Question: The figure "92.95% test accuracy" corresponds to the 10-way labels of each digit? Or to the 4-way categories of the pixels?
Evidence: We evaluate the performance of our model primarily on the MNIST dataset. Our model is able to approximate any conditional distribution. Here we demonstrate how to model missing pixels and the class digits conditioned on the observed pixels, as well as model missing pixels conditioned on class digits and observed pixels. Although MNIST is of course a small-scale problem, the goal here is to demonstrate joint inference and learning over what is still a reasonably-sized joint model, considering the number of hidden units. Nonetheless, the current experiment is admittedly largely a demonstration of the proposed method rather than a full accounting of its performance, a point we highlight in the subsequent section as well. After describing the MNIST experiments, we detail a similar experiment on CIFAR-10 to demonstrate the potential for scaling the approach.
We also show how our inference method differs from the previous ones. On the joint imputation and classification task, we train models using our updates and the updates in;, and inference each using all three update methods, with and without the monotonicity constraint. We show that our inference method is superior in both performance and convergence speed. Numerically, we also demonstrate that the other two methods could either diverge or not converging to the actual mean-field fixed point. All deferred experiments and details can be found in the appendix.
Experiment setup The original MNIST dataset has one channel representing the gray-scale intensity, ranging between 0 and 1. Here we adopt the strategy of to convert this continuous distribution to a discrete one. We bin the intensity evenly to 4 categories {0, . . . , 3}, and for each channel uses a one-hot encoding of the category so that the input data has shape 4×28×28.
We remark that the number of categories is chosen arbitrarily and can be any integer. For image with missing data, if the pixels are randomly masked, we always mask each pixel off independently with probability 60%, such that in expectation only 40% pixels are observed. If a whole patch of pixels is masked, we randomly pick a 14 × 14 patch. The patches/masks are chosenly differently for every image, similar to the query training in. To make the model class richer, in the patch case we lift the monotonicity constraint, and the model converges regardless. We also conduct the same set of MNIST experiments using a 3-layer DBM and include the results in the appendix.
Training the above described model for 40 epochs with 40% missing pixels leads to a 92.95% test accuracy, and the image reconstruction result is shown in fig.. Based on the reconstructed images and our classification results, our model successfully recovers the unimodal distribution conditioned on the observed pixels. Despite working simultaneously on two different tasks, our model can simply be trained jointly, taking full advantages of the existing auto-differentiation frameworks without additional burden. It is worth noting that while the autoregressive models of are comparable to ours, they require sampling pixels one-by-one in a sequential order at inference time, whereas our model does not assume an underlying sequence and can generate all pixels at once. Comparing to the differently-parameterized monDEQ in, whose linear module suffers from drastically increasing condition number (hence in later epochs taking around 20 steps to converge, even with tuned α), our
We additionally conduct an experiment on the simultaneous tasks of image pixel imputation and label prediction given partially observed features. Model architecture and training details are given in the appendix. With 50% of the pixels observed, the model obtains 58% test accuracy, and can impute the missing pixels effectively (see fig.).
Training the above described model for 40 epochs with 40% missing pixels leads to a 92.95% test accuracy, and the image reconstruction result is shown in fig. 4d. Based on the reconstructed images and our classification results, our model successfully recovers the unimodal distribution conditioned on the observed pixels.
Answer: 92.95% is the classification accuracy with 40% missing pixels.