We find that our probabilistic CNNs produces posteriors which are reliable and informative. For a perfectly calibrated posterior, the actual and expected counts would be identical: the model would be correct (within some given maximum error) as often as it expects to be correct. We repeat each simulation four times to reduce the risk of spurious results from random variations in performance. \end{eqnarray*}$$, Applying MC dropout to marginalize over models (equation, $$\begin{eqnarray*} With MC Dropout, our posteriors are a superposition of Binomials from each forward pass, each centred on a different |$\hat{\rho _t}$|⁠. When active learning is applied to Galaxy Zoo, volunteers will be more frequently presented with the most informative images (left-hand panel) than the least (right-hand panel). modAL is an active learning framework for Python3, designed with modularity, flexibility and extensibility in mind. Applying Bayesian CNN for the task of Image … The MC-dropout-marginalized network shows a significant improvement in calibration over the single network. 2016) to decide how may responses to collect. Recall that smooth galaxies are far more common in GZ2 but featured galaxies are strongly preferentially selected by active learning – automatically, without our instruction – apparently to compensate for the imbalanced data (Fig. To avoid the possibility of duplicated galaxies or varying depth imaging, we exclude the ‘stripe82’ subset. Petro θ is the (r-band) Petrosian radius. Results using transfer learning to classify new surveys, or to answer new morphological questions, suggest that models can be fine-tuned using only thousands (Ackermann et al. We need to know how likely we were to train a particular model w given the data available, |$p(w|\mathcal {D})$|⁠. Bayesian CNN with Variational Inference based on Bayes by Backprop. 2018). This architecture is inspired by VGG16 (Simonyan & Zisserman 2015), but scaled down to be shallower and narrower in order to fit our computational budget. When we flip a coin, there are two possible outcomes - heads or tails. If you are curious, you can read more about Bayesian Active Learning in the paper Deep Bayesian Active Learning with Image Data, by Garin et al. In particular, CNNs are ‘black box’ algorithms which are difficult to introspect and do not typically provide estimates of uncertainty. Precise classification requests from our model will enable us to ask volunteers exactly the right questions, helping them make an even greater contribution to scientific research. 2015), and can be rapidly adapted to new surveys (Domínguez Sánchez et al. 2018; Pérez-Carrasco et al. The integral over the posterior on θ in the marginalization step can likewise be approximated via sampling from q if necessary. 2018). \end{eqnarray*}$$, $$\begin{eqnarray} In this work, we combine a novel generative model of volunteer responses with Monte Carlo dropout (Gal, Islam & Ghahramani 2017a) to create Bayesian CNNs that predict posteriors for the morphology of each galaxy. This rescaling function is also used (without modification) to map Bayesian CNN GZ2 vote fraction predictions to p(NairBar|BCNN-predictedGZ2Fraction). 2016), sentiment analysis of online reviews (Zhou, Chen & Wang 2013), and Earth observation (Tuia et al. We suggest that this is a limitation of our generative model for volunteer responses. Formally, each Galaxy Zoo decision tree question asks Ni volunteers to view galaxy image xi and select the most appropriate answer Aj from the available answers {A}.

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