arXiv subjects

Yunfan Li

Publications and source records attributed to Yunfan Li.

40 records · Page 3Linked to original sources

arXiv2019

Prediction risk for the horseshoe regression

We show that prediction performance for global-local shrinkage regression can overcome two major difficulties of global shrinkage regression: (i) the amount of relative shrinkage is monotone in the singular values of the design matrix and (ii) the shrinkage is determined by a single tuning parameter. Specifically, we show that the horseshoe regression, with heavy-tailed component-specific local shrinkage parameters, in conjunction with a global parameter providing shrinkage towards zero, alleviates both these difficulties and consequently, results in an improved risk for prediction. Numerical demonstrations of improved prediction over competing approaches in simulations and in a pharmacogenomics data set confirm our theoretical findings.

math.ST↗

arXiv2019

The Graphical Horseshoe Estimator for Inverse Covariance Matrices

We develop a new estimator of the inverse covariance matrix for high-dimensional multivariate normal data using the horseshoe prior. The proposed graphical horseshoe estimator has attractive properties compared to other popular estimators, such as the graphical lasso and graphical Smoothly Clipped Absolute Deviation (SCAD). The most prominent benefit is that when the true inverse covariance matrix is sparse, the graphical horseshoe provides estimates with small information divergence from the true sampling distribution. The posterior mean under the graphical horseshoe prior can also be almost unbiased under certain conditions. In addition to these theoretical results, we also provide a full Gibbs sampler for implementing our estimator. MATLAB code is available for download from github at http://github.com/liyf1988/GHS. The graphical horseshoe estimator compares favorably to existing techniques in simulations and in a human gene network data analysis.

stat.ME↗

arXiv2010

Structured Error Recovery for Codeword-Stabilized Quantum Codes

Codeword stabilized (CWS) codes are, in general, non-additive quantum codes that can correct errors by an exhaustive search of different error patterns, similar to the way that we decode classical non-linear codes. For an n-qubit quantum code correcting errors on up to t qubits, this brute-force approach consecutively tests different errors of weight t or less, and employs a separate n-qubit measurement in each test. In this paper, we suggest an error grouping technique that allows to simultaneously test large groups of errors in a single measurement. This structured error recovery technique exponentially reduces the number of measurements by about 3^t times. While it still leaves exponentially many measurements for a generic CWS code, the technique is equivalent to syndrome-based recovery for the special case of additive CWS codes.

quant-ph↗

arXiv2010

Clustered Error Correction of Codeword-Stabilized Quantum Codes

Codeword stabilized (CWS) codes are a general class of quantum codes that includes stabilizer codes and many families of non-additive codes with good parameters. For such a non-additive code correcting all t-qubit errors, we propose an algorithm that employs a single measurement to test all errors located on a given set of t qubits. Compared with exhaustive error screening, this reduces the total number of measurements required for error recovery by a factor of about 3^t.

quant-ph↗