S2: An Efficient Graph Based Active Learning Algorithm with Application to Nonparametric Classification

This paper investigates the problem of active learning for binary label prediction on a graph. We introduce a simple and label-efficient algorithm called S2 for this task. At each step, S2 selects the vertex to be labeled based on the structure of the graph and all previously gathered labels. Specifically, S2 queries for the label of the vertex that bisects the *shortest shortest* path between any pair of oppositely labeled vertices. We present a theoretical estimate of the number of queries S2 needs in terms of a novel parametrization of the complexity of binary functions on graphs. We also present experimental results demonstrating the performance of S2 on both real and synthetic data. While other graph-based active learning algorithms have shown promise in practice, our algorithm is the first with both good performance and theoretical guarantees. Finally, we demonstrate the implications of the S2 algorithm to the theory of nonparametric active learning. In particular, we show that S2 achieves near minimax optimal excess risk for an important class of nonparametric classification problems.Comment: A version of this paper appears in the Conference on Learning Theory (COLT) 201

Secure Transmission in Multi-Cell Massive MIMO Systems

In this paper, we consider physical layer security provisioning in multi-cell massive multiple-input multiple-output (MIMO) systems. Specifically, we consider secure downlink transmission in a multi-cell massive MIMO system with matched-filter precoding and artificial noise (AN) generation at the base station (BS) in the presence of a passive multi-antenna eavesdropper. We investigate the resulting achievable ergodic secrecy rate and the secrecy outage probability for the cases of perfect training and pilot contamination. Thereby, we consider two different AN shaping matrices, namely, the conventional AN shaping matrix, where the AN is transmitted in the null space of the matrix formed by all user channels, and a random AN shaping matrix, which avoids the complexity associated with finding the null space of a large matrix. Our analytical and numerical results reveal that in multi-cell massive MIMO systems employing matched-filter precoding (1) AN generation is required to achieve a positive ergodic secrecy rate if the user and the eavesdropper experience the same path-loss, (2) even with AN generation secure transmission may not be possible if the number of eavesdropper antennas is too large and not enough power is allocated to channel estimation, (3) for a given fraction of power allocated to AN and a given number of users, in case of pilot contamination, the ergodic secrecy rate is not a monotonically increasing function of the number of BS antennas, and (4) random AN shaping matrices provide a favourable performance/complexity tradeoff and are an attractive alternative to conventional AN shaping matrices

Distribution, diversity and evolution of endogenous retroviruses in perissodactyl genomes

The evolution of mammalian genomes has been shaped by interactions with endogenous retroviruses (ERVs). In this study, we investigated the distribution and diversity of ERVs in the mammalian order Perissodactyla, with a view to understanding their impact on the evolution of modern equids (family Equidae). We characterize the major ERV lineages in the horse genome in terms of their genomic distribution, ancestral genome organization and time of activity. Our results show that subsequent to their ancestral divergence from rhinos and tapirs, equids acquired four novel ERV lineages. We show that two of these proliferated extensively in the lineage leading to modern horses, and one contains loci that are actively transcribed in specific tissues. In addition, we show that the white rhinoceros has resisted germline colonisation by retroviruses for over 54 million years - longer than any other extant mammalian species. The map of equine ERVs that we provide here will be of great utility to future studies aiming to investigate the potential functional roles of equine ERVs, and their impact on equine evolution