Calibrated Multivariate Regression with Application to Neural Semantic Basis Discovery

We propose a calibrated multivariate regression method named CMR for fitting high dimensional multivariate regression models. Compared with existing methods, CMR calibrates regularization for each regression task with respect to its noise level so that it simultaneously attains improved finite-sample performance and tuning insensitiveness. Theoretically, we provide sufficient conditions under which CMR achieves the optimal rate of convergence in parameter estimation. Computationally, we propose an efficient smoothed proximal gradient algorithm with a worst-case numerical rate of convergence \cO(1/\epsilon), where $\epsilon$ is a pre-specified accuracy of the objective function value. We conduct thorough numerical simulations to illustrate that CMR consistently outperforms other high dimensional multivariate regression methods. We also apply CMR to solve a brain activity prediction problem and find that it is as competitive as a handcrafted model created by human experts. The R package \texttt{camel} implementing the proposed method is available on the Comprehensive R Archive Network \url{http://cran.r-project.org/web/packages/camel/}.Comment: Journal of Machine Learning Research, 201

Quantum delayed-choice experiment with a beam splitter in a quantum superposition

A quantum system can behave as a wave or as a particle, depending on the experimental arrangement. When for example measuring a photon using a Mach-Zehnder interferometer, the photon acts as a wave if the second beam-splitter is inserted, but as a particle if this beam-splitter is omitted. The decision of whether or not to insert this beam-splitter can be made after the photon has entered the interferometer, as in Wheeler's famous delayed-choice thought experiment. In recent quantum versions of this experiment, this decision is controlled by a quantum ancilla, while the beam splitter is itself still a classical object. Here we propose and realize a variant of the quantum delayed-choice experiment. We configure a superconducting quantum circuit as a Ramsey interferometer, where the element that acts as the first beam-splitter can be put in a quantum superposition of its active and inactive states, as verified by the negative values of its Wigner function. We show that this enables the wave and particle aspects of the system to be observed with a single setup, without involving an ancilla that is not itself a part of the interferometer. We also study the transition of this quantum beam-splitter from a quantum to a classical object due to decoherence, as observed by monitoring the interferometer output.Comment: 9 pages, 7 figures, Accepted by Physical Review Letter