The classes are airplanes, cars, birds, cats, deer, dogs, frogs, horses, ships, and trucks, and they are all mutually exclusive.

In the supplementary material, we provide additional information and details in A.1. This section covers the introduction of data, key parameter settings, comparisons with baselines, optimization methods, and the algorithm process of our method. The statistical information of the aforementioned four real-world datasets is presented in Table 4. These datasets primarily consist of daily spatio-temporal statistics in the United States. We perform 2 dynamic routing iterations.

In this section we motivate the design choices and inductive biases that we encode into our neural encoder network e, which is the network that is used to model the relative accuracies of the weak supervision sources λ. Recall that we model the probability of a particular sample x X having the class label y Y = {1,..., C} as P Our own parameterization therefore is a more expressive variant of these latent-variable PGM models, where we are able to assign LF accuracies on a sample-by-sample basis. Furthermore, our neural encoder network outputs them as a function of the LF outputs and features, and is expected to learn the easy to misspecify dependencies and label-independent statistics implicitly. The top 2 performance scores are highlighted as First, Second. Triplet-median [11] is not listed as it only converged for IMDB with 12 LFs (F1 = 73.0

Aggregating multiple sources of weak supervision (WS) can ease the data-labeling bottleneck prevalent in many machine learning applications, by replacing the tedious manual collection of ground truth labels. Current state of the art approaches that do not use any labeled training data, however, require two separate modeling steps: Learning a probabilistic latent variable model based on the WS sources - making assumptions that rarely hold in practice - followed by downstream model training. Importantly, the first step of modeling does not consider the performance of the downstream model. To address these caveats we propose an end-to-end approach for directly learning the downstream model by maximizing its agreement with probabilistic labels generated by reparameterizing prior probabilistic posteriors with a neural network. Our results show improved performance over prior work in terms of end model performance on downstream test sets, as well as in terms of improved robustness to dependencies among weak supervision sources.