BACKGROUND: Binary classification rules based on a small-sample of high-dimensional data (for instance, gene expression data) are ubiquitous in modern bioinformatics. Constructing such classifiers is challenging due to (a) the complex nature of underlying biological traits, such as gene interactions, and (b) the need for highly interpretable glass-box models. We use the theory of high dimensional model representation (HDMR) to build interpretable low dimensional approximations of the log-likelihood ratio accounting for the effects of each individual gene as well as gene-gene interactions. We propose two algorithms approximating the second order HDMR expansion, and a hypothesis test based on the HDMR formulation to identify significantly dysregulated pairwise interactions. The theory is seen as flexible and requiring only a mild set of assumptions. RESULTS: We apply our approach to gene expression data from both synthetic and real (breast and lung cancer) datasets comparing it also against several popular state-of-the-art methods. The analyses suggest the proposed algorithms can be used to obtain interpretable prediction rules with high prediction accuracies and to successfully extract significantly dysregulated gene-gene interactions from the data. They also compare favorably against their competitors across multiple synthetic data scenarios. CONCLUSION: The proposed HDMR-based approach appears to produce a reliable classifier that additionally allows one to describe how individual genes or gene-gene interactions affect classification decisions. Both real and synthetic data analyses suggest that our methods can be used to identify gene networks with dysregulated pairwise interactions, and are therefore appropriate for differential networks analysis.

Optimal Bayesian feature filtering (OBF) is a fast and memory-efficient algorithm that optimally identifies markers with distributional differences between treatment groups under Gaussian models. Here, we study the performance and robustness of OBF for biomarker discovery. Our contributions are twofold: (1) we examine how OBF performs on data that violates modeling assumptions, and (2) we provide guidelines on how to set input parameters for robust performance. Contribution (1) addresses an important, relevant, and commonplace problem in computational biology, where it is often impossible to validate an algorithm's core assumptions. To accomplish both tasks, we present a battery of simulations that implement OBF with different inputs and challenge each assumption made by OBF. In particular, we examine the robustness of OBF with respect to incorrect input parameters, false independence, imbalanced sample size, and we address the Gaussianity assumption by considering performance on an extensive family of non-Gaussian distributions. We address advantages and disadvantages between different priors and optimization criteria throughout. Finally, we evaluate the utility of OBF in biomarker discovery using acute myeloid leukemia (AML) and colon cancer microarray datasets, and show that OBF is successful at identifying well-known biomarkers for these diseases that rank low under moderated t-test.

BACKGROUND: Many bioinformatics studies aim to identify markers, or features, that can be used to discriminate between distinct groups. In problems where strong individual markers are not available, or where interactions between gene products are of primary interest, it may be necessary to consider combinations of features as a marker family. To this end, recent work proposes a hierarchical Bayesian framework for feature selection that places a prior on the set of features we wish to select and on the label-conditioned feature distribution. While an analytical posterior under Gaussian models with block covariance structures is available, the optimal feature selection algorithm for this model remains intractable since it requires evaluating the posterior over the space of all possible covariance block structures and feature-block assignments. To address this computational barrier, in prior work we proposed a simple suboptimal algorithm, 2MNC-Robust, with robust performance across the space of block structures. Here, we present three new heuristic feature selection algorithms. RESULTS: The proposed algorithms outperform 2MNC-Robust and many other popular feature selection algorithms on synthetic data. In addition, enrichment analysis on real breast cancer, colon cancer, and Leukemia data indicates they also output many of the genes and pathways linked to the cancers under study. CONCLUSIONS: Bayesian feature selection is a promising framework for small-sample high-dimensional data, in particular biomarker discovery applications. When applied to cancer data these algorithms outputted many genes already shown to be involved in cancer as well as potentially new biomarkers. Furthermore, one of the proposed algorithms, SPM, outputs blocks of heavily correlated genes, particularly useful for studying gene interactions and gene networks.

Many bioinformatics studies aim to find features that differentiate between two or more classes. Recent work proposes a Bayesian framework for feature selection that places a prior on the label-conditioned feature distribution. Assuming independent features, the optimal Bayesian filter is obtained and has been solved for Gaussian features. Here we extend the optimal Bayesian filter for categorical data, compare it with several algorithms in synthetic simulations, and apply it to breast and colon cancer SNP datasets. For the real datasets we select the top SNP's, find the genes that map to them, and perform enrichment analysis. Literature review suggests many of the top genes and pathways are involved in cancer.

Recent work proposes new algorithms for feature selection based on a Bayesian hierarchical model that places priors on both the identity of all features, and the identity-conditioned feature-label distribution. Given training data, Bayesian inference can be used to predict the feature identities. While algorithms developed in prior work rely on certain independence assumptions, in this work we present a new algorithm, with low computational complexity, designed for a family of Bayesian models that each assume different block covariance structures. We show the new algorithm, and the previous algorithm assuming independent features, have robust performance across the family of models under synthetic data, and provide results from real colon cancer microarray data.

Popular tools to evaluate classifier performance are the false positive rate (FPR), true positive rate (TPR), receiver operator characteristic (ROC) curve, and area under the curve (AUC). Typically, these quantities are estimated from training data using simple resampling and counting methods, which have been shown to perform poorly when the sample size is small, as is typical in many applications. This work takes a model-based approach in classifier training and performance analysis, where we assume the true population densities are members of an uncertainty class of distributions. Given a prior over the uncertainty class and data, we form a posterior and derive optimal mean-squared-error (MSE) FPR and TPR estimators, as well as the sample-conditioned MSE performance of these estimators. The theory also naturally leads to optimal ROC and AUC estimators. Finally, we develop a Neyman-Pearson-based approach to optimal classifier design, which maximizes the estimated TPR for a given estimated FPR. These tools are optimal over the uncertainty class of distributions given the sample, and are available in closed form or can be easily approximated for many models. Applications are demonstrated on both synthetic and real genomic data. MATLAB code and simulations results are available in the online supplementary material.

In biomedicine, it is typical to find studies discriminating between types of pathology or stages of disease based on as few as 30 sample points and tens of thousands of genes. Unfortunately, out-of-the-box classification and error estimation rules come with no small-sample performance guarantees, which has greatly contributed to the crisis in biomarker reproducibility. Recent work addresses this by supplementing the data with expert biological knowledge via a prior distribution over an uncertainty class of feature-label distributions, and uses the resulting probabilistic framework to define minimum mean-square-error (MMSE) estimators for the misclassification rate of any fixed classifier, as well as the sample-conditioned MSE itself for arbitrary error estimators. Here, we use the same framework to also define minimum expected error (MEE) classifiers, completing a Bayesian optimized theory of classification. We also present examples on real genomic data resulting in classifiers that greatly outperform popular rules.

MOTIVATION: With the development of high-throughput genomic and proteomic technologies, coupled with the inherent difficulties in obtaining large samples, biomedicine faces difficult small-sample classification issues, in particular, error estimation. Most popular error estimation methods are motivated by intuition rather than mathematical inference. A recently proposed error estimator based on Bayesian minimum mean square error estimation places error estimation in an optimal filtering framework. In this work, we examine the application of this error estimator to gene expression microarray data, including the suitability of the Gaussian model with normal-inverse-Wishart priors and how to find prior probabilities. RESULTS: We provide an implementation for non-linear classification, where closed form solutions are not available. We propose a methodology for calibrating normal-inverse-Wishart priors based on discarded microarray data and examine the performance on synthetic high-dimensional data and a real dataset from a breast cancer study. The calibrated Bayesian error estimator has superior root mean square performance, especially with moderate to high expected true errors and small feature sizes. AVAILABILITY: We have implemented in C code the Bayesian error estimator for Gaussian distributions and normal-inverse-Wishart priors for both linear classifiers, with exact closed-form representations, and arbitrary classifiers, where we use a Monte Carlo approximation. Our code for the Bayesian error estimator and a toolbox of related utilities are available at http://gsp.tamu.edu/Publications/supplementary/dalton11a. Several supporting simulations are also included. CONTACT: [email protected]

We present a complex, full-rate quasi-orthogonal space-time block code for four transmit antennas. Using carefully tailored constellation phase rotations, we show that this code achieves full diversity for specialized PSK-based constellations. The optimal receiver for the new code decouples the symbol detection problem into pairs of symbols, thus greatly reducing complexity. Finally, we present and compare performance of the new code with several other codes in the literature. The new code is shown to perform as well as the best known code of its class.

Standard TCP is successful at low speeds but it is unfit for high speed communication due to its slow ramp-up of congestion window size. Many modern fields of study require high bandwidth connectivity. Various solutions to this, including server side modifications of TCP, like HighSpeed TCP and Fast TCP, are being advocated. In this work, we study the effectiveness of these two protocols by comparing and contrasting both of them with standard TCP.