Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of these algorithms' success and their Achilles heel: forming a graph and computing its dominant eigenvectors can indeed be computationally prohibitive when dealing with more that a few tens of thousands of points. In this paper, we review the principal research efforts aiming to reduce this computational cost. We focus on methods that come with a theoretical control on the clustering performance and incorporate some form of sampling in their operation. Such methods abound in the machine learning, numerical linear algebra, and graph signal processing literature and, amongst others, include Nystr\"om-approximation, landmarks, coarsening, coresets, and compressive spectral clustering. We present the approximation guarantees available for each and discuss practical merits and limitations. Surprisingly, despite the breadth of the literature explored, we conclude that there is still a gap between theory and practice: the most scalable methods are only intuitively motivated or loosely controlled, whereas those that come with end-to-end guarantees rely on strong assumptions or enable a limited gain of computation time.

In the early history of positive-unlabeled (PU) learning, the sample selection approach, which heuristically selects negative (N) data from U data, was explored extensively. However, this approach was later dominated by the importance reweighting approach, which carefully treats all U data as N data. May there be a new sample selection method that can outperform the latest importance reweighting method in the deep learning age? This paper is devoted to answering this question affirmatively---we propose to label large-loss U data as P, based on the memorization properties of deep networks. Since P data selected in such a way are biased, we develop a novel learning objective that can handle such biased P data properly. Experiments confirm the superiority of the proposed method.

Goats and sheep were on the lam last week in New Jersey. Scientists who said in 2017 that sheep could recognize human faces from photos may be feeling a little sheepish right now, after experts questioned one of their conclusions. Facial recognition specialists from Australia recently revisited the 2017 study. They admitted that the experiments provided "a compelling demonstration" that sheep could differentiate between human faces, but they challenged the authors' conclusion that sheep could recognize faces as well as humans and other primates can. As experts in human facial recognition, the Australian researchers reported serious reservations about sheep performing this un-ewe-sual ability on equal footing with Homo sapiens.

We were trying to get in touch with our internet service provider. I can't remember the reason. But we contacted the company through its website chat system. My partner was typing, and I noticed his language was unusually clipped, devoid of the words "please", or "thank you". "You don't have to be so rude," I said.

Abstract--A general framework of least squares support vector machine with low rank kernels, referred to as LR-LSSVM, is introduced in this paper . The special structure of low rank kernels with a controlled model size brings sparsity as well as computational efficiency to the proposed model. Meanwhile, a two-step optimization algorithm with three different criteria is proposed and various experiments are carried out using the example of the so-call robust RBF kernel to validate the model. The experiment results show that the performance of the proposed algorithm is comparable or superior to several existing kernel machines. With the proliferation of big data in scientific and business research, in practical nonlinear modeling approaches, one wishes to build sparse models with more efficient algorithms. Kernel machines (KMs) have attracted great attention since the support vector machines (SVM), a well linear binary classification model under the principle of risk minimization, was introduced in earlier 1990s [1]. In fact, KMs have extended SVM by implementing the linearity in the so-called high dimensional feature space under a feature mapping implicitly determined by a Mercer kernel function.

Modern computing and communication technologies can make data collection procedures very efficient. However, our ability to analyze large data sets and/or to extract information out from them is hard-pressed to keep up with our capacities for data collection. Among these huge data sets, some of them are not collected for any particular research purpose. For a classification problem, this means that the essential label information may not be readily obtainable, in the data set in hands, and an extra labeling procedure is required such that we can have enough label information to be used for constructing a classification model. When the size of a data set is huge, to label each subject in it will cost a lot in both capital and time. Thus, it is an important issue to decide which subjects should be labeled first in order to efficiently reduce the training cost/time. Active learning method is a promising outlet for this situation, because with the active learning ideas, we can select the unlabeled subjects sequentially without knowing their label information. In addition, there will be no confirmed information about the essential variables for constructing an efficient classification rule. Thus, how to merge a variable selection scheme with an active learning procedure is of interest. In this paper, we propose a procedure for building binary classification models when the complete label information is not available in the beginning of the training stage. We study an model-based active learning procedure with sequential variable selection schemes, and discuss the results of the proposed procedure from both theoretical and numerical aspects.

Cardiovascular diseases are one of the most common causes of death in the world. Prevention, knowledge of previous cases in the family, and early detection is the best strategy to reduce this fact. Different machine learning approaches to automatic diagnostic are being proposed to this task. As in most health problems, the imbalance between examples and classes is predominant in this problem and affects the performance of the automated solution. In this paper, we address the classification of heartbeats images in different cardiovascular diseases. We propose a two-dimensional Convolutional Neural Network for classification after using a InfoGAN architecture for generating synthetic images to unbalanced classes. We call this proposal Adversarial Oversampling and compare it with the classical oversampling methods as SMOTE, ADASYN, and RandomOversampling. The results show that the proposed approach improves the classifier performance for the minority classes without harming the performance in the balanced classes.

We propose and analyze a method for semi-supervised learning from partially-labeled network-structured data. Our approach is based on a graph signal recovery interpretation under a clustering hypothesis that labels of data points belonging to the same well-connected subset (cluster) are similar valued. This lends naturally to learning the labels by total variation (TV) minimization, which we solve by applying a recently proposed primal-dual method for non-smooth convex optimization. The resulting algorithm allows for a highly scalable implementation using message passing over the underlying empirical graph, which renders the algorithm suitable for big data applications. By applying tools of compressed sensing, we derive a sufficient condition on the underlying network structure such that TV minimization recovers clusters in the empirical graph of the data. In particular, we show that the proposed primal-dual method amounts to maximizing network flows over the empirical graph of the dataset. Moreover, the learning accuracy of the proposed algorithm is linked to the set of network flows between data points having known labels. The effectiveness and scalability of our approach is verified by numerical experiments.

We consider the problem of differential privacy accounting, i.e. estimation of privacy loss bounds, in machine learning in a broad sense. We propose two versions of a generic privacy accountant suitable for a wide range of learning algorithms. Both versions are derived in a simple and principled way using well-known tools from probability theory, such as concentration inequalities. We demonstrate that our privacy accountant is able to achieve state-of-the-art estimates of DP guarantees and can be applied to new areas like variational inference. Moreover, we show that the latter enjoys differential privacy at minor cost.

We propose a new method to evaluate GANs, namely EvalGAN. EvalGAN relies on a test set to directly measure the reconstruction quality in the original sample space (no auxiliary networks are necessary), and it also computes the (log)likelihood for the reconstructed samples in the test set. Further, EvalGAN is agnostic to the GAN algorithm and the dataset. We decided to test it on three state-of-the-art GANs over the well-known CIFAR-10 and CelebA datasets.