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. While it is interesting to look at the images, it is not exactly clear to me why these images images have high aleatoric or epistemic uncertainty. 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. Learn more. Bayesian deep learning is a field at the intersection between deep learning and Bayesian probability theory. Example image with gamma value distortion. Our goal here is to find the best combination of those hyperparameter values. Sounds like aleatoric uncertainty to me! This is a common procedure for every kind of model. 12/10/2018 ∙ by Dustin Tran, et al. i.e. This is done because the distorted average change in loss for the wrong logit case is about the same for all logit differences greater than three (because the derivative of the line is 0). Edward supports the creation of network layers with probability distributions and makes it easy to perform variational inference. There are several different types of uncertainty and I will only cover two important types in this post. Uncertainty predictions in deep learning models are also important in robotics. Suppressing the ‘not classified’ images (16 in total), accuracy increases from 0.79 to 0.83. Left side: Images & uncertainties with gamma values applied. By adding images with adjusted gamma values to images in the training set, I am attempting to give the model more images that should have high aleatoric uncertainty. We use essential cookies to perform essential website functions, e.g. The model trained on only 25% of the dataset will have higher average epistemic uncertainty than the model trained on the entire dataset because it has seen fewer examples. Deep Bayesian Active Learning on MNIST. This is because Keras … I am excited to see that the model predicts higher aleatoric and epistemic uncertainties for each augmented image compared with the original image! Using Bayesian Optimization CORRECTION: In the code below dict_params should be: The higher the probabilities, the higher the confidence. This is true because the derivative is negative on the right half of the graph. My model's categorical accuracy on the test dataset is 86.4%. Shape: (N, C + 1), bayesian_categorical_crossentropy_internal, # calculate categorical_crossentropy of, # pred - predicted logit values. 1.0 is no distortion. I am currently enrolled in the Udacity self driving car nanodegree and have been learning about techniques cars/robots use to recognize and track objects around then. Both techniques are useful to avoid misclassification, relaxing our neural network to make a prediction when there’s not so much confidence. Learn more, We use analytics cookies to understand how you use our websites so we can make them better, e.g. This is different than aleatoric uncertainty, which is predicted as part of the training process. it is difficult for the model to make an accurate prediction on this image), this feature encourages the model to find a local loss minimum during training by increasing its predicted variance. Because the probability is relative to the other classes, it does not help explain the model’s overall confidence. It is surprising that it is possible to cast recent deep learning tools as Bayesian models without changing anything! Deep learning tools have gained tremendous attention in applied machine learning. # predictive probabilities for each class, # set learning phase to 1 so that Dropout is on. For a classification task, instead of only predicting the softmax values, the Bayesian deep learning model will have two outputs, the softmax values and the input variance. I used 100 Monte Carlo simulations for calculating the Bayesian loss function. This can be done by combining InferPy with tf.layers, tf.keras or tfp.layers. It can be explained away with infinite training data. In order to have an adequate distribution of probabilities to build significative thresholds, we operate data augmentation on validation properly: in the phase of prediction, every image is augmented 100 times, i.e. Make learning your daily ritual. Even for a human, driving when roads have lots of glare is difficult. Right side: Images & uncertainties of original image. When the logit values (in a binary classification) are distorted using a normal distribution, the distortion is effectively creating a normal distribution with a mean of the original predicted 'logit difference' and the predicted variance as the distribution variance. Built on top of scikit-learn, it allows you to rapidly create active learning workflows with nearly complete freedom. They do the exact same thing, but the first is simpler and only uses numpy. Figure 2: Average change in loss & distorted average change in loss. 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. The trainable part of my model is two sets of BatchNormalization, Dropout, Dense, and relu layers on top of the ResNet50 output. If you've made it this far, I am very impressed and appreciative. Figure 1: Softmax categorical cross entropy vs. logit difference for binary classification. For a full explanation of why dropout can model uncertainty check out this blog and this white paper white paper. Additionally, the model is predicting greater than zero uncertainty when the model's prediction is correct. The uncertainty for the entire image is reduced to a single value. Hyperas is not working with latest version of keras. As I was hoping, the epistemic and aleatoric uncertainties are correlated with the relative rank of the 'right' logit. Shape: (N, C), # dist - normal distribution to sample from. 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 ~. Traditional deep learning models are not able to contribute to Kalman filters because they only predict an outcome and do not include an uncertainty term. 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. According to the scope of this post, we limit the target classes, only considering the first five species of monkeys. 'wrong' means the incorrect class for this prediction. Machine learning or deep learning model tuning is a kind of optimization problem. # Applying TimeDistributedMean()(TimeDistributed(T)(x)) to an. There are actually two types of aleatoric uncertainty, heteroscedastic and homoscedastic, but I am only covering heteroscedastic uncertainty in this post. See Kalman filters below). In this post, we evaluate two different methods which estimate a Neural Network’s confidence. What should the model predict? The combination of Bayesian statistics and deep learning in practice means including uncertainty in your deep learning model predictions. When 'logit difference' is negative, the prediction will be incorrect. Bayesian Optimization. You can notice that aleatoric uncertainty captures object boundaries where labels are noisy. Gal et. 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). You can always update your selection by clicking Cookie Preferences at the bottom of the page. al show that the use of dropout in neural networks can be interpreted as a Bayesian approximation of a Gaussian process, a well known probabilistic model. 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. Bayesian statistics is a theory in the field of statistics in which the evidence about the true state of the world is expressed in terms of degrees of belief. So I think using hyperopt directly will be a better option. Teaching the model to predict aleatoric variance is an example of unsupervised learning because the model doesn't have variance labels to learn from. Keras : Limitations. Otherwise, we mark this image as ‘not classified’. Test images with a predicted probability below the competence threshold are marked as ‘not classified’. It is surprising that it is possible to cast recent deep learning tools as Bayesian models without changing anything! The first approach we introduce is based on simple studies of probabilities computed on a validation set. 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. I ran 100 Monte Carlo simulations so it is reasonable to expect the prediction process to take about 100 times longer to predict epistemic uncertainty than aleatoric uncertainty. Figure 3: Aleatoric variance vs loss for different 'wrong' logit values, Figure 4: Minimum aleatoric variance and minimum loss for different 'wrong' logit values. After applying -elu to the change in loss, the mean of the right < wrong becomes much larger. Popular deep learning models created today produce a point estimate but not an uncertainty value. I was able to produce scores higher than 93%, but only by sacrificing the accuracy of the aleatoric uncertainty. 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. they're used to log you in. I initially attempted to train the model without freezing the convolutional layers but found the model quickly became over fit. Figure 7: If you saw the left half, you would predict dog. This image would high epistemic uncertainty because the image exhibits features that you associate with both a cat class and a dog class. The combination of Bayesian statistics and deep learning in practice means including uncertainty in your deep learning model predictions. Suppressing the ‘not classified’ images (20 in total), accuracy increases from 0.79 to 0.82. Radar and lidar data merged into the Kalman filter. In this example, it changes from -0.16 to 0.25. The loss function I created is based on the loss function in this paper. 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. While getting better accuracy scores on this dataset is interesting, Bayesian deep learning is about both the predictions and the uncertainty estimates and so I will spend the rest of the post evaluating the validity of the uncertainty predictions of my model. I found increasing the number of Monte Carlo simulations from 100 to 1,000 added about four minutes to each training epoch. # Take a mean of the results of a TimeDistributed layer. In this case, researchers trained a neural network to recognize tanks hidden in trees versus trees without tanks. I applied the elu function to the change in categorical cross entropy, i.e. a recent method based on the inference of probabilities from bayesian theories with a ‘. If there's ketchup, it's a hotdog @FunnyAsianDude #nothotdog #NotHotdogchallenge pic.twitter.com/ZOQPqChADU. It can be explained away with the ability to observe all explanatory variables with increased precision. 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. I added augmented data to the training set by randomly applying a gamma value of 0.5 or 2.0 to decrease or increase the brightness of each image. This does not imply higher accuracy. 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. Bayesian Layers: A Module for Neural Network Uncertainty. In theory, Bayesian deep learning models could contribute to Kalman filter tracking. In this way we create thresholds which we use in conjunction with the final predictions of the model: if the predicted label is below the threshold of the relative class, we refuse to make a prediction. The softmax probability is the probability that an input is a given class relative to the other classes. 2 is using tensorflow_probability package, this way we model problem as a distribution problem. Probabilistic Deep Learning is a hands-on guide to the principles that support neural networks. a classical study of probabilities on validation data, in order to establish a threshold to avoid misclassifications. Don’t Start With Machine Learning. Above are the images with the highest aleatoric and epistemic uncertainty. This is not an amazing score by any means. Probabilistic Deep Learning: With Python, Keras and TensorFlow Probability is a hands-on guide to the principles that support neural networks. I could also unfreeze the Resnet50 layers and train those as well. One way of modeling epistemic uncertainty is using Monte Carlo dropout sampling (a type of variational inference) at test time. It is only calculated at test time (but during a training phase) when evaluating test/real world examples. 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 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. The solution is the usage of dropout in NNs as a Bayesian approximation. This dataset is specifically meant to make the classifier "cope with large variations in visual appearances due to illumination changes, partial occlusions, rotations, weather conditions". The last is fundamental to regularize training and will come in handy later when we’ll account for neural network uncertainty with bayesian procedures. 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. 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. When setting up a Bayesian DL model, you combine Bayesian statistics with DL. Image data could be incorporated as well. For example, aleatoric uncertainty played a role in the first fatality involving a self driving car. Besides the code above, training a Bayesian deep learning classifier to predict uncertainty doesn't require much additional code beyond what is typically used to train a classifier. Specifically, stochastic dropouts are applied after each hidden layer, so the model output can be approximately viewed as a random sample generated from the posterior predictive distribution. In comparison, Bayesian models offer a mathematically grounded framework to reason about model uncertainty, but usually come with a prohibitive computational cost. The solution is the usage of dropout in NNs as a Bayesian approximation. In machine learning, we are trying to create approximate representations of the real world. The aleatoric uncertainty should be larger because the mock adverse lighting conditions make the images harder to understand and the epistemic uncertainty should be larger because the model has not been trained on images with larger gamma distortions. LIME, SHAP and Embeddings are nice ways to explain what the model learned and why it makes the decisions it makes. We show that the use of dropout (and its variants) in NNs can be inter-preted as a Bayesian approximation of a well known prob-Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning We load them with Keras ‘ImageDataGenerator’ performing data augmentation on train. In comparison, Bayesian models offer a mathematically grounded framework to reason about model uncertainty, but usually come with a prohibitive computational cost. Using Keras to implement Monte Carlo dropout in BNNs In this chapter you learn about two efficient approximation methods that allow you to use a Bayesian approach for probabilistic DL models: variational inference (VI) and Monte Carlo dropout (also known as MC dropout). The two prior Dense layers will train on both of these losses. Aleatoric and epistemic uncertainty are different and, as such, they are calculated differently. There are a few different hyperparameters I could play with to increase my score. The mean of the wrong < right stays about the same. # input of shape (None, ...) returns output of same size. We use optional third-party analytics cookies to understand how you use GitHub.com so we can build better products. During training, my model had a hard time picking up on this slight local minimum and the aleatoric variance predictions from my model did not make sense. A fun example of epistemic uncertainty was uncovered in the now famous Not Hotdog app. Lastly, my project is setup to easily switch out the underlying encoder network and train models for other datasets in the future. We have different types of hyperparameters for each model. ∙ 0 ∙ share . 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. As the wrong 'logit' value increases, the variance that minimizes the loss increases. 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. Brain overload? The second uses additional Keras layers (and gets GPU acceleration) to make the predictions. Learn more, # N data points, C classes, T monte carlo simulations, # pred_var - predicted logit values and variance. For an image that has high aleatoric uncertainty (i.e. To do this, I could use a library like CleverHans created by Ian Goodfellow. I have a very simple toy recurrent neural network implemented in keras which, given an input of N integers will return their mean value. They can however be compared against the uncertainty values the model predicts for other images in this dataset. Using Bayesian Optimization; Ensembling and Results; Code; 1. the original undistorted loss compared to the distorted loss, undistorted_loss - distorted_loss. This means the gamma images completely tricked my model. Visualizing a Bayesian deep learning model. Note: Epistemic uncertainty is not used to train the model. One approach would be to see how my model handles adversarial examples. These two values can't be compared directly on the same image. After training, accuracy on test is around 0.79, forcing our model to classifies all. medium.com/towards-data-science/building-a-bayesian-deep-learning-classifier-ece1845bc09, download the GitHub extension for Visual Studio, model_training_logs_resnet50_cifar10_256_201_100.csv, German Traffic Sign Recognition Benchmark. # Input should be predictive means for the C classes. Bayesian Deep Learning (MLSS 2019) Yarin Gal University of Oxford yarin@cs.ox.ac.uk Unless speci ed otherwise, photos are either original work or taken from Wikimedia, under Creative Commons license Also, in my experience, it is easier to produce reasonable epistemic uncertainty predictions than aleatoric uncertainty predictions. Taking the categorical cross entropy of the distorted logits should ideally result in a few interesting properties. After training, the network performed incredibly well on the training set and the test set. This isn't that surprising because epistemic uncertainty requires running Monte Carlo simulations on each image. Aleatoric uncertainty is a function of the input data. Below is the standard categorical cross entropy loss function and a function to calculate the Bayesian categorical cross entropy loss. We use optional third-party analytics cookies to understand how you use GitHub.com so we can build better products. GitHub is home to over 50 million developers working together to host and review code, manage projects, and build software together. The Bayesian Optimization package we are going to use is BayesianOptimization, which can be installed with the following command, I was able to use the loss function suggested in the paper to decrease the loss when the 'wrong' logit value is greater than the 'right' logit value by increasing the variance, but the decrease in loss due to increasing the variance was extremely small (<0.1). If you saw the right half you would predict cat. modAL is an active learning framework for Python3, designed with modularity, flexibility and extensibility in mind. From my own experiences with the app, the model performs very well. Introduction. For this experiment, I used the frozen convolutional layers from Resnet50 with the weights for ImageNet to encode the images. To train a deep neural network, you must specify the neural network architecture, as well as options of the training algorithm. ∙ 14 ∙ share . If nothing happens, download the GitHub extension for Visual Studio and try again. increasing the 'logit difference' results in only a slightly smaller decrease in softmax categorical cross entropy compared to an equal decrease in 'logit difference'. The most intuitive instrument to use to verify the reliability of a prediction is one that looks for the probabilities of the various classes. A standard way imposes to hold part of our data as validation in order to study probability distributions and set thresholds. An easy way to observe epistemic uncertainty in action is to train one model on 25% of your dataset and to train a second model on the entire dataset. The neural network structure we want to use is made by simple convolutional layers, max-pooling blocks and dropouts. 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. 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 case of the Tesla incident, although the car's radar could "see" the truck, the radar data was inconsistent with the image classifier data and the car's path planner ultimately ignored the radar data (radar data is known to be noisy). These are the results of calculating the above loss function for binary classification example where the 'right' logit value is held constant at 1.0 and the 'wrong' logit value changes for each line. 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. Use Git or checkout with SVN using the web URL. In Figure 5, 'first' includes all of the correct predictions (i.e logit value for the 'right' label was the largest value). The images are of good quality and balanced among classes. Epistemic uncertainty measures what your model doesn't know due to lack of training data. they're used to gather information about the pages you visit and how many clicks you need to accomplish a task. Epistemic uncertainty refers to imperfections in the model - in the limit of infinite data, this kind of uncertainty should be reducible to 0. Another way suggests applying stochastic dropouts in order to build probabilities distribution and study their differences. Think of epistemic uncertainty as model uncertainty. Applying softmax cross entropy to the distorted logit values is the same as sampling along the line in Figure 1 for a 'logit difference' value. Self driving cars use a powerful technique called Kalman filters to track objects. I could also try training a model on a dataset that has more images that exhibit high aleatoric uncertainty. 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. I spent very little time tuning the weights of the two loss functions and I suspect that changing these hyperparameters could greatly increase my model accuracy. Then, here is the function to be optimized with Bayesian optimizer, the partial function takes care of two arguments — input_shape and verbose in fit_with which have fixed values during the runtime.. In addition to trying to improve my model, I could also explore my trained model further. I suspect that keras is evolving fast and it's difficult for the maintainer to make it compatible. With this example, I will also discuss methods of exploring the uncertainty predictions of a Bayesian deep learning classifier and provide suggestions for improving the model in the future. Figure 1 is helpful for understanding the results of the normal distribution distortion. It distorts the predicted logit values by sampling from the distribution and computes the softmax categorical cross entropy using the distorted predictions. In practice I found the cifar10 dataset did not have many images that would in theory exhibit high aleatoric uncertainty. To understand using dropout to calculate epistemic uncertainty, think about splitting the cat-dog image above in half vertically. Original. As a result, the model uncertainty can be estimated by positional indexes or other statistics taken from predictions in a few repetitions. There are 2 approaches for Bayesian CNN at Keras. Related: The Truth About Bayesian Priors and Overfitting; How Bayesian Networks Are Superior in Understanding Effects of Variables

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