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Uncertain Descent / a simple baseline for bayesian uncertainty in deep learning

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UNCERTAIN DESCENT. NeurIPS 2019, ARXIV:1902.02476 / swa-gaussian (swag). a simple baseline for bayesian uncertainty in deep learning.

Real Data visualizations using PCA directions. From the authors of the paper: “Machine learning models are used to make decisions, and representing uncertainty is crucial for decision making, especially in safety-critical applications. Deep learning models trained by minimizing the loss on the train dataset tend to provide overconfident and miscalibrated predictions because they ignore uncertainty over the parameters of the model. In Bayesian machine learning we account for this uncertainty: we form a distribution over the weights of the model, known as posterior. This distribution captures different models that all explain train data well, but provide different predictions on the test data. For Neural networks the posterior distribution is very complex: there is no way to compute it exactly and we have to approximate it. A key challenge for approximate inference methods is to capture the geometry of the posterior distribution or, equivalently, the loss landscape.



The idea of our SWAG is to extract the information about the posterior geometry from the SGD trajectory. We start by pre-training a Neural Network with SGD, Adam or any other optimizer, to get a good initial solution. This part is the same as the standard training of the model. Starting from the pre-trained solution, we run SGD with a high constant learning rate. In this setting instead of converging to a single solution, SGD would bounce around different solutions that all explain the train data well. We then construct a Gaussian distribution that captures these different solutions traversed by SGD, and use it as our approximation to the posterior. It turns out that this simple procedure captures the local Geometry of the posterior remarkably well.”



Based on the paper by wesley maddox, timur garipov, pavel izmailov, dmitry vetrov, andrew gordon wilson. Visualization is a collaboration between pavel izmailov, timur garipov and javier [email protected]. NeurIPS 2019, ARXIV:1902.02476 | losslandscape.com..
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