A Variational Algorithm for Bayesian Variable Selection

There has been an intense development on the estimation of a sparse regression coefficient vector in statistics, machine learning and related fields. In this paper, we focus on the Bayesian approach to this problem, where sparsity is incorporated by the so-called spike-and-slab prior on the coefficients. Instead of replying on MCMC for posterior inference, we propose a fast and scalable algorithm based on variational approximation to the posterior distribution. The updating scheme employed by our algorithm is different from the one proposed by Carbonetto and Stephens (2012). Those changes seem crucial for us to show that our algorithm can achieve asymptotic consistency even when the feature dimension diverges exponentially fast with the sample size. Empirical results have demonstrated the effectiveness and efficiency of the proposed algorithm

Discriminative Similarity for Clustering and Semi-Supervised Learning

Similarity-based clustering and semi-supervised learning methods separate the data into clusters or classes according to the pairwise similarity between the data, and the pairwise similarity is crucial for their performance. In this paper, we propose a novel discriminative similarity learning framework which learns discriminative similarity for either data clustering or semi-supervised learning. The proposed framework learns classifier from each hypothetical labeling, and searches for the optimal labeling by minimizing the generalization error of the learned classifiers associated with the hypothetical labeling. Kernel classifier is employed in our framework. By generalization analysis via Rademacher complexity, the generalization error bound for the kernel classifier learned from hypothetical labeling is expressed as the sum of pairwise similarity between the data from different classes, parameterized by the weights of the kernel classifier. Such pairwise similarity serves as the discriminative similarity for the purpose of clustering and semi-supervised learning, and discriminative similarity with similar form can also be induced by the integrated squared error bound for kernel density classification. Based on the discriminative similarity induced by the kernel classifier, we propose new clustering and semi-supervised learning methods

Speeding Up Neural Machine Translation Decoding by Cube Pruning

Although neural machine translation has achieved promising results, it suffers from slow translation speed. The direct consequence is that a trade-off has to be made between translation quality and speed, thus its performance can not come into full play. We apply cube pruning, a popular technique to speed up dynamic programming, into neural machine translation to speed up the translation. To construct the equivalence class, similar target hidden states are combined, leading to less RNN expansion operations on the target side and less \$\mathrm{softmax}\$ operations over the large target vocabulary. The experiments show that, at the same or even better translation quality, our method can translate faster compared with naive beam search by \$3.3\times\$ on GPUs and \$3.5\times\$ on CPUs.Comment: 11pages, 11 figures, EMNLP-2018 conferenc

Critical Current Anomaly at the Topological Quantum Phase Transition in a Majorana Josephson Junction

Majorana bound states in topological Josephson junctions induce a 4? period current-phase relation. Direct detection of the 4? periodicity is complicated by the quasiparticle poisoning. We reveal that Majorana bound states are also signaled by the anomalous enhancement on the critical current of the junction. We show the landscape of the critical current for a nanowire Josephson junction under a varying Zeeman field, and reveal a sharp step feature at the topological quantum phase transition point, which comes from the anomalous enhancement of the critical current at the topological regime. In multi-band wires, the anomalous enhancement disappears for an even number of bands, where the Majorana bound states fuse into Andreev bound states. This anomalous critical current enhancement directly signals the existence of the Majorana bound states, and also provides a valid signature for the topological quantum phase transition.Comment: 20 pages, 4 figure

Landau-Zener-St\"uckelberg Interferometry for Majorana Qubit

Stimulated by a very recent experiment observing successfully two superconducting states with even- and odd-number of electrons in a nanowire topological superconductor as expected from the existence of two end Majorana quasiparticles (MQs) [Albrecht \textit{et al.}, Nature \textbf{531}, 206 (2016)], we propose a way to manipulate Majorana qubit exploiting quantum tunneling effects. The prototype setup consists of two one-dimensional (1D) topological superconductors coupled by a tunneling junction which can be controlled by gate voltage. We show that, upon current injection, the time evolution of superconducting phase difference at the junction induces an oscillation in energy levels of the Majorana parity states, whereas the level-crossing is avoided by a small coupling energy of MQs in the individual 1D superconductors. This results in a Landau-Zener-St\"{u}ckelberg (LZS) interference between the Majorana parity states. Adjusting the current pulse and gate voltage, one can build a LZS interferometry which provides an arbitrary manipulation of the Majorana qubit. The LZS rotation of Majorana qubit can be monitored by the microwave radiated from the junction

VMAV-C: A Deep Attention-based Reinforcement Learning Algorithm for Model-based Control

Recent breakthroughs in Go play and strategic games have witnessed the great potential of reinforcement learning in intelligently scheduling in uncertain environment, but some bottlenecks are also encountered when we generalize this paradigm to universal complex tasks. Among them, the low efficiency of data utilization in model-free reinforcement algorithms is of great concern. In contrast, the model-based reinforcement learning algorithms can reveal underlying dynamics in learning environments and seldom suffer the data utilization problem. To address the problem, a model-based reinforcement learning algorithm with attention mechanism embedded is proposed as an extension of World Models in this paper. We learn the environment model through Mixture Density Network Recurrent Network(MDN-RNN) for agents to interact, with combinations of variational auto-encoder(VAE) and attention incorporated in state value estimates during the process of learning policy. In this way, agent can learn optimal policies through less interactions with actual environment, and final experiments demonstrate the effectiveness of our model in control problem

Manipulating the Majorana Qubit with the Landau-Zener-St\"{u}ckelberg Interference

Constructing a universal operation scheme for Majorana qubits remains a central issue for the topological quantum computation. We study the Landau-Zener-St\"{u}ckelberg interference in a Majorana qubit and show that this interference can be used to achieve controllable operations. The Majorana qubit consists of an rf SQUID with a topological nanowire Josephson junction which hosts Majorana bound states. In the SQUID, a magnetic flux pulse can drive the quantum evolution of the Majorana qubit. The qubit experiences two Landau-Zener transitions when the amplitude of the pulse is tuned around the superconducting flux quanta $2e/\hbar$. The Landau-Zener-St\"{u}ckelberg interference between the two transitions rotates the Majorana qubit, with the angle controlled by the time scale of the pulse. This rotation operation implements a high-speed single-qubit gate on the Majorana qubit, which is a necessary ingredient for the topological quantum computation

An efficient ab-initio quasiharmonic approach for the thermodynamics of solids

A first-principles approach called the {\it{self-consistent quasiharmonic approximation}} (SC-QHA) method is formulated to calculate the thermal expansion, thermomechanics, and thermodynamic functions of solids at finite temperatures with both high efficiency and accuracy. The SC-QHA method requires fewer phonon calculations than the conventional QHA method, and also facilitates the convenient analysis of the microscopic origins of macroscopic thermal phenomena. The superior performance of the SC-QHA method is systematically examined by comparing it with the conventional QHA method and experimental measurements on silicon, diamond, and alumina. It is then used to study the effects of pressure on the anharmonic lattice properties of diamond and alumina. The thermal expansion and thermomechanics of Ca$_3$Ti$_2$O$_7$, which is a recently discovered important ferroelectric ceramic with a complex crystal structure that is computationally challenging for the conventional QHA method, are also calculated using the formulated SC-QHA method. The SC-QHA method can significantly reduce the computational expense for various quasiharmonic thermal properties especially when there are a large number of structures to consider or when the solid is structurally complex. It is anticipated that the algorithm will be useful for a variety of fields, including oxidation, corrosion, high-pressure physics, ferroelectrics, and high-throughput structure screening when temperature effects are required to accurately describe realistic properties

Proposal for a flux qubit in a dc SQUID with the 4π4\pi period Josephson effect

Constructing qubits which are suitable for quantum computation remains a notable challenge. Here, we propose a superconducting flux qubit in a dc SQUID structure, formed by a conventional insulator Josephson junction and a topological nanowire Josephson junction with Majorana bound states. The zero energy Majorana bound states transport $4\pi$ period Josephson currents in the nanowire junction. The interplay between this $4\pi$ period Josephson effect and the convectional $2\pi$ period Josephson effect in the insulator junction induces a double-well potential energy landscape in the SQUID. As a result, the two lowest energy levels of the SQUID are isolated from other levels. These two levels show contradicting circulating supercurrents, thus can be used as a flux qubit. We reveal that this flux qubit has the merits of stability to external noises, tolerance to the deviation of system parameters, and scalability to large numbers. Furthermore, we demonstrate how to couple this flux qubit with the Majorana qubit by tuning the junction parameters, and how to use this coupling to manipulate the Majorana qubit

GeV excess in the Milky Way: The Role of Diffuse Galactic gamma ray Emission template

Several groups have analyzed the publicly-available Fermi-LAT data and reported a spatially extended $\gamma-$ray excess of around $1-3$ GeV from the region surrounding the Galactic Center that might originate from annihilation of dark matter particles with a rest mass $m_\chi \sim 30-40$ GeV. In this work we examine the role of the diffuse Galactic gamma ray emission (DGE) templates played in suppressing the GeV excess. For such a purpose, we adopt in total 128 background templates that have been generated by Ackermann et al. \cite{FermiLAT:2012aa} in the study of the {Fermi-LAT} observations of the diffuse gamma ray emission considering the effects of cosmic rays and the interstellar medium. The possible GeV excess, assumed to follow the spatial distribution of the prompt gamma-rays produced in the annihilation of dark matter particles taking a generalized NFW profile with an inner slope $\alpha=1.2$, has been analyzed in some regions of interest. The introduction of such an additional component centered at the Galactic center is found to have improved the goodness of fit to the data significantly in all background template models regardless of whether the excess spectrum is fixed or not. Our results thus suggest that the presence of a statistically significant GeV excess in the inner Galaxy is robust thought its spectrum depends on the DGE model adopted in the analysis. The possible physical origin of the GeV excess component is discussed and in the dark matter model the annihilation cross section of such particles is evaluated.Comment: 14 pages, 9 figures. Accepted for publication in PRD, moderate revision but main conclusions unchange