Making Deep Networks Probabilistic via Test-time Dropout

In Quantum Mechanics, Heisenberg's Uncertainty Principle states that there is a fundamental limit to how well one can measure a particle's position and momentum. In the context of machine learning systems, a similar principle has emerged, but relating interpretability and performance. By using a manually wired or shallow machine learning model, you'll have no problem understanding the moving pieces, but you will seldom be happy with the results. Or you can use a black-box deep neural network and enjoy the model's exceptional performance. Today we'll see one simple and effective trick to make our deep black boxes a bit more intelligible. The trick allows us to convert neural network outputs into probabilities, with no cost to performance, and minimal computational overhead.

Interpretability vs Performance: Deep Neural Networks perform well on most computer vision tasks, yet they are notoriously difficult to interpret.

The desire to understand deep neural networks has triggered a flurry of research into Neural Network Visualization, but in practice we are often forced to treat deep learning systems as black-boxes. (See my recent Deep Learning Trends @ ICLR 2016 post for an overview of recent neural network visualization techniques.) But just because we can't grok the inner-workings of our favorite deep models, it doesn't mean we can't ask more out of our deep learning systems.

There exists a simple trick for upgrading black-box neural network outputs into probability distributions. 

The probabilistic approach provides confidences, or "uncertainty" measures, alongside predictions and can make almost any deep learning systems into a smarter one. For robotic applications or any kind of software that must make decisions based on the output of a deep learning system, being able to provide meaningful uncertainties is a true game-changer.

Applying Dropout to your Deep Neural Network is like occasionally zapping your brain

The key ingredient is dropout, an anti-overfitting deep learning trick handed down from Hinton himself (Krizhevsky's pioneering 2012 paper). Dropout sets some of the weights to zero during training, reducing feature co-adaptation, thus improving generalization.

Without dropout, it is too easy to make a moderately deep network attain 100% accuracy on the training set. 

The accepted knowledge is that an un-regularized network (one without dropout) is too good at memorizing the training set. For a great introductory machine learning video lecture on dropout, I highly recommend you watch Hugo Larochelle's lecture on Dropout for Deep learning.


Geoff Hinton's dropout lecture, also a great introduction, focuses on interpreting dropout as an ensemble method. If you're looking for new research ideas in the dropout space, a thorough understanding of Hinton's interpretation is a must.


But while dropout is typically used at training-time, today we'll highlight the keen observation that dropout used at test-time is one of the simplest ways to turn raw neural network outputs into probability distributions. Not only does this probabilistic "free upgrade" often improve classification results, it provides a meaningful notion of uncertainty, something typically missing in Deep Learning systems.

The idea is quite simple: to estimate the predictive mean and predictive uncertainty, simply collect the results of stochastic forward passes through the model using dropout. 

How to use dropout: 2016 edition

1. Start with a moderately sized network
2. Increase your network size with dropout turned off until you perfectly fit your data
3. Then, train with dropout turned on
4. At test-time, turn on dropout and run the network T times to get T samples
5. The mean of the samples is your output and the variance is your measure of uncertainty

Remember that drawing more samples will increase computation time during testing unless you're clever about re-using partial computations in the network. Please note that if you're only using dropout near the end of your network, you can reuse most of the computations. If you're not happy with the uncertainty estimates, consider adding more layers of dropout at test-time. Since you'll already have a pre-trained network, experimenting with test-time dropout layers is easy.

Bayesian Convolutional Neural Networks

To be truly Bayesian about a deep network's parameters, we wouldn't learn a single set of parameters w, we would infer a distribution over weights given the data, p(w|X,Y). Training is already quite expensive, requiring large datasets and expensive GPUs.

Bayesian learning algorithms can in theory provide much better parameter estimates for ConvNets and I'm sure some of our friends at Google are working on this already. 

But today we aren't going to talk about such full Bayesian Deep Learning systems, only systems that "upgrade" the model prediction y to p(y|x,w). In other words, only the network outputs gain a probabilistic interpretation.

An excellent deep learning computer vision system which uses test-time dropout comes from a recent University of Cambridge technique called SegNet. The SegNet approach introduced an Encoder-Decoder framework for dense semantic segmentation. More recently, SegNet includes a Bayesian extension that uses dropout at test-time for providing uncertainty estimates. Because the system provides a dense per-pixel labeling, the confidences can be visualized as per-pixel heatmaps. Segmentation system is not performing well? Just look at the confidence heatmaps!

Bayesian SegNet. A fully convolutional neural network architecture which provides 

per-pixel class uncertainty estimates using dropout.

The Bayesian SegNet authors tested different strategies for dropout placement and determined that a handful of dropout layers near the encoder-decoder bottleneck is better than simply using dropout near the output layer. Interestingly, Bayesian SegNet improves the accuracy over vanilla SegNet. Their confidence maps shown high uncertainty near object boundaries, but different test-time dropout schemes could provide a more diverse set of uncertainty estimates.

Bayesian SegNet: Model Uncertainty in Deep Convolutional Encoder-Decoder Architectures for Scene Understanding Alex Kendall, Vijay Badrinarayanan, Roberto Cipolla, in arXiv:1511.02680, November 2015. [project page with videos]

Confidences are quite useful for evaluation purposes, because instead of providing a single average result across all pixels in all images, we can sort the pixels and/or images by the overall confidence in prediction. When evaluation the top 10% most confident pixels, we should expect significantly higher performance. For example, the Bayesian SegNet approach achieves 75.4% global accuracy on the SUN RGBD dataset, and an astonishing 97.6% on most confident 10% of the test-set [personal communication with Bayesian SegNet authors]. This kind of sort-by-confidence evaluation was popularized by the PASCAL VOC Object Detection Challenge, where precision/recall curves were the norm. Unfortunately, as the research community moved towards large-scale classification, the notion of confidence was pushed aside. Until now.

Theoretical Bayesian Deep Learning

Deep networks that model uncertainty are truly meaningful machine learning systems. It ends up that we don't really have to understand how a deep network's neurons process image features to trust the system to make decisions. As long as the model provides uncertainty estimates, we'll know when the model is struggling. This is particularly important when your network is given inputs that are far from the training data.

The Gaussian Process: A machine learning approach with built-in uncertainty modeling

In a recent ICML 2016 paper, Yarin Gal and Zoubin Ghahramani develop a new theoretical framework casting dropout training in deep neural networks as approximate Bayesian inference in deep Gaussian processes. Gal's paper gives a complete theoretical treatment of the link between Gaussian processes and dropout, and develops the tools necessary to represent uncertainty in deep learning. They show that a neural network with arbitrary depth and non-linearities, with dropout applied before every weight layer, is mathematically equivalent to an approximation to the probabilistic deep Gaussian process. I have yet to see researchers use dropout between every layer, so the discrepancy between theory and practice suggests that more research is necessary.

Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning Yarin Gal, Zoubin Ghahramani, in ICML. June 2016. [Appendix with relationship to Gaussian Processes]
A Theoretically Grounded Application of Dropout in Recurrent Neural Networks Yarin Gal, in arXiv:1512.05287. May 2016.

What My Deep Model Doesn't Know. Yarin Gal. Blog Post. July 2015 

Homoscedastic and Heteroscedastic Regression with Dropout Uncertainty. Yarin Gal. Blog Post. February 2016.

Test-time dropout is used to provide uncertainty estimates for deep learning systems.

In conclusion, maybe we can never get both interpretability and performance when it comes to deep learning systems. But, we can all agree that providing confidences, or uncertainty estimates, alongside predictions is always a good idea. Dropout, the very single regularization trick used to battle overfitting in deep models, shows up, yet again. Sometimes all you need is to add some random variations to your input, and average the results over many trials. Dropout lets you not only wiggle the network inputs but the entire architecture.

I do wonder what Yann LeCun thinks about Bayesian ConvNets... Last I heard, he was allergic to sampling.

Related Posts 
Deep Learning vs Probabilistic Graphical Models vs Logic April 2015
Deep Learning Trends @ ICLR 2016 June 2016

Machine Learning Doesn't Matter?

Bagpipes and International Conference of Machine Learning (ICML) in Edinburgh

Two weeks ago, I attended the ICML 2012 Conference in Edinburgh, UK.  First of all, Edinburgh is a great place for a conference!  The scenery is marvelous, the weather is comfortable, and most notably, the sound of bagpipes adds an inimitable charm to the city.  I attended the conference because I was invited to give an invited applications talk during the invited talks session.  In case you’re wondering, I did not have a plenary session (a plenary session is a session attended by all conference members) which is preserved for titans such as Yann Lecun, David MacKay, and Andrew Ng.  My presentation was on the last day of ICML and was titled “Exemplar-SVMs for Visual Object Detection, Label Transfer and Image Retrieval,” during which I gave an overview of my ICCV 2011 paper on visual object detection as well as the SIGGRAPH ASIA 2011 paper on cross-domain image retrieval.  As part of the invited talk, we submitted a 2 page extended abstract which summarizes some key ideas behind the exemplar-svm project: you can check out the abstract as well as the presentation slides online.  I believe the talk was recorded, so I will post the video link once it becomes available.  It was a great opportunity to convey some of my ideas to a non-vision audience.  I think I got a handful of new people excited about single example SVMs (i.e., Exemplar-SVMs)!

Tomasz Malisiewicz, Abhinav Shrivastava, Abhinav Gupta, and Alexei A. Efros. Exemplar-SVMs for Visual Object Detection, Label Transfer and Image Retrieval. To be presented as an invited applications talk at ICML, 2012. PDF | Talk Slides

Getting Ready for Edinburgh with David Hume

To get ready for my first visit to Edinburgh (pronounced Ed-in-bur-ah which does not rhyme with Pittsburgh), I bought a Kindle Touch and proceeded to read David Hume’s An Enquiry Concerning Human Understanding.  David Hume is one of the great British Empiricists (together with John Locke and George Berkeley) who stood by the empiricist motto: impressions are the source of all ideas.  Empiricists can be contrasted to rationalists who appeal to reason as the source of knowledge.  [Of course, I am neither an empiricist nor a rationalist.  Such polarizing extremes are a thing of the past.  I am a pragmatists and my world-view combines elements from many different philosophies.]  I choose Hume’s treatise because he is the one whom Kant credits for awakening him from his dogmatic slumber.  I found Hume’s words rejuvenating, full of gedankenexperiments which show the limits of radical empiricism, and most notably is free on the Kindle store!  In your attempts to build intelligent machines, maybe you will also words of inspiration in the classics.  It was a great book to get into the Edinburgh mindset (although the ICML crowd is probably more familiar with a different University of Edinburgh figure, namely Reverend Bayes).

Impressions of ICML

I would first like to first say that the ICML website is well-organized and serves as a great tool during the conference!  Good job ICML!  There is a great mobile version of the ICML website which is excellent for visiting on your iPhone when figuring out which talk to go to next.  The ICML website also provides a forum for discussing papers and every paper gets a presentation and a poster.  The discussion boards do not seem heavily utilized but it would be great to use a moderator-style system to have the actual after-presentation questions come from this forum.  I’m sure something like this will actually arise in the upcoming years.  ICML is much smaller than CVPR (compare ~700 attendees with ~2000 attendees) which makes for a much more intimate environment.  I was amazed by the number of people proving bounds and doing “theoretical” non-applied machine learning.  Its like some people really don't care about anything other than analysis.  However, this is not my style, and I personally prefer to build “real” systems and combine insights from disparate disciplines such as mathematics, cognitive science, philosophy, physics, and computer science.  There is a bit of ICML and Machine Learning conferences which I think of as nothing more than mathturbation.  I understand there's merit to doing analysis of this sort -- somebody’s gotta do it, but if you’re gonna do it, please at least try to understand the implications of the real-world problem your dataset and task are trying to address.

Machine Learning doesn’t Matter?

The highlight of the conference by far was Kiri Wagstaff’s plenary talk “Machine Learning that Matters.”  Kiri gave an enchanting 30 minute presentation regarding what is rotten in the state of Edinburgh (aka what is wrong with the style of machine learning conferences).  Her words were gentle, yet harsh, while simultaneously enlightening, yet morbid.  She showed us, machine learning researchers, just how useless much of machine learning research is today.  Let’s not forget that Machine Learning is one of the most revolutionary ideas if the modern computer science classroom.  Trying to get a PhD in Computer Science and avoiding Machine Learning is like avoiding Calculus while getting and undergraduate degree in Engineering.  There is nothing wrong with machine learning as a discipline, but there is something wrong with researchers making the field overly academic.  Making a discipline overly academic means creating a self-contained, overly-mathematical, self-citing, and jargon-filled discipline which doesn’t care about world-impact but only cares to propagate a small community’s citation count.  Note that much of these arguments also apply to the CVPR world. But do not take my words for granted, read Kiri’s treatise yourself.  Abstract Below:

"Machine Learning that Matters" Abstract: Much of current machine learning (ML) research has lost its connection to problems of import to the larger world of science and society. From this perspective, there exist glaring limitations in the data sets we investigate, the metrics we employ for evaluation, and the degree to which results are communicated back to their originating domains. What changes are needed to how we conduct research to increase the impact that ML has? We present six Impact Challenges to explicitly focus the field’s energy and attention, and we discuss existing obstacles that must be addressed. We aim to inspire ongoing discussion and focus on ML that matters.

Kiri Wagstaff, "Machine Learning that Matters," ICML 2012.

PDF Link: http://icml.cc/2012/papers/298.pdf

If you have something to say in response to Kiri's treatise, check out her Machine Learning Impact Forum on http://mlimpact.com/.