link. I could also unfreeze the Resnet50 layers and train those as well. Learn more. This is a common procedure for every kind of model. Our goal here is to find the best combination of those hyperparameter values. In September 2019, Tensorflow 2.0 was released with major improvements, notably in user-friendliness. When setting up a Bayesian DL model, you combine Bayesian statistics with DL. The 'distorted average change in loss' should should stay near 0 as the variance increases on the right half of Figure 1 and should always increase when the variance increases on the right half of Figure 1. Learn to improve network performance with the right distribution for different data types, and discover Bayesian variants that can state their own uncertainty to increase accuracy. Before diving into the specific training example, I will cover a few important high level concepts: I will then cover two techniques for including uncertainty in a deep learning model and will go over a specific example using Keras to train fully connected layers over a frozen ResNet50 encoder on the cifar10 dataset. Epistemic uncertainty measures what your model doesn't know due to lack of training data. This post is based on material from two blog posts (here and here) and a white paper on Bayesian deep learning from the University of Cambridge machine learning group. So if the model is shown a picture of your leg with ketchup on it, the model is fooled into thinking it is a hotdog. In the Keras Tuner, a Gaussian process is used to “fit” this objective function with a “prior” and in turn another function called an acquisition function is used to generate new data about our objective function. If my model understands aleatoric uncertainty well, my model should predict larger aleatoric uncertainty values for images with low contrast, high brightness/darkness, or high occlusions To test this theory, I applied a range of gamma values to my test images to increase/decrease the pixel intensity and predicted outcomes for the augmented images. We load them with Keras ‘ImageDataGenerator’ performing data augmentation on train. For example, epistemic uncertainty would have been helpful with this particular neural network mishap from the 1980s. For example, aleatoric uncertainty played a role in the first fatality involving a self driving car. In this paper we develop a new theoretical … Deep learning tools have gained tremendous attention in applied machine learning. The combination of Bayesian statistics and deep learning in practice means including uncertainty in your deep learning model predictions. The trainable part of my model is two sets of BatchNormalization, Dropout, Dense, and relu layers on top of the ResNet50 output. Keras : Limitations. The loss function runs T Monte Carlo samples and then takes the average of the T samples as the loss. However such tools for regression and classification do not capture model uncertainty. Related: The Truth About Bayesian Priors and Overfitting; How Bayesian Networks Are Superior in Understanding Effects of Variables Think of epistemic uncertainty as model uncertainty. This image would high epistemic uncertainty because the image exhibits features that you associate with both a cat class and a dog class. InferPy’s API gives support to this powerful and flexible modeling framework. The softmax probability is the probability that an input is a given class relative to the other classes. To ensure the loss is greater than zero, I add the undistorted categorical cross entropy. The model detailed in this post explores only the tip of the Bayesian deep learning iceberg and going forward there are several ways in which I believe I could improve the model's predictions. 2. Also, in my experience, it is easier to produce reasonable epistemic uncertainty predictions than aleatoric uncertainty predictions. It is often times much easier to understand uncertainty in an image segmentation model because it is easier to compare the results for each pixel in an image. This is an implementation of the paper Deep Bayesian Active Learning with Image Data using keras and modAL. After applying -elu to the change in loss, the mean of the right < wrong becomes much larger. To understand using dropout to calculate epistemic uncertainty, think about splitting the cat-dog image above in half vertically. Additionally, the model is predicting greater than zero uncertainty when the model's prediction is correct. The only problem was that all of the images of the tanks were taken on cloudy days and all of the images without tanks were taken on a sunny day. Sampling a normal distribution along a line with a slope of -1 will result in another normal distribution and the mean will be about the same as it was before but what we want is for the mean of the T samples to decrease as the variance increases. The neural network structure we want to use is made by simple convolutional layers, max-pooling blocks and dropouts. The mean of the wrong < right stays about the same. Shape: (N, C). If you want to learn more about Bayesian deep learning after reading this post, I encourage you to check out all three of these resources. # Input should be predictive means for the C classes. Everyone who has tried to fit a classification model and checked its performance has faced the problem of verifying not only KPI (like accuracy, precision and recall) but also how confident the model is in what it says. If there's ketchup, it's a hotdog @FunnyAsianDude #nothotdog #NotHotdogchallenge Image data could be incorporated as well. In the past, Bayesian deep learning models were not used very often because they require more parameters to optimize, which can make the models difficult to work with. LIME, SHAP and Embeddings are nice ways to explain what the model learned and why it makes the decisions it makes. This is true because the derivative is negative on the right half of the graph. Note: Epistemic uncertainty is not used to train the model. The two prior Dense layers will train on both of these losses. An image segmentation classifier that is able to predict aleatoric uncertainty would recognize that this particular area of the image was difficult to interpret and predicted a high uncertainty. Tesla has said that during this incident, the car's autopilot failed to recognize the white truck against a bright sky. When the 'wrong' logit is much larger than the 'right' logit (the left half of graph) and the variance is ~0, the loss should be ~. I have a very simple toy recurrent neural network implemented in keras which, given an input of N integers will return their mean value. It’s typical to also have misclassifications with high probabilities. Shape: (N,), # returns - total differences for all classes (N,), # model - the trained classifier(C classes), # where the last layer applies softmax, # T - the number of monte carlo simulations to run, # prob - prediction probability for each class(C). Above are the images with the highest aleatoric and epistemic uncertainty. Learn more. The elu is also ~linear for very small values near 0 so the mean for the right half of Figure 1 stays the same. What is Bayesian deep learning? The combination of Bayesian statistics and deep learning in practice means including uncertainty in your deep learning model predictions. I believe this happens because the slope of Figure 1 on the left half of the graph is ~ -1. When the 'logit difference' is positive in Figure 1, the softmax prediction will be correct. Shape: (N, C), # dist - normal distribution to sample from. One approach would be to see how my model handles adversarial examples. Figure 1 is helpful for understanding the results of the normal distribution distortion. We carry out this task in two ways: I found the data for this experiment on Kaggle. Suppressing the ‘not classified’ images (20 in total), accuracy increases from 0.79 to 0.82. As they start being a vital part of business decision making, methods that try to open the neural network “black box” are becoming increasingly popular. According to the scope of this post, we limit the target classes, only considering the first five species of monkeys. For this experiment, I used the frozen convolutional layers from Resnet50 with the weights for ImageNet to encode the images. If the image classifier had included a high uncertainty with its prediction, the path planner would have known to ignore the image classifier prediction and use the radar data instead (this is oversimplified but is effectively what would happen. Hyperas is not working with latest version of keras. I used 100 Monte Carlo simulations for calculating the Bayesian loss function. Bayesian probability theory offers mathematically grounded tools to reason about model uncertainty, but these usually come with a prohibitive computational cost. I found increasing the number of Monte Carlo simulations from 100 to 1,000 added about four minutes to each training epoch. When the 'wrong' logit value is less than 1.0 (and thus less than the 'right' logit value), the minimum variance is 0.0. # x - prediction probability for each class(C), # Keras TimeDistributed can only handle a single output from a model :(. In keras master you can set this, # freeze encoder layers to prevent over fitting. Make learning your daily ritual. We use essential cookies to perform essential website functions, e.g. You can always update your selection by clicking Cookie Preferences at the bottom of the page. What we do now is to extract the best results from our fitted model, studying the probability distributions and trying to limit mistakes when our neural network is forced to make a decision. Gal et. A fun example of epistemic uncertainty was uncovered in the now famous Not Hotdog app. the original undistorted loss compared to the distorted loss, undistorted_loss - distorted_loss. Put simply, Bayesian deep learning adds a prior distribution over each weight and bias parameter found in a typical neural network model. You can then calculate the predictive entropy (the average amount of information contained in the predictive distribution). Our validation is composed of 10% of train images. 12/10/2018 ∙ by Dustin Tran, et al. 86.4% of the samples are in the 'first' group, 8.7% are in the 'second' group, and 4.9% are in the 'rest' group. As the wrong 'logit' value increases, the variance that minimizes the loss increases. Whoops. deep learning tools as Bayesian models – without chang-ing either the models or the optimisation. Concrete examples of aleatoric uncertainty in stereo imagery are occlusions (parts of the scene a camera can't see), lack of visual features (i.e a blank wall), or over/under exposed areas (glare & shading). This isn't that surprising because epistemic uncertainty requires running Monte Carlo simulations on each image. It is clear that if we iterate predictions 100 times for each test sample, we will be able to build a distribution of probabilities for every sample in each class. A Bayesian deep learning model would predict high epistemic uncertainty in these situations. Below are two ways of calculating epistemic uncertainty. There are actually two types of aleatoric uncertainty, heteroscedastic and homoscedastic, but I am only covering heteroscedastic uncertainty in this post. To get a more significant loss change as the variance increases, the loss function needed to weight the Monte Carlo samples where the loss decreased more than the samples where the loss increased. In Figure 5, 'first' includes all of the correct predictions (i.e logit value for the 'right' label was the largest value). The second uses additional Keras layers (and gets GPU acceleration) to make the predictions. Given the above reasons, it is no surprise that Keras is increasingly becoming popular as a deep learning library. This example shows how to apply Bayesian optimization to deep learning and find optimal network hyperparameters and training options for convolutional neural networks. Figure 2: Average change in loss & distorted average change in loss. However, more recently, Bayesian deep learning has become more popular and new techniques are being developed to include uncertainty in a model while using the same number of parameters as a traditional model. Note: In a classification problem, the softmax output gives you a probability value for each class, but this is not the same as uncertainty. One way of modeling epistemic uncertainty is using Monte Carlo dropout sampling (a type of variational inference) at test time. We use optional third-party analytics cookies to understand how you use so we can build better products. Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning: Yarin Gal, Zoubin Ghahramani, Hands-on real-world examples, research, tutorials, and cutting-edge techniques delivered Monday to Thursday. The model's accuracy on the augmented images is 5.5%. Self driving cars use a powerful technique called Kalman filters to track objects. Feel free to play with it if you want a deeper dive into training your own Bayesian deep learning classifier. ∙ 0 ∙ share . # In the case of a single classification, output will be (None,). GitHub is home to over 50 million developers working together to host and review code, manage projects, and build software together. It is surprising that it is possible to cast recent deep learning tools as Bayesian models without changing anything! I could also try training a model on a dataset that has more images that exhibit high aleatoric uncertainty. There are several different types of uncertainty and I will only cover two important types in this post. To enable the model to learn aleatoric uncertainty, when the 'wrong' logit value is greater than the 'right' logit value (the left half of graph), the loss function should be minimized for a variance value greater than 0. Deep learning (DL) is one of the hottest topics in data science and artificial intelligence today.DL has only been feasible since 2012 with the widespread usage of GPUs, but you’re probably already dealing with DL technologies in various areas of your daily life. Because the probability is relative to the other classes, it does not help explain the model’s overall confidence. 2 is using tensorflow_probability package, this way we model problem as a distribution problem. High epistemic uncertainty is a red flag that a model is much more likely to make inaccurate predictions and when this occurs in safety critical applications, the model should not be trusted. The bottom row shows a failure case of the segmentation model, when the model is unfamiliar with the footpath, and the corresponding increased epistemic uncertainty." Test images with a predicted probability below the competence threshold are marked as ‘not classified’. Reposted with permission. I initially attempted to train the model without freezing the convolutional layers but found the model quickly became over fit. Don’t Start With Machine Learning. Figure 5 shows the mean and standard deviation of the aleatoric and epistemic uncertainty for the test set broken out by these three groups. Learn more, # N data points, C classes, T monte carlo simulations, # pred_var - predicted logit values and variance. This is probably by design. I call the mean of the lower graphs in Figure 2 the 'distorted average change in loss'. The logit and variance layers are then recombined for the aleatoric loss function and the softmax is calculated using just the logit layer. The elu shifts the mean of the normal distribution away from zero for the left half of Figure 1. a classical study of probabilities on validation data, in order to establish a threshold to avoid misclassifications. Figure 1: Softmax categorical cross entropy vs. logit difference for binary classification. Shape: (N, C), # undistorted_loss - the crossentropy loss without variance distortion. 1.0 is no distortion. From my own experiences with the app, the model performs very well. This procedure is particularly appealing because it is easy to implement, and directly applicable to any existing neural networks without the loss in performances. Even for a human, driving when roads have lots of glare is difficult. These deep architectures can model complex tasks by leveraging the hierarchical representation power of deep learning, while also being able to infer complex multi-modal posterior distributions. This article has one purpose; to maintain an up-to-date list of available hyperparameter optimization and tuning solutions for deep learning and other machine learning uses. When we reactivate dropout we are permuting our neural network structure making also results stochastic. Take a look, x = Conv2D(32, (3, 3), activation='relu')(inp), x = Conv2D(64, (3, 3), activation='relu')(x), Machine learning or deep learning model tuning is a kind of optimization problem. As I was hoping, the epistemic and aleatoric uncertainties are correlated with the relative rank of the 'right' logit. I would like to be able to modify this to a bayesian neural network with either pymc3 or edward.lib so that I can get a posterior distribution on the output value The dataset consists of two files, training and validation. This can be done by combining InferPy with tf.layers, tf.keras or tfp.layers. Understanding if your model is under-confident or falsely over-confident can help you reason about your model and your dataset. # Take a mean of the results of a TimeDistributed layer. # Applying TimeDistributedMean()(TimeDistributed(T)(x)) to an. Aleatoric uncertainty is a function of the input data. This allows the last Dense layer, which creates the logits, to learn only how to produce better logit values while the Dense layer that creates the variance learns only about predicting variance. These values can help to minimize model loss … I am excited to see that the model predicts higher aleatoric and epistemic uncertainties for each augmented image compared with the original image! Figure 6 shows the predicted uncertainty for eight of the augmented images on the left and eight original uncertainties and images on the right. In Figure 1, the y axis is the softmax categorical cross entropy. You signed in with another tab or window. A standard way imposes to hold part of our data as validation in order to study probability distributions and set thresholds. Representing Model Uncertainty in Deep Learning Photo by Rob Schreckhise on Unsplash. Suppressing the ‘not classified’ images (16 in total), accuracy increases from 0.79 to 0.83. 06/06/2015 ∙ by Yarin Gal, et al. This is different than aleatoric uncertainty, which is predicted as part of the training process. 'second', includes all of the cases where the 'right' label is the second largest logit value. 1 is using dropout: this way we give CNN opportunity to pay attention to different portions of image at different iterations. The aleatoric uncertainty loss function is weighted less than the categorical cross entropy loss because the aleatoric uncertainty loss includes the categorical cross entropy loss as one of its terms. In this post, we evaluate two different methods which estimate a Neural Network’s confidence. modAL is an active learning framework for Python3, designed with modularity, flexibility and extensibility in mind. To ensure the variance that minimizes the loss is less than infinity, I add the exponential of the variance term. If you saw the right half you would predict cat. There are a few different hyperparameters I could play with to increase my score. Bayesian CNN with Dropout or FlipOut. Uncertainty predictions in deep learning models are also important in robotics. If nothing happens, download the GitHub extension for Visual Studio and try again. Unfortunately, predicting epistemic uncertainty takes a considerable amount of time. The solution is the usage of dropout in NNs as a Bayesian approximation. As a result, the model uncertainty can be estimated by positional indexes or other statistics taken from predictions in a few repetitions. This is not an amazing score by any means. Each folder contains 10 subfolders labeled as n0~n9, each corresponding a species form Wikipedia’s monkey cladogram. Teaching the model to predict aleatoric variance is an example of unsupervised learning because the model doesn't have variance labels to learn from. It takes about 2-3 seconds on my Mac CPU for the fully connected layers to predict all 50,000 classes for the training set but over five minutes for the epistemic uncertainty predictions. After training, the network performed incredibly well on the training set and the test set.

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