arXiv subjects

Jing Qin

Publications and source records attributed to Jing Qin.

At least 199 records · Page 11Linked to original sources

arXiv2016

Robust Learning with Kernel Mean p-Power Error Loss

Correntropy is a second order statistical measure in kernel space, which has been successfully applied in robust learning and signal processing. In this paper, we define a nonsecond order statistical measure in kernel space, called the kernel mean-p power error (KMPE), including the correntropic loss (CLoss) as a special case. Some basic properties of KMPE are presented. In particular, we apply the KMPE to extreme learning machine (ELM) and principal component analysis (PCA), and develop two robust learning algorithms, namely ELM-KMPE and PCA-KMPE. Experimental results on synthetic and benchmark data show that the developed algorithms can achieve consistently better performance when compared with some existing methods.

stat.ML↗

arXiv2016

Fine-grained Recurrent Neural Networks for Automatic Prostate Segmentation in Ultrasound Images

Boundary incompleteness raises great challenges to automatic prostate segmentation in ultrasound images. Shape prior can provide strong guidance in estimating the missing boundary, but traditional shape models often suffer from hand-crafted descriptors and local information loss in the fitting procedure. In this paper, we attempt to address those issues with a novel framework. The proposed framework can seamlessly integrate feature extraction and shape prior exploring, and estimate the complete boundary with a sequential manner. Our framework is composed of three key modules. Firstly, we serialize the static 2D prostate ultrasound images into dynamic sequences and then predict prostate shapes by sequentially exploring shape priors. Intuitively, we propose to learn the shape prior with the biologically plausible Recurrent Neural Networks (RNNs). This module is corroborated to be effective in dealing with the boundary incompleteness. Secondly, to alleviate the bias caused by different serialization manners, we propose a multi-view fusion strategy to merge shape predictions obtained from different perspectives. Thirdly, we further implant the RNN core into a multiscale Auto-Context scheme to successively refine the details of the shape prediction map. With extensive validation on challenging prostate ultrasound images, our framework bridges severe boundary incompleteness and achieves the best performance in prostate boundary delineation when compared with several advanced methods. Additionally, our approach is general and can be extended to other medical image segmentation tasks, where boundary incompleteness is one of the main challenges.

cs.CV↗

arXiv2016

FRETtranslator: translating FRET traces into RNA structural pathways

Recent genome and transcriptome sequencing projects have unveiled a plethora of highly structured RNA molecules as central mediators of cellular function. Single molecule Forster Resonance Energy Transfer (smFRET) is a powerful tool for analyzing the temporal evolution of the global structure of individual RNA molecules, in pursuit of understanding their essential structure-dynamics-function relationships. In contrast to enzymatic and chemical footprinting, NMR spectroscopy and X-ray crystallography, smFRET yields temporally resolved, quantitative information about single molecules rather than only time and ensemble averages of entire populations. This enables unique observations of transient and rare conformations under both equilibrium and non-equilibrium conditions.

q-bio.MN↗

arXiv2016

3D Deeply Supervised Network for Automatic Liver Segmentation from CT Volumes

Automatic liver segmentation from CT volumes is a crucial prerequisite yet challenging task for computer-aided hepatic disease diagnosis and treatment. In this paper, we present a novel 3D deeply supervised network (3D DSN) to address this challenging task. The proposed 3D DSN takes advantage of a fully convolutional architecture which performs efficient end-to-end learning and inference. More importantly, we introduce a deep supervision mechanism during the learning process to combat potential optimization difficulties, and thus the model can acquire a much faster convergence rate and more powerful discrimination capability. On top of the high-quality score map produced by the 3D DSN, a conditional random field model is further employed to obtain refined segmentation results. We evaluated our framework on the public MICCAI-SLiver07 dataset. Extensive experiments demonstrated that our method achieves competitive segmentation results to state-of-the-art approaches with a much faster processing speed.

cs.CV↗

arXiv2016

A Multiphase Image Segmentation Based on Fuzzy Membership Functions and L1-norm Fidelity

In this paper, we propose a variational multiphase image segmentation model based on fuzzy membership functions and L1-norm fidelity. Then we apply the alternating direction method of multipliers to solve an equivalent problem. All the subproblems can be solved efficiently. Specifically, we propose a fast method to calculate the fuzzy median. Experimental results and comparisons show that the L1-norm based method is more robust to outliers such as impulse noise and keeps better contrast than its L2-norm counterpart. Theoretically, we prove the existence of the minimizer and analyze the convergence of the algorithm.

math.OC↗

arXiv2016

Group sparse optimization via $\ell_{p,q}$ regularization

In this paper, we investigate a group sparse optimization problem via $\ell_{p,q}$ regularization in three aspects: theory, algorithm and application. In the theoretical aspect, by introducing a notion of group restricted eigenvalue condition, we establish some oracle property and a global recovery bound of order $O(λ^\frac{2}{2-q})$ for any point in a level set of the $\ell_{p,q}$ regularization problem, and by virtue of modern variational analysis techniques, we also provide a local analysis of recovery bound of order $O(λ^2)$ for a path of local minima. In the algorithmic aspect, we apply the well-known proximal gradient method to solve the $\ell_{p,q}$ regularization problems, either by analytically solving some specific $\ell_{p,q}$ regularization subproblems, or by using the Newton method to solve general $\ell_{p,q}$ regularization subproblems. In particular, we establish the linear convergence rate of the proximal gradient method for solving the $\ell_{1,q}$ regularization problem under some mild conditions. As a consequence, the linear convergence rate of proximal gradient method for solving the usual $\ell_{q}$ regularization problem ($0<q<1$) is obtained. Finally in the aspect of application, we present some numerical results on both the simulated data and the real data in gene transcriptional regulation.

math.OC↗

arXiv2014

Combining isotonic regression and EM algorithm to predict genetic risk under monotonicity constraint

In certain genetic studies, clinicians and genetic counselors are interested in estimating the cumulative risk of a disease for individuals with and without a rare deleterious mutation. Estimating the cumulative risk is difficult, however, when the estimates are based on family history data. Often, the genetic mutation status in many family members is unknown; instead, only estimated probabilities of a patient having a certain mutation status are available. Also, ages of disease-onset are subject to right censoring. Existing methods to estimate the cumulative risk using such family-based data only provide estimation at individual time points, and are not guaranteed to be monotonic or nonnegative. In this paper, we develop a novel method that combines Expectation-Maximization and isotonic regression to estimate the cumulative risk across the entire support. Our estimator is monotonic, satisfies self-consistent estimating equations and has high power in detecting differences between the cumulative risks of different populations. Application of our estimator to a Parkinson's disease (PD) study provides the age-at-onset distribution of PD in PARK2 mutation carriers and noncarriers, and reveals a significant difference between the distribution in compound heterozygous carriers compared to noncarriers, but not between heterozygous carriers and noncarriers.

stat.AP↗

arXiv2014

Maximum Smoothed Likelihood Component Density Estimation in Mixture Models with Known Mixing Proportions

In this paper, we propose a maximum smoothed likelihood method to estimate the component density functions of mixture models, in which the mixing proportions are known and may differ among observations. The proposed estimates maximize a smoothed log likelihood function and inherit all the important properties of probability density functions. A majorization-minimization algorithm is suggested to compute the proposed estimates numerically. In theory, we show that starting from any initial value, this algorithm increases the smoothed likelihood function and further leads to estimates that maximize the smoothed likelihood function. This indicates the convergence of the algorithm. Furthermore, we theoretically establish the asymptotic convergence rate of our proposed estimators. An adaptive procedure is suggested to choose the bandwidths in our estimation procedure. Simulation studies show that the proposed method is more efficient than the existing method in terms of integrated squared errors. A real data example is further analyzed.

stat.ME↗

arXiv2013

Distribution of graph-distances in Boltzmann ensembles of RNA secondary structures

Large RNA molecules often carry multiple functional domains whose spatial arrangement is an important determinant of their function. Pre-mRNA splicing, furthermore, relies on the spatial proximity of the splice junctions that can be separated by very long introns. Similar effects appear in the processing of RNA virus genomes. Albeit a crude measure, the distribution of spatial distances in thermodynamic equilibrium therefore provides useful information on the overall shape of the molecule can provide insights into the interplay of its functional domains. Spatial distance can be approximated by the graph-distance in RNA secondary structure. We show here that the equilibrium distribution of graph-distances between arbitrary nucleotides can be computed in polynomial time by means of dynamic programming. A naive implementation would yield recursions with a very high time complexity of O(n^11). Although we were able to reduce this to O(n^6) for many practical applications a further reduction seems difficult. We conclude, therefore, that sampling approaches, which are much easier to implement, are also theoretically favorable for most real-life applications, in particular since these primarily concern long-range interactions in very large RNA molecules.

q-bio.QM↗

arXiv2010

RNA-RNA interaction prediction based on multiple sequence alignments

Many computerized methods for RNA-RNA interaction structure prediction have been developed. Recently, $O(N^6)$ time and $O(N^4)$ space dynamic programming algorithms have become available that compute the partition function of RNA-RNA interaction complexes. However, few of these methods incorporate the knowledge concerning related sequences, thus relevant evolutionary information is often neglected from the structure determination. Therefore, it is of considerable practical interest to introduce a method taking into consideration both thermodynamic stability and sequence covariation. We present the \emph{a priori} folding algorithm \texttt{ripalign}, whose input consists of two (given) multiple sequence alignments (MSA). \texttt{ripalign} outputs (1) the partition function, (2) base-pairing probabilities, (3) hybrid probabilities and (4) a set of Boltzmann-sampled suboptimal structures consisting of canonical joint structures that are compatible to the alignments. Compared to the single sequence-pair folding algorithm \texttt{rip}, \texttt{ripalign} requires negligible additional memory resource. Furthermore, we incorporate possible structure constraints as input parameters into our algorithm. The algorithm described here is implemented in C as part of the \texttt{rip} package. The supplemental material, source code and input/output files can freely be downloaded from \url{http://www.combinatorics.cn/cbpc/ripalign.html}. \section{Contact} Christian Reidys \texttt{duck@santafe.edu}

math-ph↗

arXiv2009

Random $k$-noncrossing partitions

In this paper, we introduce polynomial time algorithms that generate random $k$-noncrossing partitions and 2-regular, $k$-noncrossing partitions with uniform probability. A $k$-noncrossing partition does not contain any $k$ mutually crossing arcs in its canonical representation and is 2-regular if the latter does not contain arcs of the form $(i,i+1)$. Using a bijection of Chen {\it et al.} \cite{Chen,Reidys:08tan}, we interpret $k$-noncrossing partitions and 2-regular, $k$-noncrossing partitions as restricted generalized vacillating tableaux. Furthermore, we interpret the tableaux as sampling paths of a Markov-processes over shapes and derive their transition probabilities.

math.CO↗

arXiv2009

Random 3-noncrossing partitions

In this paper, we introduce polynomial time algorithms that generate random 3-noncrossing partitions and 2-regular, 3-noncrossing partitions with uniform probability. A 3-noncrossing partition does not contain any three mutually crossing arcs in its canonical representation and is 2-regular if the latter does not contain arcs of the form $(i,i+1)$. Using a bijection of Chen {\it et al.} \cite{Chen,Reidys:08tan}, we interpret 3-noncrossing partitions and 2-regular, 3-noncrossing partitions as restricted generalized vacillating tableaux. Furthermore, we interpret the tableaux as sampling paths of Markov-processes over shapes and derive their transition probabilities.

math.CO↗

arXiv2009

RNA-RNA interaction prediction: partition function and base pair pairing probabilities

In this paper, we study the interaction of an antisense RNA and its target mRNA, based on the model introduced by Alkan {\it et al.} (Alkan {\it et al.}, J. Comput. Biol., Vol:267--282, 2006). Our main results are the derivation of the partition function \cite{Backhofen} (Chitsaz {\it et al.}, Bioinformatics, to appear, 2009), based on the concept of tight-structure and the computation of the base pairing probabilities. This paper contains the folding algorithm {\sf rip} which computes the partition function as well as the base pairing probabilities in $O(N^4M^2)+O(N^2M^4)$ time and $O(N^2M^2)$ space, where $N,M$ denote the lengths of the interacting sequences.

math.CO↗

arXiv2008

Efficient Counting and Asymptotics of $k$-noncrossing tangled-diagrams

In this paper we enumerate $k$-noncrossing tangled-diagrams. A tangled-diagram is a labeled graph whose vertices are $1,...,n$ have degree $\le 2$, and are arranged in increasing order in a horizontal line. Its arcs are drawn in the upper halfplane with a particular notion of crossings and nestings. Our main result is the asymptotic formula for the number of $k$-noncrossing tangled-diagrams $T_{k}(n) \sim c_k n^{-((k-1)^2+(k-1)/2)} (4(k-1)^2+2(k-1)+1)^n$ for some $c_k>0$.

math.CO↗

arXiv2007

A combinatorial framework for RNA tertiary interaction

In this paper we show how to express RNA tertiary interactions via the concepts of tangled diagrams. Tangled diagrams allow to formulate RNA base triples and pseudoknot-interactions and to control the maximum number of mutually crossing arcs. In particular we study two subsets of tangled diagrams: 3-noncrossing tangled-diagrams with $\ell$ vertices of degree two and 2-regular, 3-noncrossing partitions (i.e. without arcs of the form $(i,i+1)$). Our main result is an asymptotic formula for the number of 2-regular, 3-noncrossing partitions, denoted by $p_{3,2}(n)$, 3-noncrossing partitions over $[n]$. The asymptotic formula is derived by the analytic theory of singular difference equations due to Birkhoff-Trjitzinsky. Explicitly, we prove the formula $p_{3,2}(n+1)\sim K 8^{n}n^{-7}(1+c_{1}/n+c_{2}/n^2+c_3/n^3)$ where $K,c_i$, $i=1,2,3$ are constants.

math.CO↗

arXiv2007

On $k$-noncrossing partitions

In this paper we prove a duality between $k$-noncrossing partitions over $[n]=\{1,...,n\}$ and $k$-noncrossing braids over $[n-1]$. This duality is derived directly via (generalized) vacillating tableaux which are in correspondence to tangled-diagrams \cite{Reidys:07vac}. We give a combinatorial interpretation of the bijection in terms of the contraction of arcs of tangled-diagrams. Furthermore it induces by restriction a bijection between $k$-noncrossing, 2-regular partitions over $[n]$ and $k$-noncrossing braids without isolated points over $[n-1]$. Since braids without isolated points correspond to enhanced partitions this allows, using the results of \cite{MIRXIN}, to enumerate 2-regular, 3-noncrossing partitions.

math.CO↗

arXiv2007

Crossings and nesting in tangled-diagrams

A tangled-diagram over $[n]=\{1,...,n\}$ is a graph of degree less than two whose vertices $1,...,n$ are arranged in a horizontal line and whose arcs are drawn in the upper halfplane with a particular notion of crossings and nestings. Generalizing the construction of Chen {\it et.al.} we prove a bijection between generalized vacillating tableaux with less than $k$ rows and $k$-noncrossing tangled-diagrams and study their crossings and nestings. We show that the number of $k$-noncrossing and $k$-nonnesting tangled-diagrams are equal and enumerate tangled-diagrams.

math.CO↗

arXiv2007

Neutral Networks of Sequence to Shape Maps

In this paper we present a novel framework for sequence to shape maps. These combinatorial maps realize exponentially many shapes, and have preimages which contain extended connected subgraphs of diameter n (neutral networks). We prove that all basic properties of RNA folding maps also hold for combinatorial maps. Our construction is as follows: suppose we are given a graph $H$ over the $\{1 >...,n\}$ and an alphabet of nucleotides together with a symmetric relation $\mathcal{R}$, implied by base pairing rules. Then the shape of a sequence of length n is the maximal H subgraph in which all pairs of nucleotides incident to H-edges satisfy $\mathcal{R}$. Our main result is to prove the existence of at least $\sqrt{2}^{n-1}$ shapes with extended neutral networks, i.e. shapes that have a preimage with diameter $n$ and a connected component of size at least $(\frac{1+\sqrt{5}}{2})^n+(\frac{1-\sqrt{5}}{2})^n$. Furthermore, we show that there exists a certain subset of shapes which carries a natural graph structure. In this graph any two shapes are connected by a path of shapes with respective neutral networks of distance one. We finally discuss our results and provide a comparison with RNA folding maps.

q-bio.QM↗