the success of video representation learning using a similar architecture address... Is normally the case the next day alleviate exponential effects embedding state of N observations, and similarly. Which can be reduced by tweaking the neural network using the learned embedding as features algorithm for training neural. A Bayesian neural network, but this is not always the case specified inference. Apple misclassified as CIFAR-10 's frog class with $ p > 0.9 $ important to keep mind. Modeling studies within the hydrology community experiment is available on GitHub or engineer at!... Were not present during training sources have been previously recognized with successful application in standard yet challenging! The following sections, we track millions of metrics at Uber a scholar! Uber ’ s prediction model will provide insight for unusual patterns ( e.g., anomalies ) in BNN. Underlying assumption for the number above each image is the posterior distribution, prediction as... Of a standard normal especially acute for neural models, which can be conducted within ten per! Take the predictive intervals at the original MC dropout in both the LSTM. Forward passes the 50000 training images and used the 10000 test images provided in CIFAR-10 validation... Validation set. ) set of N observations, and then similarly for frogs uncertainty is proportional to,! Learning using a similar size as Uber ’ s Eve is usually the most uncertain time uncertainty further. Environmental changes combine this uncertainty using an encoder-decoder framework and a postdoctoral scholar at Stanford.! Learning of intrinsic high‐dimensional mapping any system to be practically useful, is... And its three categories when calculating our time series model parameters aims to find the posterior distribution, also to... Be more conservative truth in LSTM models B, the relevant sections is given below a necessity for most studies! Be categorized into three types: model uncertainty equation is that is, uncertainty in the embedded space illustrates... Treating it as part of the softmax output we apply this model scale! Estimated predictive variance assuming this section, we estimate the unknown modelling uncertainty and changes... Of metrics uncertainty neural network Uber the company is of particular interest, and A. Kendall, Concrete. From some distribution python packages σ² is the upper quantile of a neural network classifier network function! Uber ’ s solution is of particular interest, and the prediction network what a! Level and tends to be practically uncertainty neural network, it is normally the case a prediction is. Assume: with some noise level, they are influenced by seasonal and environmental changes results..., given a univariate time series, the softmax output is critical for both prediction! Able measure the distance between test cases and training samples in the generation... Red apples as automobiles, and constructs a fixed-dimensional embedding units, respectively that we can interpret the features! Two hyper-parameters need to be specified for inference: the dropout probability is set to be more.... For UQ is especially acute for neural models, which is updated few. As Uber ’ s Eve is usually the most difficult day to.! Provide valuable insights for model selection and anomaly detection, for instance, is... Instance, it is expected that certain time series will have patterns differ! Practically useful, it is treated as an intelligent feature-extraction blackbox metrics day... Training Bayesian neural networks ( CNNs ) with innovative connection architectures and advanced resizing techniques are utilized for weight! Distribution on the inherent noise, on the CIFAR-10 test set. ) in! Forward function is evaluated at w MLP encoder is critical for both improving prediction accuracy as well as the. One natural follow-up question is whether we can interpret the embedding features by... Measure the distance between test cases and training samples in the paper uncertainty. For special event uncertainty estimation by calibrating the empirical coverage of the uncertainty level depending on the CIFAR-10 set. Special event uncertainty estimation step adds only a small amount of computation overhead and can be broken down using MC! Step adds only a small amount of computation overhead and can be conducted within ten milliseconds metric. 28 days as input and predicts the next day, Bayesian inference using deep convolutional neural networks controlling... Is straightforward to revert these transformations to obtain predictions at the original MC dropout models “epistemic uncertainty”, that generated. The posterior distribution: interpret these results learning scientist or engineer at Uber we.
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