arXiv subjects

Xu Gao

Publications and source records attributed to Xu Gao.

29 records · Page 2Linked to original sources

arXiv2021

Addressing patient heterogeneity in disease predictive model development

This paper addresses patient heterogeneity associated with prediction problems in biomedical applications. We propose a systematic hypothesis testing approach to determine the existence of patient subgroup structure and the number of subgroups in patient population if subgroups exist. A mixture of generalized linear models is considered to model the relationship between the disease outcome and patient characteristics and clinical factors, including targeted biomarker profiles. We construct a test statistic based on expectation maximization (EM) algorithm and derive its asymptotic distribution under the null hypothesis. An important computational advantage of the test is that the involved parameter estimates under the complex alternative hypothesis can be obtained through a small number of EM iterations, rather than optimizing the objective function. We demonstrate the finite sample performance of the proposed test in terms of type-I error rate and power, using extensive simulation studies. The applicability of the proposed method is illustrated through an application to a multi-center prostate cancer study.

stat.ME↗

arXiv2019

Novel two-dimensional photocatalyst SnN3 for overall water splitting with enhanced visible-light absorption

We propose a novel excellent two-dimensional photocatalyst SnN3 monolayer using first-principles calculations. The stability of SnN3 monolayer have been examined via formation energy, phonon spectrum and ab initio molecular dynamics calculations. Large optical absorption capacity plays significant role in the enhancement of photocatalytic splitting of water. The SnN3 monolayer have ultra-high optical absorption capacity in visible region, which is as three and four times as that of SnP3 and MoS2 monolayer, respectively. Available potential and appropriate band positions indicating the ability of overall water splitting even in a wide strain range. Electronic properties of SnN3 monolayer can also be engineered effectively via the external strain, such as the conversion from in-direct band gap to direct band gap. The applied electric field splits the energy levels due to Stark effect, resulting in states accumulation and smaller gap width

cond-mat.mtrl-sci↗

arXiv2018

Fisher information matrix of binary time series

A common approach to analyzing categorical correlated time series data is to fit a generalized linear model (GLM) with past data as covariate inputs. There remain challenges to conducting inference for short time series length. By treating the historical data as covariate inputs, standard errors of estimates of GLM parameters computed using the empirical Fisher information do not fully account the auto-correlation in the data. To overcome this serious limitation, we derive the exact conditional Fisher information matrix of a general logistic autoregressive model with endogenous covariates for any series length $T$. Moreover, we also develop an iterative computational formula that allows for relatively easy implementation of the proposed estimator. Our simulation studies show that confidence intervals derived using the exact Fisher information matrix tend to be narrower than those utilizing the empirical Fisher information matrix while maintaining type I error rates at or below nominal levels. Further, we establish that the exact Fisher information matrix approaches, as T tends to infinity, the asymptotic Fisher information matrix previously derived for binary time series data. The developed exact conditional Fisher information matrix is applied to time-series data on respiratory rate among a cohort of expectant mothers where it is found to provide narrower confidence intervals for functionals of scientific interest and lead to greater statistical power when compared to the empirical Fisher information matrix.

math.ST↗

arXiv2018

Modeling Binary Time Series Using Gaussian Processes with Application to Predicting Sleep States

Motivated by the problem of predicting sleep states, we develop a mixed effects model for binary time series with a stochastic component represented by a Gaussian process. The fixed component captures the effects of covariates on the binary-valued response. The Gaussian process captures the residual variations in the binary response that are not explained by covariates and past realizations. We develop a frequentist modeling framework that provides efficient inference and more accurate predictions. Results demonstrate the advantages of improved prediction rates over existing approaches such as logistic regression, generalized additive mixed model, models for ordinal data, gradient boosting, decision tree and random forest. Using our proposed model, we show that previous sleep state and heart rates are significant predictors for future sleep states. Simulation studies also show that our proposed method is promising and robust. To handle computational complexity, we utilize Laplace approximation, golden section search and successive parabolic interpolation. With this paper, we also submit an R-package (HIBITS) that implements the proposed procedure.

stat.ME↗

arXiv2018

Evolutionary State-Space Model and Its Application to Time-Frequency Analysis of Local Field Potentials

We propose an evolutionary state space model (E-SSM) for analyzing high dimensional brain signals whose statistical properties evolve over the course of a non-spatial memory experiment. Under E-SSM, brain signals are modeled as mixtures of components (e.g., AR(2) process) with oscillatory activity at pre-defined frequency bands. To account for the potential non-stationarity of these components (since the brain responses could vary throughout the entire experiment), the parameters are allowed to vary over epochs. Compared with classical approaches such as independent component analysis and filtering, the proposed method accounts for the entire temporal correlation of the components and accommodates non-stationarity. For inference purpose, we propose a novel computational algorithm based upon using Kalman smoother, maximum likelihood and blocked resampling. The E-SSM model is applied to simulation studies and an application to a multi-epoch local field potentials (LFP) signal data collected from a non-spatial (olfactory) sequence memory task study. The results confirm that our method captures the evolution of the power for different components across different phases in the experiment and identifies clusters of electrodes that behave similarly with respect to the decomposition of different sources. These findings suggest that the activity of different electrodes does change over the course of an experiment in practice, treating these epoch recordings as realizations of an identical process could lead to misleading results. In summary, the proposed method underscores the importance of capturing the evolution in brain responses over the study period.

stat.ME↗

arXiv2018

Modeling Brain Connectivity with Graphical Models on Frequency Domain

Multichannel electroencephalograms (EEGs) have been widely used to study cortical connectivity during acquisition of motor skills. In this paper, we introduce copula Gaussian graphical models on spectral domain to characterize dependence in oscillatory activity between channels. To obtain a simple and robust representation of brain connectivity that can explain the most variation in the observed signals, we propose a framework based on maximizing penalized likelihood with Lasso regularization to search for the sparse precision matrix. To address the optimization problem, graphical Lasso, Ledoit-Wolf and sparse estimation of a covariance matrix (SPCOV) algorithms were modified and implemented. Simulations show the benefit of using the proposed algorithms in terms of robustness and small estimation errors. Furthermore, analysis of the EEG data in a motor skill task conducted using algorithms of modified graphical LASSO and Ledoit-Wolf, reveal a sparse pattern of brain connectivity among cortices which is consistent with the results from other work in the literature.

stat.AP↗

arXiv2018

Regularized matrix data clustering and its application to image analysis

In this paper, we propose a regularized mixture probabilistic model to cluster matrix data and apply it to brain signals. The approach is able to capture the sparsity (low rank, small/zero values) of the original signals by introducing regularization terms into the likelihood function. Through a modified EM algorithm, our method achieves the optimal solution with low computational cost. Theoretical results are also provided to establish the consistency of the proposed estimators. Simulations show the advantages of the proposed method over other existing methods. We also apply the approach to two real datasets from different experiments. Promising results imply that the proposed method successfully characterizes signals with different patterns while yielding insightful scientific interpretation.

stat.ME↗

arXiv2016

Rota-Baxter operators on Witt and Virasoro algebras

The homogeneous Rota-Baxter operators on the Witt and Virasoro algebras are classified. As applications, the induced solutions of the classical Yang-Baxter equation and the induced pre-Lie and PostLie algebra structures are obtained.

math-ph↗

arXiv2016

Addition formulae of discrete KP, q-KP and two-component BKP systems

In this paper, we constructed the addition formulae for several integrable hierarchies, including the discrete KP, the q-deformed KP, the two-component BKP and the D type Drinfeld-Sokolov hierarchies. With the help of the Hirota bilinear equations and $τ$ functions of different kinds of KP hierarchies, we prove that these addition formulae are equivalent to these hierarchies. These studies show that the addition formula in the research of the integrable systems has good universality.

nlin.SI↗

arXiv2014

Exact prior-free probabilistic inference on the heritability coefficient in a linear mixed model

Linear mixed-effect models with two variance components are often used when variability comes from two sources. In genetics applications, variation in observed traits can be attributed to biological and environmental effects, and the heritability coefficient is a fundamental quantity that measures the proportion of total variability due to the biological effect. We propose a new inferential model approach which yields exact prior-free probabilistic inference on the heritability coefficient. In particular we construct exact confidence intervals and demonstrate numerically our method's efficiency compared to that of existing methods.

stat.ME↗

arXiv2009

Unipolar Resistance Switching in Amorphous High-k dielectrics Based on Correlated Barrier Hopping Theory

We have proposed a kind of nonvolatile resistive switching memory based on amorphous LaLuO3, which has already been established as a promising candidate of high-k gate dielectric employed in transistors. Well-developed unipolar switching behaviors in amorphous LaLuO3 make it suited for not only logic but memory applications using the conventional semiconductor or the emerging nano/CMOS architectures. The conduction transition between high- and low- resistance states is attributed to the change in the separation between oxygen vacancy sites in the light of the correlated barrier hopping theory. The mean migration distances of vacancies responsible for the resistive switching are demonstrated in nanoscale, which could account for the ultrafast programming speed of 6 ns. The origin of the distributions in switching parameters in oxides can be well understood according to the switching principle. Furthermore, an approach has also been developed to make the operation voltages predictable for the practical applications of resistive memories.

cond-mat.mtrl-sci↗