Searcharxiv⌕ Search

arXiv subjects

Jun Yu

Publications and source records attributed to Jun Yu.

At least 307 records · Page 17Linked to original sources
arXiv2017

Comparison of hidden Markov chain models and hidden Markov random field models in estimation of computed tomography images

There is an interest to replace computed tomography (CT) images with magnetic resonance (MR) images for a number of diagnostic and therapeutic workflows. In this article, predicting CT images from a number of magnetic resonance imaging (MRI) sequences using regression approach is explored. Two principal areas of application for estimated CT images are dose calculations in MRI-based radiotherapy treatment planning and attenuation correction for positron emission tomography (PET)/MRI. The main purpose of this work is to investigate the performance of hidden Markov (chain) models (HMMs) in comparison to hidden Markov random field (HMRF) models when predicting CT images of head. Our study shows that HMMs have clear advantages over HMRF models in this particular application. Obtained results suggest that HMMs deserve a further study for investigating their potential in modelling applications where the most natural theoretical choice would be the class of HMRF models.

stat.AP↗
arXiv2017

Model Selection for Explosive Models

This paper examines the limit properties of information criteria (such as AIC, BIC, HQIC) for distinguishing between the unit root model and the various kinds of explosive models. The explosive models include the local-to-unit-root model, the mildly explosive model and the regular explosive model. Initial conditions with different order of magnitude are considered. Both the OLS estimator and the indirect inference estimator are studied. It is found that BIC and HQIC, but not AIC, consistently select the unit root model when data come from the unit root model. When data come from the local-to-unit-root model, both BIC and HQIC select the wrong model with probability approaching 1 while AIC has a positive probability of selecting the right model in the limit. When data come from the regular explosive model or from the mildly explosive model in the form of $1+n^{α}/n$ with $α\in (0,1)$, all three information criteria consistently select the true model. Indirect inference estimation can increase or decrease the probability for information criteria to select the right model asymptotically relative to OLS, depending on the information criteria and the true model. Simulation results confirm our asymptotic results in finite sample.

math.ST↗
arXiv2017

Contrast Agent Quantification by Using Spatial Information in Dynamic Contrast Enhanced MRI

The purpose of this study is to investigate a method, using simulations, to improve contrast agent quantification in Dynamic Contrast Enhanced MRI. Bayesian hierarchical models (BHMs) are applied to smaller images ($10\times10\times10$) such that spatial information can be incorporated. Then exploratory analysis is done for larger images ($64\times64\times64$) by using maximum a posteriori (MAP). For smaller images: the estimators of proposed BHMs show improvements in terms of the root mean squared error compared to the estimators in existing method for a noise level equivalent of a 12-channel head coil at 3T. Moreover, Leroux model outperforms Besag models. For larger images: MAP estimators also show improvements by assigning Leroux prior.

stat.AP↗
arXiv2016

Shrinkage estimation of covariance matrix for portfolio choice with high frequency data

This paper examines the usefulness of high frequency data in estimating the covariance matrix for portfolio choice when the portfolio size is large. A computationally convenient nonlinear shrinkage estimator for the integrated covariance (ICV) matrix of financial assets is developed in two steps. The eigenvectors of the ICV are first constructed from a designed time variation adjusted realized covariance matrix of noise-free log-returns of relatively low frequency data. Then the regularized eigenvalues of the ICV are estimated by quasi-maximum likelihood based on high frequency data. The estimator is always positive definite and its inverse is the estimator of the inverse of ICV. It minimizes the limit of the out-of-sample variance of portfolio returns within the class of rotation-equivalent estimators. It works when the number of underlying assets is larger than the number of time series observations in each asset and when the asset price follows a general stochastic process. Our theoretical results are derived under the assumption that the number of assets (p) and the sample size (n) satisfy p/n \to y >0 as n goes to infty . The advantages of our proposed estimator are demonstrated using real data.

math.ST↗
arXiv2016

Constrained Low-Rank Learning Using Least Squares-Based Regularization

Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional subspace for supervised learning tasks, e.g., classification and regression. This paper aims to learn both the discriminant low-rank representation (LRR) and the robust projecting subspace in a supervised manner. To achieve this goal, we cast the problem into a constrained rank minimization framework by adopting the least squares regularization. Naturally, the data label structure tends to resemble that of the corresponding low-dimensional representation, which is derived from the robust subspace projection of clean data by low-rank learning. Moreover, the low-dimensional representation of original data can be paired with some informative structure by imposing an appropriate constraint, e.g., Laplacian regularizer. Therefore, we propose a novel constrained LRR method. The objective function is formulated as a constrained nuclear norm minimization problem, which can be solved by the inexact augmented Lagrange multiplier algorithm. Extensive experiments on image classification, human pose estimation, and robust face recovery have confirmed the superiority of our method.

cs.CV↗
arXiv2016

Whole-brain substitute CT generation using Markov random field mixture models

Computed tomography (CT) equivalent information is needed for attenuation correction in PET imaging and for dose planning in radiotherapy. Prior work has shown that Gaussian mixture models can be used to generate a substitute CT (s-CT) image from a specific set of MRI modalities. This work introduces a more flexible class of mixture models for s-CT generation, that incorporates spatial dependency in the data through a Markov random field prior on the latent field of class memberships associated with a mixture model. Furthermore, the mixture distributions are extended from Gaussian to normal inverse Gaussian (NIG), allowing heavier tails and skewness. The amount of data needed to train a model for s-CT generation is of the order of 100 million voxels. The computational efficiency of the parameter estimation and prediction methods are hence paramount, especially when spatial dependency is included in the models. A stochastic Expectation Maximization (EM) gradient algorithm is proposed in order to tackle this challenge. The advantages of the spatial model and NIG distributions are evaluated with a cross-validation study based on data from 14 patients. The study show that the proposed model enhances the predictive quality of the s-CT images by reducing the mean absolute error with 17.9%. Also, the distribution of CT values conditioned on the MR images are better explained by the proposed model as evaluated using continuous ranked probability scores.

stat.AP↗
arXiv2015

Rigidity for F_4(p)

We prove the existence of certain rationally rigid triples in F_4(p) for good primes p (i.e., p>3), thereby showing that these groups occur as regular Galois groups over Q(t) and so also over Q. We show that these triples give rise to rigid triples in the algebraic group and prove that they generate an interesting subgroup in characteristic 0.

math.NT↗
arXiv2015

Bayesian and empirical Bayesian forests

We derive ensembles of decision trees through a nonparametric Bayesian model, allowing us to view random forests as samples from a posterior distribution. This insight provides large gains in interpretability, and motivates a class of Bayesian forest (BF) algorithms that yield small but reliable performance gains. Based on the BF framework, we are able to show that high-level tree hierarchy is stable in large samples. This leads to an empirical Bayesian forest (EBF) algorithm for building approximate BFs on massive distributed datasets and we show that EBFs outperform sub-sampling based alternatives by a large margin.

stat.AP↗
arXiv2015

A Prime Decomposition of Probabilistic Automata

A definition of a probabilistic automaton is formulated in which its prime decomposition follows as a direct consequence of Krohn-Rhodes theorem. We first characterize the local structure of probabilistic automata. The prime decomposition is presented as a framework to study the global structure of probabilistic automata. We prove that the representation theory of a probabilistic automaton is determined by that of the finite groups in its holonomy decomposition.

math.RT↗
arXiv2014

New interaction solutions from Lax pair related symmetry of the Generalized fifth order KdV equation

The nonlocal symmetry of the generalized fifth order KdV equation (FOKdV) is first obtained by using the related Lax pair and then localized in a new enlarged system by introducing some new variables. On this basis, new Backlund transformation is obtained through Lie's first theorem. Furthermore, the general form of Lie point symmetry for the enlarged FOKdV system is found and new interaction solutions for the FOKdV equation are explored by using classical symmetry reduction method.

nlin.SI↗
arXiv2014

Fine gradings of complex simple Lie algebras and Finite Root Systems

A $G$-grading on a complex semisimple Lie algebra $L$, where $G$ is a finite abelian group, is called quasi-good if each homogeneous component is 1-dimensional and 0 is not in the support of the grading. Analogous to classical root systems, we define a finite root system $R$ to be some subset of a finite symplectic abelian group satisfying certain axioms. There always corresponds to $R$ a semisimple Lie algebra $L(R)$ together with a quasi-good grading on it. Thus one can construct nice basis of $L(R)$ by means of finite root systems. We classify finite maximal abelian subgroups $T$ in $\Aut(L)$ for complex simple Lie algebras $L$ such that the grading induced by the action of $T$ on $L$ is quasi-good, and show that the set of roots of $T$ in $L$ is always a finite root system. There are five series of such finite maximal abelian subgroups, which occur only if $L$ is a classical simple Lie algebra.

math.GR↗
arXiv2014

Maximal abelian subgroups of compact matrix groups

We classify closed abelian subgroups of the automorphism group of any compact classical simple Lie algebra whose centralizer has the same dimension as the dimension of the subgroup, and describe Weyl groups of maximal abelian subgroups.

math.GR↗
arXiv2014

Backlund transformations for Burgers Equation via localization of residual symmetries

In this paper, we obtained the non-local residual symmetry related to truncated Painlevé expansion of Burgers equation. In order to localize the residual symmetry, we introduced new variables to prolong the original Burgers equation into a new system. By using Lie's first theorem, we got the finite transformation for the localized residual symmetry. More importantly, we also localized the linear superposition of multiple residual symmetries to find the corresponding finite transformations. It is interesting to find that the nth Backlund transformation for Burgers equation can be expressed by determinants in a compact way.

nlin.SI↗
arXiv2013

Pointwise convergence of the Lloyd algorithm in higher dimension

We establish the pointwise convergence of the iterative Lloyd algorithm, also known as $k$-means algorithm, when the quadratic quantization error of the starting grid (with size $N\ge 2$) is lower than the minimal quantization error with respect to the input distribution is lower at level $N-1$. Such a protocol is known as the splitting method and allows for convergence even when the input distribution has an unbounded support. We also show under very light assumption that the resulting limiting grid still has full size $N$. These results are obtained without continuity assumption on the input distribution. A variant of the procedure taking advantage of the asymptotic of the optimal quantizer radius is proposed which always guarantees the boundedness of the iterated grids.

math.PR↗
arXiv2013

New interaction solutions of Kadomtsev-Petviashvili equation

The residual symmetry coming from truncated Painleve expansion of KP equation is nonlocal, which is localized in this paper by introducing multiple new dependent variables. By using the standard Lie group approach, the symmetry reduction solutions for KP equation is obtained based on the general form of Lie point symmetry for the prolonged system. In this way, the interaction solutions between solitons and background waves is obtained, which is hard to study by other traditional methods.

nlin.SI↗