arXiv subjects

Han Liu

Publications and source records attributed to Han Liu.

At least 397 records · Page 22Linked to original sources

arXiv2015

A General Theory of Hypothesis Tests and Confidence Regions for Sparse High Dimensional Models

We consider the problem of uncertainty assessment for low dimensional components in high dimensional models. Specifically, we propose a decorrelated score function to handle the impact of high dimensional nuisance parameters. We consider both hypothesis tests and confidence regions for generic penalized M-estimators. Unlike most existing inferential methods which are tailored for individual models, our approach provides a general framework for high dimensional inference and is applicable to a wide range of applications. From the testing perspective, we develop general theorems to characterize the limiting distributions of the decorrelated score test statistic under both null hypothesis and local alternatives. These results provide asymptotic guarantees on the type I errors and local powers of the proposed test. Furthermore, we show that the decorrelated score function can be used to construct point and confidence region estimators that are semiparametrically efficient. We also generalize this framework to broaden its applications. First, we extend it to handle high dimensional null hypothesis, where the number of parameters of interest can increase exponentially fast with the sample size. Second, we establish the theory for model misspecification. Third, we go beyond the likelihood framework, by introducing the generalized score test based on general loss functions. Thorough numerical studies are conducted to back up the developed theoretical results.

stat.ML↗

arXiv2015

Robust Inference of Risks of Large Portfolios

We propose a bootstrap-based robust high-confidence level upper bound (Robust H-CLUB) for assessing the risks of large portfolios. The proposed approach exploits rank-based and quantile-based estimators, and can be viewed as a robust extension of the H-CLUB method (Fan et al., 2015). Such an extension allows us to handle possibly misspecified models and heavy-tailed data. Under mixing conditions, we analyze the proposed approach and demonstrate its advantage over the H-CLUB. We further provide thorough numerical results to back up the developed theory. We also apply the proposed method to analyze a stock market dataset.

math.ST↗

arXiv2014

Testing and Confidence Intervals for High Dimensional Proportional Hazards Model

This paper proposes a decorrelation-based approach to test hypotheses and construct confidence intervals for the low dimensional component of high dimensional proportional hazards models. Motivated by the geometric projection principle, we propose new decorrelated score, Wald and partial likelihood ratio statistics. Without assuming model selection consistency, we prove the asymptotic normality of these test statistics, establish their semiparametric optimality. We also develop new procedures for constructing pointwise confidence intervals for the baseline hazard function and baseline survival function. Thorough numerical results are provided to back up our theory.

stat.ML↗

arXiv2014

Challenges of Big Data Analysis

Big Data bring new opportunities to modern society and challenges to data scientists. On one hand, Big Data hold great promises for discovering subtle population patterns and heterogeneities that are not possible with small-scale data. On the other hand, the massive sample size and high dimensionality of Big Data introduce unique computational and statistical challenges, including scalability and storage bottleneck, noise accumulation, spurious correlation, incidental endogeneity, and measurement errors. These challenges are distinguished and require new computational and statistical paradigm. This article give overviews on the salient features of Big Data and how these features impact on paradigm change on statistical and computational methods as well as computing architectures. We also provide various new perspectives on the Big Data analysis and computation. In particular, we emphasis on the viability of the sparsest solution in high-confidence set and point out that exogeneous assumptions in most statistical methods for Big Data can not be validated due to incidental endogeneity. They can lead to wrong statistical inferences and consequently wrong scientific conclusions.

stat.ML↗

arXiv2014

Smooth projected density estimation

We introduce and analyse a new nonparametric estimator of a multi-dimensional density. Our smooth projection estimator (SPE) is defined by a least squares projection of the sample onto an infinite dimensional mixture class via an undersmoothed nonparametric pilot estimate, which acts as a structural filter to regularise the solution. The undersmoothing is required to optimise the convergence rate of the SPE, which is jointly determined by that of the pilot estimator to the true density in squared $\mathbb{L}_{2}$ norm, and by that of the pilot distribution function to the empirical distribution function in uniform norm. Our procedure was conceived with a view to exploiting well known results in convex analysis and their connection to mixture densities. In the context of our work, this translates to the observation that the infinite dimensional minimisation problem, implicit in the construction of the SPE, possesses a solution of dimension at most $n+1$, where $n$ is the sample size. The SPE thus enjoys practical advantages such as computational efficiency, ease of storage and rapid evaluation at a new data point.

stat.ME↗

arXiv2014

Stochastic Compositional Gradient Descent: Algorithms for Minimizing Compositions of Expected-Value Functions

Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value functions, i.e., problems of the form $\min_x \mathbf{E}_v [f_v\big(\mathbf{E}_w [g_w(x)]\big)]$. In order to solve this stochastic composition problem, we propose a class of stochastic compositional gradient descent (SCGD) algorithms that can be viewed as stochastic versions of quasi-gradient method. SCGD update the solutions based on noisy sample gradients of $f_v,g_{w}$ and use an auxiliary variable to track the unknown quantity $\mathbf{E}_w[g_w(x)]$. We prove that the SCGD converge almost surely to an optimal solution for convex optimization problems, as long as such a solution exists. The convergence involves the interplay of two iterations with different time scales. For nonsmooth convex problems, the SCGD achieve a convergence rate of $O(k^{-1/4})$ in the general case and $O(k^{-2/3})$ in the strongly convex case, after taking $k$ samples. For smooth convex problems, the SCGD can be accelerated to converge at a rate of $O(k^{-2/7})$ in the general case and $O(k^{-4/5})$ in the strongly convex case. For nonconvex problems, we prove that any limit point generated by SCGD is a stationary point, for which we also provide the convergence rate analysis. Indeed, the stochastic setting where one wants to optimize compositions of expected-value functions is very common in practice. The proposed SCGD methods find wide applications in learning, estimation, dynamic programming, etc.

stat.ML↗

arXiv2014

Semiconducting Black Phosphorus: Synthesis, Transport Properties and Electronic Applications

Phosphorus is one of the most abundant elements preserved in earth, constructing with a fraction of ~0.1% of the earth crust. In general, phosphorus has several allotropes. The two most commonly seen allotropes, white and red phosphorus, are widely used in explosives and safety matches. In addition, black phosphorus, though rarely mentioned, is a layered semiconductor and have great potentials in optical and electronic applications. Remarkably, this layered material can be reduced to one single atomic layer in the vertical direction owing to the van der Waals structure, known as phosphorene, where the physical properties can be tremendously different from its bulk counterpart. In this review article, we trace back to the 100 years research history on black phosphorus from the synthesis to material properties, and extend the topic from black phosphorus to phosphorene. The physical and transport properties are highlighted, aiming at further applications in electronic and optoelectronics devices.

cond-mat.mtrl-sci↗

arXiv2014

A Direct Estimation of High Dimensional Stationary Vector Autoregressions

The vector autoregressive (VAR) model is a powerful tool in modeling complex time series and has been exploited in many fields. However, fitting high dimensional VAR model poses some unique challenges: On one hand, the dimensionality, caused by modeling a large number of time series and higher order autoregressive processes, is usually much higher than the time series length; On the other hand, the temporal dependence structure in the VAR model gives rise to extra theoretical challenges. In high dimensions, one popular approach is to assume the transition matrix is sparse and fit the VAR model using the "least squares" method with a lasso-type penalty. In this manuscript, we propose an alternative way in estimating the VAR model. The main idea is, via exploiting the temporal dependence structure, to formulate the estimating problem into a linear program. There is instant advantage for the proposed approach over the lasso-type estimators: The estimation equation can be decomposed into multiple sub-equations and accordingly can be efficiently solved in a parallel fashion. In addition, our method brings new theoretical insights into the VAR model analysis. So far the theoretical results developed in high dimensions (e.g., Song and Bickel (2011) and Kock and Callot (2012)) mainly pose assumptions on the design matrix of the formulated regression problems. Such conditions are indirect about the transition matrices and not transparent. In contrast, our results show that the operator norm of the transition matrices plays an important role in estimation accuracy. We provide explicit rates of convergence for both estimation and prediction. In addition, we provide thorough experiments on both synthetic and real-world equity data to show that there are empirical advantages of our method over the lasso-type estimators in both parameter estimation and forecasting.

stat.ML↗

arXiv2014

Device Perspective for Black Phosphorus Field-Effect Transistors: Contact Resistance, Ambipolar and Scaling

Although monolayer black phosphorus (BP) or phosphorene has been successfully exfoliated and its optical properties have been explored, most of electrical performance of the devices is demonstrated on few-layer phosphorene and ultra-thin BP films. In this paper, we study the channel length scaling of ultra-thin BP field-effect transistors (FETs), and discuss a scheme for using various contact metals to change transistor characteristics. Through studying transistor behaviors with various channel lengths, the contact resistance can be extracted from the transfer length method (TLM). With different contact metals, we find out that the metal/BP interface has different Schottky barrier heights, leading to a significant difference in contact resistance, which is quite different from previous studies of transition metal dichalcogenides (TMDs) such as MoS2 where Fermi-level is strongly pinned near conduction band edge at metal/MoS2 interface. The nature of BP transistors are Schottky barrier FETs, where the on and off states are controlled by tuning the Schottky barriers at the two contacts. We also observe the ambipolar characteristics of BP transistors with enhanced n-type drain current and demonstrate that the p-type carriers can be easily shifted to n-type or vice versus by controlling the gate bias and drain bias, showing the potential to realize BP CMOS logic circuits.

cond-mat.mtrl-sci↗

arXiv2014

Contact Research Strategy for Emerging Molybdenum Disulfide and Other Two-Dimensional Field-effect Transistors

Layered two-dimensional (2D) semiconducting transition metal dichalcogenides (TMD) have been widely isolated, synthesized, and characterized recently. Numerous 2D materials are identified as the potential candidates as channel materials for future thin film technology due to their high mobility and the exhibiting bandgaps. While many TMD filed-effect transistors (FETs) have been widely demonstrated along with a significant progress to clearly understand the device physics, large contact resistance at metal/semiconductor interface still remain a challenge. From 2D device research point of view, how to minimize the Schottky barrier effects on contacts thus reduce the contact resistance of metals on 2D materials is very critical for the further development of the field. Here, we present a review of contact research on molybdenum disulfide and other TMD FETs from the fundamental understanding of metal-semiconductor interfaces on 2D materials. A clear contact research strategy on 2D semiconducting materials is developed for future high-performance 2D FETs with aggressively scaled dimensions.

cond-mat.mtrl-sci↗

arXiv2014

On the Impact of Dimension Reduction on Graphical Structures

Statisticians and quantitative neuroscientists have actively promoted the use of independence relationships for investigating brain networks, genomic networks, and other measurement technologies. Estimation of these graphs depends on two steps. First is a feature extraction by summarizing measurements within a parcellation, regional or set definition to create nodes. Secondly, these summaries are then used to create a graph representing relationships of interest. In this manuscript we study the impact of dimension reduction on graphs that describe different notions of relations among a set of random variables. We are particularly interested in undirected graphs that capture the random variables' independence and conditional independence relations. A dimension reduction procedure can be any mapping from high dimensional spaces to low dimensional spaces. We exploit a general framework for modeling the raw data and advocate that in estimating the undirected graphs, any acceptable dimension reduction procedure should be a graph-homotopic mapping, i.e., the graphical structure of the data after dimension reduction should inherit the main characteristics of the graphical structure of the raw data. We show that, in terms of inferring undirected graphs that characterize the conditional independence relations among random variables, many dimension reduction procedures, such as the mean, median, or principal components, cannot be theoretically guaranteed to be a graph-homotopic mapping. The implications of this work are broad. In the most charitable setting for researchers, where the correct node definition is known, graphical relationships can be contaminated merely via the dimension reduction. The manuscript ends with a concrete example, characterizing a subset of graphical structures such that the dimension reduction procedure using the principal components can be a graph-homotopic mapping.

stat.ME↗

arXiv2014

Chloride Molecular Doping Technique on 2D Materials: WS2 and MoS2

Low-resistivity metal-semiconductor (M-S) contact is one of the urgent challenges in the research of 2D transition metal dichalcogenides (TMDs). Here, we report a chloride molecular doping technique which greatly reduces the contact resistance (Rc) in the few-layer WS2 and MoS2. After doping, the Rc of WS2 and MoS2 have been decreased to 0.7 kohm*um and 0.5 kohm*um, respectively. The significant reduction of the Rc is attributed to the achieved high electron doping density thus significant reduction of Schottky barrier width. As a proof-ofconcept, high-performance few-layer WS2 field-effect transistors (FETs) are demonstrated, exhibiting a high drain current of 380 uA/um, an on/off ratio of 4*106, and a peak field-effect mobility of 60 cm2/V*s. This doping technique provides a highly viable route to diminish the Rc in TMDs, paving the way for high-performance 2D nano-electronic devices.

cond-mat.mtrl-sci↗

arXiv2014

Joint Estimation of Multiple Graphical Models from High Dimensional Time Series

In this manuscript we consider the problem of jointly estimating multiple graphical models in high dimensions. We assume that the data are collected from n subjects, each of which consists of T possibly dependent observations. The graphical models of subjects vary, but are assumed to change smoothly corresponding to a measure of closeness between subjects. We propose a kernel based method for jointly estimating all graphical models. Theoretically, under a double asymptotic framework, where both (T,n) and the dimension d can increase, we provide the explicit rate of convergence in parameter estimation. It characterizes the strength one can borrow across different individuals and impact of data dependence on parameter estimation. Empirically, experiments on both synthetic and real resting state functional magnetic resonance imaging (rs-fMRI) data illustrate the effectiveness of the proposed method.

stat.ML↗

arXiv2014

Temporal and Thermal Stability of Al2O3-passivated Phosphorene MOSFETs

This letter evaluates temporal and thermal stability of a state-of-the-art few-layer phosphorene MOSFET with Al2O3 surface passivation and Ti/Au top gate. As fabricated, the phosphorene MOSFET was stable in atmosphere for at least 100 h. With annealing at 200°C in dry nitrogen for 1 h, its drain current increased by an order of magnitude to approximately 100 mA/mm, which could be attributed to the reduction of trapped charge in Al2O3 and/or Schottky barrier at the source and drain contacts. Thereafter, the drain current was stable between -50°C and 150°C up to at least 1000 h. These promising results suggest that environmental protection of phosphorene should not be a major concern, and passivation of phosphorene should focus on its effect on electronic control and transport as in conventional silicon MOSFETs. With cutoff frequencies approaching the gigahertz range, the present phosphorene MOSFET, although far from being optimized, can meet the frequency and stability requirements of most flexible electronics for which phosphorene is intrinsically advantageous due to its corrugated lattice structure.

cond-mat.mtrl-sci↗

arXiv2014

Nonconvex Statistical Optimization: Minimax-Optimal Sparse PCA in Polynomial Time

Sparse principal component analysis (PCA) involves nonconvex optimization for which the global solution is hard to obtain. To address this issue, one popular approach is convex relaxation. However, such an approach may produce suboptimal estimators due to the relaxation effect. To optimally estimate sparse principal subspaces, we propose a two-stage computational framework named "tighten after relax": Within the 'relax' stage, we approximately solve a convex relaxation of sparse PCA with early stopping to obtain a desired initial estimator; For the 'tighten' stage, we propose a novel algorithm called sparse orthogonal iteration pursuit (SOAP), which iteratively refines the initial estimator by directly solving the underlying nonconvex problem. A key concept of this two-stage framework is the basin of attraction. It represents a local region within which the `tighten' stage has desired computational and statistical guarantees. We prove that, the initial estimator obtained from the 'relax' stage falls into such a region, and hence SOAP geometrically converges to a principal subspace estimator which is minimax-optimal within a certain model class. Unlike most existing sparse PCA estimators, our approach applies to the non-spiked covariance models, and adapts to non-Gaussianity as well as dependent data settings. Moreover, through analyzing the computational complexity of the two stages, we illustrate an interesting phenomenon that larger sample size can reduce the total iteration complexity. Our framework motivates a general paradigm for solving many complex statistical problems which involve nonconvex optimization with provable guarantees.

stat.ML↗

arXiv2014

Two-Dimensional TaSe2 Metallic Crystals: Spin-Orbit Scattering Length and Breakdown Current Density

We have determined the spin-orbit scattering length of two-dimensional layered 2H-TaSe2 metallic crystals by detailed characterization of the weak anti-localization phenomena in this strong spin-orbit interaction material. By fitting the observed magneto-conductivity, the spin-orbit scattering length for 2H-TaSe2 is determined to be 17 nm in the few-layer films. This small spin-orbit scattering length is comparable to that of Pt, which is widely used to study the spin Hall effect, and indicates the potential of TaSe2 for use in spin Hall effect devices. In addition to strong spin-orbit coupling, a material must also support large charge currents to achieve spin-transfer-torque via the spin Hall effect. Therefore, we have characterized the room temperature breakdown current density of TaSe2 in air, where the best breakdown current density reaches 3.7$\times$10$^7$ A/cm$^2$. This large breakdown current further indicates the potential of TaSe2 for use in spin-torque devices and two-dimensional device interconnect applications.

cond-mat.mes-hall↗

arXiv2014

Black Phosphorus-Monolayer MoS2 van der Waals Heterojunction P-N Diode

Phosphorene, an elemental 2D material, which is the monolayer of black phosphorus, has been mechanically exfoliated recently. In its bulk form, black phosphorus shows high carrier mobility (~10000 cm2/Vs) and a ~0.3 eV direct bandgap. Well-behaved p-type field-effect transistors with mobilities of up to 1000 cm2/Vs, as well as phototransistors, have been demonstrated on few-layer black phosphorus, showing its promise for electronics and optoelectronics applications due to its high hole mobility and thickness-dependence direct bandgap. However, p-n junctions, the basic building blocks of modern electronic and optoelectronic devices, have not yet been realized based on black phosphorus. In this paper, we demonstrate a gate tunable p-n diode based on a p-type black phosphorus/n-type monolayer MoS2 van der Waals p-n heterojunction. Upon illumination, these ultra-thin p-n diodes show a maximum photodetection responsivity of 418 mA/W at the wavelength of 633 nm, and photovoltaic energy conversion with an external quantum efficiency of 0.3%. These p-n diodes show promise for broadband photodetection and solar energy harvesting.

cond-mat.mes-hall↗

arXiv2014

High-Performance MoS2 Field-Effect Transistors Enabled by Chloride Doping: Record Low Contact Resistance (0.5 kohm*um) and Record High Drain Current (460 uA/um)

In this paper, we report a novel chemical doping technique to reduce the contact resistance (Rc) of transition metal dichalcogenides (TMDs) - eliminating two major roadblocks (namely, doping and high Rc) towards demonstration of high-performance TMDs field-effect transistors (FETs). By using 1,2 dichloroethane (DCE) as the doping reagent, we demonstrate an active n-type doping density > 2*1019 cm-3 in a few-layer MoS2 film. This enabled us to reduce the Rc value to a record low number of 0.5 kohm*um, which is ~10x lower than the control sample without doping. The corresponding specific contact resistivity (pc) is found to decrease by two orders of magnitude. With such low Rc, we demonstrate 100 nm channel length (Lch) MoS2 FET with a drain current (Ids) of 460 uA/um at Vds = 1.6 V, which is twice the best value reported so far on MoS2 FETs.

cond-mat.mtrl-sci↗