Quantum Uncertainty Based on Metric Adjusted Skew Information

Prompted by the open questions in Gibilisco [Int. J. Software Informatics, 8(3-4): 265, 2014], in which he introduced a family of measurement-induced quantum uncertainty measures via metric adjusted skew informations, we investigate these measures' fundamental properties (including basis independence and spectral representation), and illustrate their applications to detect quantum nonlocality and entanglement.Comment: 14 page

A Probabilistic Characterization of g-Harmonic Functions

This paper gives a definition of g-harmonic functions and shows the relation between the g-harmonic functions and g-martingales. It's direct to construct such relation under smooth case, but for continuous case we need the theory of viscosity solution. The results show that under the nonlinear expectation mechanism, we also can get the similar relation between harmonic functions and martingales. Finally, we will give a result about the strict converse problem of mean value property of g-harmonic functions

Quantifying and Estimating the Predictive Accuracy for Censored Time-to-Event Data with Competing Risks

This paper focuses on quantifying and estimating the predictive accuracy of prognostic models for time-to-event outcomes with competing events. We consider the time-dependent discrimination and calibration metrics, including the receiver operating characteristics curve and the Brier score, in the context of competing risks. To address censoring, we propose a unified nonparametric estimation framework for both discrimination and calibration measures, by weighting the censored subjects with the conditional probability of the event of interest given the observed data. We demonstrate through simulations that the proposed estimator is unbiased, efficient and robust against model misspecification in comparison to other methods published in the literature. In addition, the proposed method can be extended to time-dependent predictive accuracy metrics constructed from a general class of loss functions. We apply the methodology to a data set from the African American Study of Kidney Disease and Hypertension to evaluate the predictive accuracy of a prognostic risk score in predicting end-stage renal disease (ESRD), accounting for the competing risk of pre-ESRD death

2.4GHZ Class AB power Amplifier For Healthcare Application

The objective of this research was to design a 2.4 GHz class AB Power Amplifier, with 0.18 um SMIC CMOS technology by using Cadence software, for health care applications. The ultimate goal for such application is to minimize the trade-offs between performance and cost, and between performance and low power consumption design. The performance of the power amplifier meets the specification requirements of the desired.Comment: 6 page

Predictive regressions for macroeconomic data

Researchers have constantly asked whether stock returns can be predicted by some macroeconomic data. However, it is known that macroeconomic data may exhibit nonstationarity and/or heavy tails, which complicates existing testing procedures for predictability. In this paper we propose novel empirical likelihood methods based on some weighted score equations to test whether the monthly CRSP value-weighted index can be predicted by the log dividend-price ratio or the log earnings-price ratio. The new methods work well both theoretically and empirically regardless of the predicting variables being stationary or nonstationary or having an infinite variance.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS708 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Geometric Inference for General High-Dimensional Linear Inverse Problems

This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix estimation, and noisy matrix completion. We propose computationally feasible convex programs for statistical inference including estimation, confidence intervals and hypothesis testing. A theoretical framework is developed to characterize the local estimation rate of convergence and to provide statistical inference guarantees. Our results are built based on the local conic geometry and duality. The difficulty of statistical inference is captured by the geometric characterization of the local tangent cone through the Gaussian width and Sudakov minoration estimate.Comment: 39 pages, 6 figure

Weighted Message Passing and Minimum Energy Flow for Heterogeneous Stochastic Block Models with Side Information

We study the misclassification error for community detection in general heterogeneous stochastic block models (SBM) with noisy or partial label information. We establish a connection between the misclassification rate and the notion of minimum energy on the local neighborhood of the SBM. We develop an optimally weighted message passing algorithm to reconstruct labels for SBM based on the minimum energy flow and the eigenvectors of a certain Markov transition matrix. The general SBM considered in this paper allows for unequal-size communities, degree heterogeneity, and different connection probabilities among blocks. We focus on how to optimally weigh the message passing to improve misclassification.Comment: 31 pages, 1 figure

Computational and Statistical Boundaries for Submatrix Localization in a Large Noisy Matrix

The interplay between computational efficiency and statistical accuracy in high-dimensional inference has drawn increasing attention in the literature. In this paper, we study computational and statistical boundaries for submatrix localization. Given one observation of (one or multiple non-overlapping) signal submatrix (of magnitude $\lambda$ and size $k_m \times k_n$) contaminated with a noise matrix (of size $m \times n$), we establish two transition thresholds for the signal to noise $\lambda/\sigma$ ratio in terms of $m$, $n$, $k_m$, and $k_n$. The first threshold, $\sf SNR_c$, corresponds to the computational boundary. Below this threshold, it is shown that no polynomial time algorithm can succeed in identifying the submatrix, under the \textit{hidden clique hypothesis}. We introduce adaptive linear time spectral algorithms that identify the submatrix with high probability when the signal strength is above the threshold $\sf SNR_c$. The second threshold, $\sf SNR_s$, captures the statistical boundary, below which no method can succeed with probability going to one in the minimax sense. The exhaustive search method successfully finds the submatrix above this threshold. The results show an interesting phenomenon that $\sf SNR_c$ is always significantly larger than $\sf SNR_s$, which implies an essential gap between statistical optimality and computational efficiency for submatrix localization.Comment: 37 pages, 1 figur

On Detection and Structural Reconstruction of Small-World Random Networks

In this paper, we study detection and fast reconstruction of the celebrated Watts-Strogatz (WS) small-world random graph model \citep{watts1998collective} which aims to describe real-world complex networks that exhibit both high clustering and short average length properties. The WS model with neighborhood size $k$ and rewiring probability probability $\beta$ can be viewed as a continuous interpolation between a deterministic ring lattice graph and the Erd\H{o}s-R\'{e}nyi random graph. We study both the computational and statistical aspects of detecting the deterministic ring lattice structure (or local geographical links, strong ties) in the presence of random connections (or long range links, weak ties), and for its recovery. The phase diagram in terms of $(k,\beta)$ is partitioned into several regions according to the difficulty of the problem. We propose distinct methods for the various regions.Comment: 22 pages, 3 figure

Inference via Message Passing on Partially Labeled Stochastic Block Models

We study the community detection and recovery problem in partially-labeled stochastic block models (SBM). We develop a fast linearized message-passing algorithm to reconstruct labels for SBM (with $n$ nodes, $k$ blocks, $p,q$ intra and inter block connectivity) when $\delta$ proportion of node labels are revealed. The signal-to-noise ratio ${\sf SNR}(n,k,p,q,\delta)$ is shown to characterize the fundamental limitations of inference via local algorithms. On the one hand, when ${\sf SNR}>1$, the linearized message-passing algorithm provides the statistical inference guarantee with mis-classification rate at most $\exp(-({\sf SNR}-1)/2)$, thus interpolating smoothly between strong and weak consistency. This exponential dependence improves upon the known error rate $({\sf SNR}-1)^{-1}$ in the literature on weak recovery. On the other hand, when ${\sf SNR}<1$ (for $k=2$) and ${\sf SNR}<1/4$ (for general growing $k$), we prove that local algorithms suffer an error rate at least $\frac{1}{2} - \sqrt{\delta \cdot {\sf SNR}}$, which is only slightly better than random guess for small $\delta$.Comment: 33 pages, 4 figure