In this paper, we focus on the supervised learning problem with corrupt training data. We assume that the training dataset is generated from a mixture of a target distribution and other unknown distributions. We estimate the quality of each data by revealing the correlation between the generated distribution and the target distribution. To this end, we present a novel framework referred to here as ChoiceNet that can robustly infer the target distribution in the presence of inconsistent data. We demonstrate that the proposed framework is applicable to both classification and regression tasks. Particularly, ChoiceNet is evaluated in comprehensive experiments, where we show that it constantly outperforms existing baseline methods in the handling of noisy data in synthetic regression tasks as well as behavior cloning problems. In the classification tasks, we apply the proposed method to the MNIST and CIFAR-10 datasets and it shows superior performances in terms of robustness to different types of noisy labels.
The paper presents a framework, called ChoiceNet, for learning when the 
supervision outputs (e.g., labels) are corrupted by noise. The method relies on 
estimating the correlation between the training data distribution and a 
target distribution, where training data distribution is assumed to be a mixture 
of that target distribution and other unknown distributions. The paper also 
presents some compelling results on synthetic and real datasets, for both 
regression and classification problems.
The proposed idea builds on top of previously published work on Mixture Density 
Networks (MDNs) and Mixup (Zhang et al, 2017). The main difference is the MDN 
are modified to construct the Mixture of Correlated Density Network (MCDN) 
block, that forms the main component of ChoiceNets.
I like the overall direction and idea of modelling correlation between the 
target distribution and the data distribution to deal with noisy labels. The 
results are also compelling and I thus lean towards accepting this paper. My 
decision on "marginal accept" is based primarily on my unfamiliarity with this 
specific area and that some parts of the paper are not very easy or intuitive 
to read through.
== Related Work ==
I like the related work discussion, but would emphasize more the connection to 
MDNs and to Mixup. Only one sentence is mentioned about Mixup but reading 
through the abstract and the introduction that is the first paper that came to 
my mind and thus I believe that it may deserve a bit more discussion.
Also, there are a couple more papers that felt relevant to this work but are 
not mentioned:
  - Estimating Accuracy from Unlabeled Data: A Bayesian Approach, Platanios et al., ICML 2016.
    I believe this is related in how noisy labels are modeled (i.e., section 3 
    in the reviewed paper) and in the idea of correlation/consistency as a means 
    to detect errors. There are couple more papers in this line of work that 
    may be relevant.
  - ADIOS: Architectures Deep In Output Space, Al-Shedivat et al., ICML 2016.
    I believe this is related in learning some structure in the output space, 
    even though not directly dealing with noisy labels.
== Method ==
I believe the methods section could have been written in a more 
clear/easy-to-follow way, but this may also be due to my unfamiliarity with this 
area. Figure 1 is hard to parse and does not really offer much more than section 
3.2 currently does. If the figure is improved with some more text/labels on 
boxes rather than plain equations, it may go a long way in making the methods 
section easier to follow.
I would also point out MCDN as the key contribution of this paper as ChoiceNet 
is just any base network with an MCDN block stacked on top of this. Thus, I 
believe this should be emphasized more to make your key contribution clear.
== Experiments ==
The experiments are nicely presented and are quite thorough. A couple minor 
comments I have are:
  - It would be nice to run regression experiments for bigger real-world 
    datasets, as the ones used seem to be quite small.
  - I am a bit confused at the fact that in table 3 you compare your method to 
    mixup and in table 4 you also show results when using both your method and 
    mixup combined. Up until that point I thought that mixup was posed as an 
    alternative method, but here it seems it's quite orthogonal and can be used 
    together, which I think makes sense, but would be good to clarify. Also, 
    given that you show combined results in table 4, why not also perform 
    exactly the same analysis for table 3 and also show numbers for CN + Mixup?
It would also be nice to use the same naming scheme for both tables. I would 
use: ConvNet, ConvNet + CN, ConvNet + CN + Mixup, and the same with WRN for 
table 4. This would make the tables easier to read because currently the first 
thing that comes to mind is what may be different between the two setups given 
that they are presented side-by-side but use different naming conventions.
One question that comes to mind is that you make certain assumptions on the 
kinds of noise your model can capture, so are there any cases where you have 
good intuition as to why your model may fail? It would be good to present a 
short discussion on this to help readers understand whether they can benefit by 
using your model or not.