We consider maximum likelihood estimation (MLE) of heteroscedastic regression models based on a new “parametrization” of the likelihood in terms of the Sharpe ratio function, or the ratio of the mean and volatility functions. While with a standard parametrization the MLE problem is not convex and hence hard to solve globally, our parametrization leads to a functional that is jointly convex in the Sharpe ratio and inverse volatility functions. The major difficulty with the resulting infinite-dimensional convex program is the shape constraint on the inverse volatility function. We propose to solve the problem by solving a sequence of finite-dimensional convex programs with increasing dimensions, which can be done globally and efficiently. We demonstrate that, when the goal is to estimate the Sharpe ratio function directly, the finite-sample performance of the proposed estimation method is superior to existing methods that estimate the mean and variance functions separately. When applied to a financial dataset, our method captures a well-known covariate-dependent effect on the Shape ratio.

BACKGROUND: Gene regulatory networks reveal how genes work together to carry out their biological functions. Reconstructions of gene networks from gene expression data greatly facilitate our understanding of underlying biological mechanisms and provide new opportunities for biomarker and drug discoveries. In gene networks, a gene that has many interactions with other genes is called a hub gene, which usually plays an essential role in gene regulation and biological processes. In this study, we developed a method for reconstructing gene networks using a partial correlation-based approach that incorporates prior information about hub genes. Through simulation studies and two real-data examples, we compare the performance in estimating the network structures between the existing methods and the proposed method. RESULTS: In simulation studies, we show that the proposed strategy reduces errors in estimating network structures compared to the existing methods. When applied to Escherichia coli, the regulation network constructed by our proposed ESPACE method is more consistent with current biological knowledge than the SPACE method. Furthermore, application of the proposed method in lung cancer has identified hub genes whose mRNA expression predicts cancer progress and patient response to treatment. CONCLUSIONS: We have demonstrated that incorporating hub gene information in estimating network structures can improve the performance of the existing methods.

BACKGROUND: A key objective in many microarray association studies is the identification of individual genes associated with clinical outcome. It is often of additional interest to identify sets of genes, known a priori to have similar biologic function, associated with the outcome. RESULTS: In this paper, we propose a general permutation-based framework for gene set testing that controls the false discovery rate (FDR) while accounting for the dependency among the genes within and across each gene set. The application of the proposed method is demonstrated using three public microarray data sets. The performance of our proposed method is contrasted to two other existing Gene Set Enrichment Analysis (GSEA) and Gene Set Analysis (GSA) methods. CONCLUSIONS: Our simulations show that the proposed method controls the FDR at the desired level. Through simulations and case studies, we observe that our method performs better than GSEA and GSA, especially when the number of prognostic gene sets is large.

Image segmentation is an important preprocessing step in a sophisticated and complex image processing algorithm. In segmenting real-world images, the cost of misclassification could depend on the true class. For example, in a two-class (negative or positive class) problem, the cost of misclassifying positive to negative class could not be equal to that of misclassifying negative to positive class. However, existing algorithms do not take into account the unequal misclassification cost. In this letter, motivated by recent advances in machine learning theory, we introduce a procedure to minimize the misclassification cost with class-dependent cost. The procedure assumes the hidden Markov model (HMM) which has been popularly used for image segmentation in recent years. We represent all feasible HMM-based segmenters (or classifiers) as a set of points in the receiver operating characteristic (ROC) space. Then, the optimal segmenter (or classifier) is found by computing the tangential point between the iso-cost line with given slope and the convex hull of the feasible set in the ROC space. We illustrate the procedure by segmenting aerial images with different selection of misclassification costs.

Noise is ubiquitous in real life and changes image acquisition, communication, and processing characteristics in an uncontrolled manner. Gaussian noise and Salt and Pepper noise, in particular, are prevalent in noisy communication channels, camera and scanner sensors, and medical MRI images. It is not unusual for highly sophisticated image processing algorithms developed for clean images to malfunction when used on noisy images. For example, hidden Markov Gauss mixture models (HMGMM) have been shown to perform well in image segmentation applications, but they are quite sensitive to image noise. We propose a modified HMGMM procedure specifically designed to improve performance in the presence of noise. The key feature of the proposed procedure is the adjustment of covariance matrices in Gauss mixture vector quantizer codebooks to minimize an overall minimum discrimination information distortion (MDI). In adjusting covariance matrices, we expand or shrink their elements based on the noisy image. While most results reported in the literature assume a particular noise type, we propose a framework without assuming particular noise characteristics. Without denoising the corrupted source, we apply our method directly to the segmentation of noisy sources. We apply the proposed procedure to the segmentation of aerial images with Salt and Pepper noise and with independent Gaussian noise, and we compare our results with those of the median filter restoration method and the blind deconvolution-based method, respectively. We show that our procedure has better performance than image restoration-based techniques and closely matches to the performance of HMGMM for clean images in terms of both visual segmentation results and error rate.

Noise is ubiquitous in real life and changes image acquisition and processing characteristics in an uncontrolled manner. Highly sophisticated image processing algorithms developed for clean images often malfunction when they are used for noisy images. For example, hidden Markov Gauss mixture models (HMGMM) have been shown to perform well in image segmentation applications, but they have also proved to be quite sensitive to uncontrolled noise in test images. To resolve this difficulty, we propose a modified procedure to adjust covariance matrix estimates of test images. We shrink (or expand) the covariance matrix estimates of the noisy image to make them consistent with those in the codebooks. Note that the covariance matrices in the codebooks are those of the noiseless image. The novelty of this paper is that our method is equivalent to adjusting the covariance matrices of codebooks for noiseless images to be consistent wit those of noisy test images without retraining. The adjusted covariance matrices shrink (or expand) the covariance matrix estimates in the codebooks to minimize the overall minimum discrimination information distortion between test images and codebooks. To illustrate the proposed procedure, we apply it to segmenting aerial images with Salt and Pepper noise and with Gaussian noise. We compare our method with the median filter restoration method and the blind deconvolution method and show that our procedure has better performance than these image-restoration-based techniques in terms of both visual segmentation results and error rate. Further, we find that the suggested procedure performs almost as well as the HMGMM for clean images, which is the benchmark in comparison.

Image segmentation is an important tool in image processing and can serve as an efficient front end to sophisticated algorithms and thereby simplify subsequent processing. We develop a multiclass image segmentation method using hidden Markov Gauss mixture models (HMGMMs) and provide examples of segmentation of aerial images and textures. HMGMMs incorporate supervised learning, fitting the observation probability distribution given each class by a Gauss mixture estimated using vector quantization with a minimum discrimination information (MDI) distortion. We formulate the image segmentation problem using a maximum a posteriori criteria and find the hidden states that maximize the posterior density given the observation. We estimate both the hidden Markov parameter and hidden states using a stochastic expectation-maximization algorithm. Our results demonstrate that HMGMM provides better classification in terms of Bayes risk and spatial homogeneity of the classified objects than do several popular methods, including classification and regression trees, learning vector quantization, causal hidden Markov models (HMMs), and multiresolution HMMs. The computational load of HMGMM is similar to that of the causal HMM.

We consider the problem of choosing a linear classifier that minimizes misclassification probabilities in two-class classification, which is a bi-criterion problem, involving a trade-off between two objectives. We assume that the class-conditional distributions are Gaussian. This assumption makes it computationally tractable to find Pareto optimal linear classifiers whose classification capabilities are inferior to no other linear ones. The main purpose of this paper is to establish several robustness properties of those classifiers with respect to variations and uncertainties in the distributions. We also extend the results to kernel-based classification. Finally, we show how to carry out trade-off analysis empirically with a finite number of given labeled data.

We propose a novel image classification method using a non-causal hidden Markov Gauss mixture model (HMGMM) We apply supervised learning assuming that the observation probability distribution given each class can be estimated using Gauss mixture vector quantization (GMVQ) designed using the generalized Lloyd algorithm with a minimum discrimination information (MDI) distortion. The maximum a posteriori (MAP) hidden states in an Ising model are estimated by a stochastic EM algorithm. We demonstrate that HMGMM obtains better classification than several popular methods, including CART, LVQ, causal HMM, and multiresolution HMM, in terms of Bayes risk and the spatial homogeneity of the classified objects. A heuristic solution for the number of clusters achieves a robust image classification.

We propose a texture classification method using multiple Gauss mixture vector quantizers (GMVQ). We designed a separate model codebook or Gauss mixture for each texture using the generalized Lloyd algorithm with a minimum discrimination information (MDI) distortion based on a training data set. The multi-codebook structure of the GMVQ classifier is an extension to images of the isolated utterance speech recognizer of J.E. Shore and D. Burton (see Proc. Int. Conf. Acoust., Speech, and Sig. Processing, IEEE82Ch.1746-7, p.907-10, 1982). We applied the algorithm to the Brodatz texture database and showed it to be competitive in performance in comparison to other texture classifiers. Its low complexity implementation and real-time operation make the approach suitable for content-based image retrieval.