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### The Sample Complexity of Semi-Supervised Learning with Nonparametric Mixture Models

We study the sample complexity of semi-supervised learning (SSL) and introduce new assumptions based on the mismatch between a mixture model learned from unlabeled data and the true mixture model induced by the (unknown) class conditional distributions. Under these assumptions, we establish an $\Omega(K\log K)$ labeled sample complexity bound without imposing parametric assumptions, where $K$ is the number of classes. Our results suggest that even in nonparametric settings it is possible to learn a near-optimal classifier using only a few labeled samples. Unlike previous theoretical work which focuses on binary classification, we consider general multiclass classification ($K>2$), which requires solving a difficult permutation learning problem. This permutation defines a classifier whose classification error is controlled by the Wasserstein distance between mixing measures, and we provide finite-sample results characterizing the behaviour of the excess risk of this classifier. Finally, we describe three algorithms for computing these estimators based on a connection to bipartite graph matching, and perform experiments to illustrate the superiority of the MLE over the majority vote estimator.

### On Defending Against Label Flipping Attacks on Malware Detection Systems

Label manipulation attacks are a subclass of data poisoning attacks in adversarial machine learning used against different applications, such as malware detection. These types of attacks represent a serious threat to detection systems in environments having high noise rate or uncertainty, such as complex networks and Internet of Thing (IoT). Recent work in the literature has suggested using the $K$-Nearest Neighboring (KNN) algorithm to defend against such attacks. However, such an approach can suffer from low to wrong detection accuracy. In this paper, we design an architecture to tackle the Android malware detection problem in IoT systems. We develop an attack mechanism based on Silhouette clustering method, modified for mobile Android platforms. We proposed two Convolutional Neural Network (CNN)-type deep learning algorithms against this \emph{Silhouette Clustering-based Label Flipping Attack (SCLFA)}. We show the effectiveness of these two defense algorithms - \emph{Label-based Semi-supervised Defense (LSD)} and \emph{clustering-based Semi-supervised Defense (CSD)} - in correcting labels being attacked. We evaluate the performance of the proposed algorithms by varying the various machine learning parameters on three Android datasets: Drebin, Contagio, and Genome and three types of features: API, intent, and permission. Our evaluation shows that using random forest feature selection and varying ratios of features can result in an improvement of up to 19\% accuracy when compared with the state-of-the-art method in the literature.

### Curriculum Labeling: Self-paced Pseudo-Labeling for Semi-Supervised Learning

Semi-supervised learning aims to take advantage of a large amount of unlabeled data to improve the accuracy of a model that only has access to a small number of labeled examples. We propose curriculum labeling, an approach that exploits pseudo-labeling for propagating labels to unlabeled samples in an iterative and self-paced fashion. This approach is surprisingly simple and effective and surpasses or is comparable with the best methods proposed in the recent literature across all the standard benchmarks for image classification. Notably, we obtain 94.91% accuracy on CIFAR-10 using only 4,000 labeled samples, and 88.56% top-5 accuracy on Imagenet-ILSVRC using 128,000 labeled samples. In contrast to prior works, our approach shows improvements even in a more realistic scenario that leverages out-of-distribution unlabeled data samples.

### Lautum Regularization for Semi-supervised Transfer Learning

Transfer learning is a very important tool in deep learning as it allows propagating information from one "source dataset" to another "target dataset", especially in the case of a small number of training examples in the latter. Yet, discrepancies between the underlying distributions of the source and target data are commonplace and are known to have a substantial impact on algorithm performance. In this work we suggest a novel information theoretic approach for the analysis of the performance of deep neural networks in the context of transfer learning. We focus on the task of semi-supervised transfer learning, in which unlabeled samples from the target dataset are available during the network training on the source dataset. Our theory suggests that one may improve the transferability of a deep neural network by imposing a Lautum information based regularization that relates the network weights to the target data. We demonstrate in various transfer learning experiments the effectiveness of the proposed approach.

### Improvability Through Semi-Supervised Learning: A Survey of Theoretical Results

Semi-supervised learning is a setting in which one has labeled and unlabeled data available. In this survey we explore different types of theoretical results when one uses unlabeled data in classification and regression tasks. Most methods that use unlabeled data rely on certain assumptions about the data distribution. When those assumptions are not met in reality, including unlabeled data may actually decrease performance. Studying such methods, it therefore is particularly important to have an understanding of the underlying theory. In this review we gather results about the possible gains one can achieve when using semi-supervised learning as well as results about the limits of such methods. More precisely, this review collects the answers to the following questions: What are, in terms of improving supervised methods, the limits of semi-supervised learning? What are the assumptions of different methods? What can we achieve if the assumptions are true? Finally, we also discuss the biggest bottleneck of semi-supervised learning, namely the assumptions they make.