Paper:
Attention to semi-supervised learning grows in machine learning as the price to expertly label data increases. Like most previous works in the area, we focus on improving an algorithm's ability to discover the inherent property of the entire dataset from a few expertly labelled samples. In this paper we introduce Boosting via Self Labelling (BSL), a solution to semi-supervised boosting when there is only limited access to labelled instances. Our goal is to learn a classifier that is trained on a data set that is generated by combining the generalization of different algorithms which have been trained with a limited amount of supervised training samples. Our method builds upon a combination of several different components. First, an inference aided ensemble algorithm developed on a set of weak classifiers will offer the initial noisy labels. Second, an agreement based estimation approach will return the average error rates of the noisy labels. Third and finally, a noiseresistant boosting algorithm will train over the noisy labels and their error rates to describe the underlying structure as closely as possible. We provide both analytical justifications and experimental results to back the performance of our model. Based on several benchmark datasets, our results demonstrate that BSL is able to outperform state-of-the-art semi-supervised methods consistently, achieving over 90% test accuracy with only 10% of the data being labelled.

Review:
In this paper, the authors present an approach for semi-supervised learning which combines noisy labels with boosting. In a first step, the labeled instances are used to train a set of classifiers, and these are used to create noisy labels for the unlabeled instances. Then, an EM procedure is used to estimate the noise level of each instance. Finally, a version of AdaBoost which accounts for instance noise levels is proposed to create a final classifier. A limited set of experiments suggests the proposed approach is competitive with existing approaches.
Major Comments
As a non-expert in this area, I had trouble identifying the novel contributions of this work. For example, many of the results in Section 3 (noise-resistant AdaBoost) seem to replicate, or follow closely, the results of [Natarajan et al., 2013]. Similarly, using EM to assign pseudo-labels has been extensively studied in the literature [Lee, WREPL 2013; Chapelle and Zien, AISTATS 2005; Kang et al., ECCV 2018; Rottman et al., ICMLA 2018]. 
The experiments are very poorly described, so it is difficult to gauge if they are valid:
Most importantly, the authors point out that the estimated error rates do not always match the actual error rates. Since this seems to be one of the most important factors of the proposed approach, further investigation should be performed to answer questions like: why is the error rate not estimated well? on what type of datasets? can more/better supervised learners help? In some cases (Diabetes, Thyroid, Heart), the actual noise rate increases with more labeled samples. What does that mean?
Second, the proposed approach seems to have a number of important hyperparameters, including the number of supervised models trained and their hyperparameters, the parameters of the Beta distribution used as a prior on the noise estimation, and the hyperparameters of the AdaBoost algorithm. Likewise, all of the competing algorithms also have hyperparameters which are known to affect performance (e.g., learning rate for NNs). The paper does not mention how (or if) a validation set was used to select these.
Third, while the caption of Table 1 mentions that 20 trials were used, it is not clear if this was some sort of k-fold cross validation, Monte Carlo, cross validation, the same splits but with different random seeds, etc. Additionally, the variance across the different trials should be given; otherwise, it is not possible to tell if any of the empirical results are significant.
Minor Comments:
The references are not consistently formatted.
This paper is very notation heavy. It would be helpful to include a “table of symbols” for the reader in an appendix.
Additionally, the notation in the paper is not consistent. For example, both “$M$” and “$\mathcal{M}$ are used to indicate the number of models trained on the labeled data. Later on, “$\mathcal{M}$” is also used to refer to the set of trained classifiers. The first bullet point in Step 3 of the pseudocode seems to suggest that each classifier is trained on a single labeled data point. The equation at the bottom of Page 5 used \theta, but it does not seem to be defined.
The discussion on experts, spammers, and adversaries could be helpful if this terminology were used throughout the paper; however, it is used in only one paragraph. 
The main body of the paper should mention that proofs are given in the appendices.
For context, if may be helpful to mention that graph convolutional networks and other representation learning techniques are commonly used for semi-supervised learning (e.g., [Kipf and Welling, ICML 2016]). Those approaches are quite different (and lack any sort of theoretical guarantees, for the most part), though, so empirical comparisons may not be so meaningful.
It would be helpful to give a sentence or two on the intuition behind what the proofs are showing. For a non-expert, they are very difficult to follow.
Do the various proofs still hold when the datasets are artificially balanced (with respect to the last paragraph in Section 4)?
It would be helpful to include the performance using the complete labeled dataset for comparison.
Stratified sampling could be used to ensure both classes are present in the training data. Also, “0.99%” -> “99%”.
Besides accuracy, some measure like AuROC or the F1 score which account for class imbalance should be given.
Typos, etc.
“Logitboost tested against” -> “Logitboost were tested against”
“therefore is not” -> “therefore, having a lot of labeled data is not”