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. Note: In a classification problem, the softmax output gives you a probability value for each class, but this is not the same as uncertainty. This is not an amazing score by any means. However such tools for regression and classification do not capture model uncertainty. # and we technically only need the softmax outputs. Otherwise, we mark this image as ‘not classified’. 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). He is especially interested in deep generative models, Bayesian deep learning methods, and variational inference to improve data efficiency in complex learning regimes. 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. For example, I could continue to play with the loss weights and unfreeze the Resnet50 convolutional layers to see if I can get a better accuracy score without losing the uncertainty characteristics detailed above. Bayesian Layers: A Module for Neural Network Uncertainty. For this experiment, I used the frozen convolutional layers from Resnet50 with the weights for ImageNet to encode the images. To ensure the loss is greater than zero, I add the undistorted categorical cross entropy. The first approach we introduce is based on simple studies of probabilities computed on a validation set. 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. Both techniques are useful to avoid misclassification, relaxing our neural network to make a prediction when there’s not so much confidence. The elu is also ~linear for very small values near 0 so the mean for the right half of Figure 1 stays the same. The model's accuracy on the augmented images is 5.5%. 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. 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. We use optional third-party analytics cookies to understand how you use GitHub.com so we can build better products. 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. Figure 7: For example, epistemic uncertainty would have been helpful with this particular neural network mishap from the 1980s. InferPy’s API gives support to this powerful and flexible modeling framework. It is surprising that it is possible to cast recent deep learning tools as Bayesian models without changing anything! This procedure is particularly appealing because it is easy to implement, and directly applicable to any existing neural networks without the loss in performances. Don’t Start With Machine Learning. To further explore the uncertainty, I broke the test data into three groups based on the relative value of the correct logit. Aleatoric and epistemic uncertainty are different and, as such, they are calculated differently. 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 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. Whoops. As the wrong 'logit' value increases, the variance that minimizes the loss increases. When the 'logit difference' is positive in Figure 1, the softmax prediction will be correct. 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). The combination of Bayesian statistics and deep learning in practice means including uncertainty in your deep learning model predictions. Related: The Truth About Bayesian Priors and Overfitting; How Bayesian Networks Are Superior in Understanding Effects of Variables If you saw the right half you would predict cat. According to the scope of this post, we limit the target classes, only considering the first five species of monkeys. Unlike Random Search and Hyperband models, Bayesian Optimization keeps track of its past evaluation results and uses it to build the probability model. 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. Self driving cars use a powerful technique called Kalman filters to track objects. Test images with a predicted probability below the competence threshold are marked as ‘not classified’. Uncertainty is the state of having limited knowledge where it is impossible to exactly describe the existing state, a future outcome, or more than one possible outcome. I suspect that keras is evolving fast and it's difficult for the maintainer to make it compatible. 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. they're used to gather information about the pages you visit and how many clicks you need to accomplish a task. Using Bayesian Optimization; Ensembling and Results; Code; 1. For more information, see our Privacy Statement. PS: I am new to bayesian optimization for hyper parameter tuning and hyperopt. I found increasing the number of Monte Carlo simulations from 100 to 1,000 added about four minutes to each training epoch. Epistemic uncertainty measures what your model doesn't know due to lack of training data. The images are of good quality and balanced among classes. Dropout is used in many models in deep learning as a way to avoid over-fitting, and they show that dropout approximately integrates over the models’ weights. The logits and variance are calculated using separate Dense layers. In Figure 1, the y axis is the softmax categorical cross entropy. 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. Deep Bayesian Active Learning on MNIST. 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. This blog post uses Edward to train a Bayesian deep learning classifier on the MNIST dataset. Machine learning engineers hope our models generalize well to situations that are different from the training data; however, in safety critical applications of deep learning hope is not enough. See Kalman filters below). There are a few different hyperparameters I could play with to increase my score. Suppressing the ‘not classified’ images (16 in total), accuracy increases from 0.79 to 0.83. Right side: Images & uncertainties of original image. It offers principled uncertainty estimates from deep learning architectures. Shape: (N, C + 1), bayesian_categorical_crossentropy_internal, # calculate categorical_crossentropy of, # pred - predicted logit values. 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. 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. To train a deep neural network, you must specify the neural network architecture, as well as options of the training algorithm. The aleatoric uncertainty values tend to be much smaller than the epistemic uncertainty. The solution is the usage of dropout in NNs as a Bayesian approximation. Bayesian probability theory offers mathematically grounded tools to reason about model uncertainty, but these usually come with a prohibitive computational cost. Figure 3: Aleatoric variance vs loss for different 'wrong' logit values, Figure 4: Minimum aleatoric variance and minimum loss for different 'wrong' logit values. In comparison, Bayesian models offer a mathematically grounded framework to reason about model uncertainty, but usually come with a prohibitive computational cost. 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. 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. My model's categorical accuracy on the test dataset is 86.4%. i.e. This isn't that surprising because epistemic uncertainty requires running Monte Carlo simulations on each image. Learn more, # N data points, C classes, T monte carlo simulations, # pred_var - predicted logit values and variance. Learn more, We use analytics cookies to understand how you use our websites so we can make them better, e.g. Think of epistemic uncertainty as model uncertainty. 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. .. I’m not sure why the question presupposes that Bayesian networks and neural networks are comparable, nor am I sure why the other answers readily accepts this premise that they can be compared. We load them with Keras ‘ImageDataGenerator’ performing data augmentation on train. Figure 5: uncertainty mean and standard deviation for test set. We present a deep learning framework for probabilistic pixel-wise semantic segmentation, which we term Bayesian SegNet. You can then calculate the predictive entropy (the average amount of information contained in the predictive distribution). In Figure 2 right < wrong corresponds to a point on the left half of Figure 1 and wrong < right corresponds to a point on the right half of Figure 2. The x axis is the difference between the 'right' logit value and the 'wrong' logit value. Tesla has said that during this incident, the car's autopilot failed to recognize the white truck against a bright sky. It took about 70 seconds per epoch. In Figure 5, 'first' includes all of the correct predictions (i.e logit value for the 'right' label was the largest value). The loss function runs T Monte Carlo samples and then takes the average of the T samples as the loss. 100 more probabilities for every sample. modAL is an active learning framework for Python3, designed with modularity, flexibility and extensibility in mind. 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. Using Bayesian Optimization CORRECTION: In the code below dict_params should be: In the paper, the loss function creates a normal distribution with a mean of zero and the predicted variance. 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. In the Bayesian deep learning literature, a distinction is commonly made between epistemic uncertainty and aleatoric uncertainty (Kendall and Gal 2017). Use Git or checkout with SVN using the web URL. Aleatoric uncertainty is a function of the input data. 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. 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. I think that having a dependency on low level libraries like Theano / TensorFlow is a double edged sword. You can see that the distribution of outcomes from the 'wrong' logit case, looks similar to the normal distribution and the 'right' case is mostly small values near zero. The uncertainty for the entire image is reduced to a single value. After applying -elu to the change in loss, the mean of the right < wrong becomes much larger. We carry out this task in two ways: I found the data for this experiment on Kaggle. Reposted with permission. I expected the model to exhibit this characteristic because the model can be uncertain even if it's prediction is correct. Brain overload? When training the model, I only ran 100 Monte Carlo simulations as this should be sufficient to get a reasonable mean. 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 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. link. The combination of Bayesian statistics and deep learning in practice means including uncertainty in your deep learning model predictions. Images with highest aleatoric uncertainty, Images with the highest epistemic uncertainty. 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. 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. 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. After training, the network performed incredibly well on the training set and the test set. Shape: (N, C), # undistorted_loss - the crossentropy loss without variance distortion. 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. Below are two ways of calculating epistemic uncertainty. It can be explained away with the ability to observe all explanatory variables with increased precision. 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. This example shows how to apply Bayesian optimization to deep learning and find optimal network hyperparameters and training options for convolutional neural networks. This is an implementation of the paper Deep Bayesian Active Learning with Image Data using keras and modAL. This is probably by design. If there's ketchup, it's a hotdog @FunnyAsianDude #nothotdog #NotHotdogchallenge pic.twitter.com/ZOQPqChADU. These two values can't be compared directly on the same image. The two types of uncertainty explained above are import for different reasons. For example, aleatoric uncertainty played a role in the first fatality involving a self driving car. In keras master you can set this, # freeze encoder layers to prevent over fitting. It is surprising that it is possible to cast recent deep learning tools as Bayesian models without changing anything! Teaching the model to predict aleatoric variance is an example of unsupervised learning because the model doesn't have variance labels to learn from. When the predicted logit value is much larger than any other logit value (the right half of Figure 1), increasing the variance should only increase the loss. Note: Epistemic uncertainty is not used to train the model. Built on top of scikit-learn, it allows you to rapidly create active learning workflows with nearly complete freedom. Understanding if your model is under-confident or falsely over-confident can help you reason about your model and your dataset. We have different types of hyperparameters for each model. 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. LIME, SHAP and Embeddings are nice ways to explain what the model learned and why it makes the decisions it makes. We describe Bayesian Layers, a module designed for fast experimentation with neural network uncertainty. 'right' means the correct class for this prediction. This can be done by combining InferPy with tf.layers, tf.keras or tfp.layers. As I was hoping, the epistemic and aleatoric uncertainties are correlated with the relative rank of the 'right' logit. Lastly, my project is setup to easily switch out the underlying encoder network and train models for other datasets in the future. Popular deep learning models created today produce a point estimate but not an uncertainty value. An example of ambiguity. Gal et. In comparison, Bayesian models offer a mathematically grounded framework to reason about model uncertainty, but usually come with a prohibitive computational cost. Want to Be a Data Scientist? A perfect 50-50 split. It is only calculated at test time (but during a training phase) when evaluating test/real world examples. The minimum loss should be close to 0 in this case. This procedure enables us to know when our neural network fails and the confidences of mistakes for every class. When 'logit difference' is negative, the prediction will be incorrect. # In the case of a single classification, output will be (None,). 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. In this case, researchers trained a neural network to recognize tanks hidden in trees versus trees without tanks. In machine learning, we are trying to create approximate representations of the real world. Neural networks have been pushing what is possible in a lot of domains and are becoming a standard tool in industry. 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. Left side: Images & uncertainties with gamma values applied. 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. I could also unfreeze the Resnet50 layers and train those as well. In this post, we evaluate two different methods which estimate a Neural Network’s confidence. This library uses an adversarial neural network to help explore model vulnerabilities. In this blog post, I am going to teach you how to train a Bayesian deep learning classifier using Keras and tensorflow.