arXiv subjects

Zhe Liu

Publications and source records attributed to Zhe Liu.

349 records · Page 20Linked to original sources

arXiv2016

Graphical Exponential Screening

In high dimensions we propose and analyze an aggregation estimator of the precision matrix for Gaussian graphical models. This estimator, called graphical Exponential Screening (gES), linearly combines a suitable set of individual estimators with different underlying graphs, and balances the estimation error and sparsity. We study the risk of this aggregation estimator and show that it is comparable to that of the best estimator based on a single graph, chosen by an oracle. Numerical performance of our method is investigated using both simulated and real datasets, in comparison with some state-of-art estimation procedures.

stat.ML↗

arXiv2016

Learning Nonparametric Forest Graphical Models with Prior Information

We present a framework for incorporating prior information into nonparametric estimation of graphical models. To avoid distributional assumptions, we restrict the graph to be a forest and build on the work of forest density estimation (FDE). We reformulate the FDE approach from a Bayesian perspective, and introduce prior distributions on the graphs. As two concrete examples, we apply this framework to estimating scale-free graphs and learning multiple graphs with similar structures. The resulting algorithms are equivalent to finding a maximum spanning tree of a weighted graph with a penalty term on the connectivity pattern of the graph. We solve the optimization problem via a minorize-maximization procedure with Kruskal's algorithm. Simulations show that the proposed methods outperform competing parametric methods, and are robust to the true data distribution. They also lead to improvement in predictive power and interpretability in two real data sets.

stat.ME↗

arXiv2015

Tunable mid-infrared coherent perfect absorption in a graphene meta-surface

We exploited graphene nanoribbons based meta-surface to realize coherent perfect absorption (CPA) in the mid-infrared regime. It was shown that quasi-CPA frequencies, at which CPA can be demonstrated with proper phase modulations, exist for the graphene meta-surface with strong resonant behaviors. The CPA can be tuned substantially by merging the geometric design of the meta-surface and the electrical tunability of graphene. Furthermore, we found that the graphene nanoribbon meta-surface based CPA is realizable with experimental graphene data. The findings of CPA with graphene meta-surface can be generalized for potential applications in optical detections and signal processing with two-dimensional optoelectronic materials.

physics.optics↗

arXiv2015

An Aggregation Method for Sparse Logistic Regression

$L_1$ regularized logistic regression has now become a workhorse of data mining and bioinformatics: it is widely used for many classification problems, particularly ones with many features. However, $L_1$ regularization typically selects too many features and that so-called false positives are unavoidable. In this paper, we demonstrate and analyze an aggregation method for sparse logistic regression in high dimensions. This approach linearly combines the estimators from a suitable set of logistic models with different underlying sparsity patterns and can balance the predictive ability and model interpretability. Numerical performance of our proposed aggregation method is then investigated using simulation studies. We also analyze a published genome-wide case-control dataset to further evaluate the usefulness of the aggregation method in multilocus association mapping.

stat.ML↗

arXiv2014

Is Twitter a Public Sphere for Online Conflicts? A Cross-Ideological and Cross-Hierarchical Look

The rise in popularity of Twitter has led to a debate on its impact on public opinions. The optimists foresee an increase in online participation and democratization due to social media's personal and interactive nature. Cyber-pessimists, on the other hand, explain how social media can lead to selective exposure and can be used as a disguise for those in power to disseminate biased information. To investigate this debate empirically, we evaluate Twitter as a public sphere using four metrics: equality, diversity, reciprocity and quality. Using these measurements, we analyze the communication patterns between individuals of different hierarchical levels and ideologies. We do this within the context of three diverse conflicts: Israel-Palestine, US Democrats-Republicans, and FC Barcelona-Real Madrid. In all cases, we collect data around a central pair of Twitter accounts representing the two main parties. Our results show in a quantitative manner that Twitter is not an ideal public sphere for democratic conversations and that hierarchical effects are part of the reason why it is not.

cs.SI↗

arXiv2014

The Heisenberg Relation - Mathematical Formulations

We study some of the possibilities for formulating the Heisenberg relation of quantum mechanics in mathematical terms. In particular, we examine the framework discussed by Murray and von Neumann, the family (algebra) of operators affiliated with a finite factor (of infinite linear dimension).

math.OA↗

arXiv2013

Laterally emitted surface second harmonic generation in a single ZnTe nanowire

We report a direct observation on the unique laterally emitted surface second harmonic generation (SHG) in a single ZnTe nanowire. The highly directional surface SHG signal that polarizes along the direction vertical to the nanowire growth axis, is significantly larger than the bulk SHG contribution, indicating a high efficiency of surface SHG. Two strong SHG peaks are observed on both sides of the nanowire surfaces in the far-field scanning images, which is further supported by FDTD simulations, demonstrating that the unique laterally emitted signal is ascribed to surface SHG in the ZnTe nanowire. The surface SHG in a single ZnTe nanowire with unique lateral emission and high conversion efficiency shows great potential applications in short-wavelength nanolasers, nonlinear microscopy and polarization dependent photonic integrating.

physics.optics↗