17702260
An algorithm for computing exact least-trimmed squares estimate of simple linear regression with constraints
Abstract The least-trimmed squares estimation (LTS) is a robust solution for regression problems. On the one hand, it can achieve any given breakdown value by setting a proper trimming fraction. On the other hand, it has n -consistency and asymptotic normality under some conditions. In addition, the LTS estimator is regression, scale, and affine equivariant. In practical regression problems, we often need to impose constraints on slopes. In this paper, we describe a stable algorithm to compute the exact LTS solution for simple linear regression with constraints on the slope parameter. Without constraints, the overall complexity of the algorithm is O (n 2 log n) in time and O( n 2 ) in storage. According to our numerical tests, constraints can reduce computing load substantially. In order to achieve stability, we design the algorithm in such a way that we can take advantage of well-developed sorting algorithms and softwares. We illustrate the algorithm by some examples.
11083681
MARD: a new method to detect differential gene expression in treatment-control time courses
MOTIVATION
Characterizing the dynamic regulation of gene expression by time course experiments is becoming more and more important. A common problem is to identify differentially expressed genes between the treatment and control time course. It is often difficult to compare expression patterns of a gene between two time courses for the following reasons: (1) the number of sampling time points may be different or hard to be aligned between the treatment and the control time courses; (2) estimation of the function that describes the expression of a gene in a time course is difficult and error-prone due to the limited number of time points. We propose a novel method to identify the differentially expressed genes between two time courses, which avoids direct comparison of gene expression patterns between the two time courses.


RESULTS
Instead of attempting to 'align' and compare the two time courses directly, we first convert the treatment and control time courses into neighborhood systems that reflect the underlying relationships between genes. We then identify the differentially expressed genes by comparing the two gene relationship networks. To verify our method, we apply it to two treatment-control time course datasets. The results are consistent with the previous results and also give some new biologically meaningful findings.


AVAILABILITY
The algorithm in this paper is coded in C++ and is available from http://leili-lab.cmb.usc.edu/yeastaging/projects/MARD/
8735726
Explore Biological Pathways from Noisy Array Data by Directed Acyclic Boolean Networks
We consider the structure of directed acyclic Boolean (DAB) networks as a tool for exploring biological pathways. In a DAB network, the basic objects are binary elements and their Boolean duals. A DAB is characterized by two kinds of pairwise relations: similarity and prerequisite. The latter is a partial order relation, namely, the on-status of one element is necessary for the on-status of another element. A DAB network is uniquely determined by the state space of its elements. We arrange samples from the state space of a DAB network in a binary array and introduce a random mechanism of measurement error. Our inference strategy consists of two stages. First, we consider each pair of elements and try to identify their most likely relation. In the meantime, we assign a score, s-p-score, to this relation. Second, we rank the s-p-scores obtained from the first stage. We expect that relations with smaller s-p-scores are more likely to be true, and those with larger s-p-scores are more likely to be false. The key idea is the definition of s-scores (referring to similarity), p-scores (referring to prerequisite), and s-p-scores. As with classical statistical tests, control of false negatives and false positives are our primary concerns. We illustrate the method by a simulated example, the classical arginine biosynthetic pathway, and show some exploratory results on a published microarray expression dataset of yeast Saccharomyces cerevisiae obtained from experiments with activation and genetic perturbation of the pheromone response MAPK pathway.
15608177
Gene selection for sample classification based on gene expression data: study of sensitivity to choice of parameters of the GA/KNN method
MOTIVATION
We recently introduced a multivariate approach that selects a subset of predictive genes jointly for sample classification based on expression data. We tested the algorithm on colon and leukemia data sets. As an extension to our earlier work, we systematically examine the sensitivity, reproducibility and stability of gene selection/sample classification to the choice of parameters of the algorithm.


METHODS
Our approach combines a Genetic Algorithm (GA) and the k-Nearest Neighbor (KNN) method to identify genes that can jointly discriminate between different classes of samples (e.g. normal versus tumor). The GA/KNN method is a stochastic supervised pattern recognition method. The genes identified are subsequently used to classify independent test set samples.


RESULTS
The GA/KNN method is capable of selecting a subset of predictive genes from a large noisy data set for sample classification. It is a multivariate approach that can capture the correlated structure in the data. We find that for a given data set gene selection is highly repeatable in independent runs using the GA/KNN method. In general, however, gene selection may be less robust than classification.


AVAILABILITY
The method is available at http://dir.niehs.nih.gov/microarray/datamining


CONTACT
LI3@niehs.nih.gov
2369815
Multiclass boosting with repartitioning
A multiclass classification problem can be reduced to a collection of binary problems with the aid of a coding matrix. The quality of the final solution, which is an ensemble of base classifiers learned on the binary problems, is affected by both the performance of the base learner and the error-correcting ability of the coding matrix. A coding matrix with strong error-correcting ability may not be overall optimal if the binary problems are too hard for the base learner. Thus a trade-off between error-correcting and base learning should be sought. In this paper, we propose a new multiclass boosting algorithm that modifies the coding matrix according to the learning ability of the base learner. We show experimentally that our algorithm is very efficient in optimizing the multiclass margin cost, and outperforms existing multiclass algorithms such as AdaBoost.ECC and one-vs-one. The improvement is especially significant when the base learner is not very powerful.
32109138
Rewriting Queries for XML Integration Systems
A data integration system typically creates a target XML schema to represent an application domain and source schemas are mapped to the target schema. A user poses a query over the target schema, and the system rewrites the query into a set of queries over the data sources. Existing algorithms generate a set of static rules based on the target schema and mappings, and rewrite the target query using these rules. We design a flexible and dynamic approach that rewrites XML queries directly based on the mappings between the target and source schemas. Theoretical analysis and experiments on both synthetic and real-world datasets indicate that the proposed approach is efficient and scalable.
15147687
GAPWM: a genetic algorithm method for optimizing a position weight matrix
MOTIVATION
Position weight matrices (PMWs) are simple models commonly used in motif-finding algorithms to identify short functional elements, such as cis-regulatory motifs, on genes. When few experimentally verified motifs are available, estimation of the PWM may be poor. The resultant PWM may not reliably discriminate a true motif from a false one. While experimentally identifying such motifs remains time-consuming and expensive, low-resolution binding data from techniques such as ChIP-on-chip and ChIP-PET have become available. We propose a novel but simple method to improve a poorly estimated PWM using ChIP data.


METHODOLOGY
Starting from an existing PWM, a set of ChIP sequences, and a set of background sequences, our method, GAPWM, derives an improved PWM via a genetic algorithm that maximizes the area under the receiver operating characteristic (ROC) curve. GAPWM can easily incorporate prior information such as base conservation. We tested our method on two PMWs (Oct4/Sox2 and p53) using three recently published ChIP data sets (human Oct4, mouse Oct4 and human p53).


RESULTS
GAPWM substantially increased the sensitivity/specificity of a poorly estimated PWM and further improved the quality of a good PWM. Furthermore, it still functioned when the starting PWM contained a major error. The ROC performance of GAPWM compared favorably with that of MEME and others. With increasing availability of ChIP data, our method provides an alternative for obtaining high-quality PWMs for genome-wide identification of transcription factor binding sites.


AVAILABILITY
The C source code and all data used in this report are available at http://dir.niehs.nih.gov/dirbb/gapwm.


SUPPLEMENTARY INFORMATION
Supplementary data are available at Bioinformatics online.
27925816
A fuzzy approach to the multiobjective transportation problem
The aim of this paper is to present a fuzzy compromise programming approach to multiobjective transportation problems. A characteristic feature of the approach proposed is that various objectives are synthetically considered with the marginal evaluation for individual objectives and the global evaluation for all objectives. The decision-maker’s preference is taken into account by his/her assigning the weights of objectives. With the global evaluation for all objectives, a compromise programming model is formulated. This model covers a wide spectrum of methods with Zimmermann’s fuzzy programming approach essentially equivalent to one of its special cases. Using ordinary optimization technique, we solve the fuzzy compromise programming model to obtain a non-dominated compromise solution at which the synthetic membership degree of the global evaluation for all objectives is maximum. A numerical example is given to demonstrate the efficiency of the proposed fuzzy compromise programming approach. 
 
 
Scope and purpose 
 
In many real-world situations for transportation problems, decisions are often made in the presence of multiple, conflicting, incommensurate objectives. Intensive investigations on multiobjective linear transportation problem have been made. Among them Zimmermann’s fuzzy programming appears to be an ideal approach for obtaining the optimal compromise solution to a multiobjective transportation problem. However, due to the ease of computation, the aggregate operator used in Zimmermann’s fuzzy programming is the “min” operator, which does not guarantee a non-dominated solution. In this paper, we propose a new fuzzy compromise programming approach to multiobjective transportation problems. It is shown that the approach proposed can give a compromise solution that is not only non-dominated but also optimal in a certain sense. The proposed approach is robust enough to cover a wide spectrum of methods. Zimmermann’s fuzzy programming approach is essentially equivalent to one of the proposed method’s special cases.