Gene Selection for Multiclass Prediction by Weighted Fisher Criterion

Gene expression profiling has been widely used to study molecular signatures of many diseases and to develop molecular diagnostics for disease prediction. Gene selection, as an important step for improved diagnostics, screens tens of thousands of genes and identifies a small subset that discriminates between disease types. A two-step gene selection method is proposed to identify informative gene subsets for accurate classification of multiclass phenotypes. In the first step, individually discriminatory genes (IDGs) are identified by using one-dimensional weighted Fisher criterion (wFC). In the second step, jointly discriminatory genes (JDGs) are selected by sequential search methods, based on their joint class separability measured by multidimensional weighted Fisher criterion (wFC). The performance of the selected gene subsets for multiclass prediction is evaluated by artificial neural networks (ANNs) and/or support vector machines (SVMs). By applying the proposed IDG/JDG approach to two microarray studies, that is, small round blue cell tumors (SRBCTs) and muscular dystrophies (MDs), we successfully identified a much smaller yet efficient set of JDGs for diagnosing SRBCTs and MDs with high prediction accuracies (96.9% for SRBCTs and 92.3% for MDs, resp.). These experimental results demonstrated that the two-step gene selection method is able to identify a subset of highly discriminative genes for improved multiclass prediction

A new regularized least squares support vector regression for gene selection

<p>Abstract</p> <p>Background</p> <p>Selection of influential genes with microarray data often faces the difficulties of a large number of genes and a relatively small group of subjects. In addition to the curse of dimensionality, many gene selection methods weight the contribution from each individual subject equally. This equal-contribution assumption cannot account for the possible dependence among subjects who associate similarly to the disease, and may restrict the selection of influential genes.</p> <p>Results</p> <p>A novel approach to gene selection is proposed based on kernel similarities and kernel weights. We do not assume uniformity for subject contribution. Weights are calculated via regularized least squares support vector regression (RLS-SVR) of class levels on kernel similarities and are used to weight subject contribution. The cumulative sum of weighted expression levels are next ranked to select responsible genes. These procedures also work for multiclass classification. We demonstrate this algorithm on acute leukemia, colon cancer, small, round blue cell tumors of childhood, breast cancer, and lung cancer studies, using kernel Fisher discriminant analysis and support vector machines as classifiers. Other procedures are compared as well.</p> <p>Conclusion</p> <p>This approach is easy to implement and fast in computation for both binary and multiclass problems. The gene set provided by the RLS-SVR weight-based approach contains a less number of genes, and achieves a higher accuracy than other procedures.</p

Kernel methods in genomics and computational biology

Support vector machines and kernel methods are increasingly popular in genomics and computational biology, due to their good performance in real-world applications and strong modularity that makes them suitable to a wide range of problems, from the classification of tumors to the automatic annotation of proteins. Their ability to work in high dimension, to process non-vectorial data, and the natural framework they provide to integrate heterogeneous data are particularly relevant to various problems arising in computational biology. In this chapter we survey some of the most prominent applications published so far, highlighting the particular developments in kernel methods triggered by problems in biology, and mention a few promising research directions likely to expand in the future

High-dimensional Ising model selection using ℓ1{\ell_1}-regularized logistic regression

We consider the problem of estimating the graph associated with a binary Ising Markov random field. We describe a method based on $\ell_1$-regularized logistic regression, in which the neighborhood of any given node is estimated by performing logistic regression subject to an $\ell_1$-constraint. The method is analyzed under high-dimensional scaling in which both the number of nodes $p$ and maximum neighborhood size $d$ are allowed to grow as a function of the number of observations $n$. Our main results provide sufficient conditions on the triple $(n,p,d)$ and the model parameters for the method to succeed in consistently estimating the neighborhood of every node in the graph simultaneously. With coherence conditions imposed on the population Fisher information matrix, we prove that consistent neighborhood selection can be obtained for sample sizes $n=\Omega(d^3\log p)$ with exponentially decaying error. When these same conditions are imposed directly on the sample matrices, we show that a reduced sample size of $n=\Omega(d^2\log p)$ suffices for the method to estimate neighborhoods consistently. Although this paper focuses on the binary graphical models, we indicate how a generalization of the method of the paper would apply to general discrete Markov random fields.Comment: Published in at http://dx.doi.org/10.1214/09-AOS691 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A general approach to simultaneous model fitting and variable elimination in response models for biological data with many more variables than observations

<p>Abstract</p> <p>Background</p> <p>With the advent of high throughput biotechnology data acquisition platforms such as micro arrays, SNP chips and mass spectrometers, data sets with many more variables than observations are now routinely being collected. Finding relationships between response variables of interest and variables in such data sets is an important problem akin to finding needles in a haystack. Whilst methods for a number of response types have been developed a general approach has been lacking.</p> <p>Results</p> <p>The major contribution of this paper is to present a unified methodology which allows many common (statistical) response models to be fitted to such data sets. The class of models includes virtually any model with a linear predictor in it, for example (but not limited to), multiclass logistic regression (classification), generalised linear models (regression) and survival models. A fast algorithm for finding sparse well fitting models is presented. The ideas are illustrated on real data sets with numbers of variables ranging from thousands to millions. R code implementing the ideas is available for download.</p> <p>Conclusion</p> <p>The method described in this paper enables existing work on response models when there are less variables than observations to be leveraged to the situation when there are many more variables than observations. It is a powerful approach to finding parsimonious models for such datasets. The method is capable of handling problems with millions of variables and a large variety of response types within the one framework. The method compares favourably to existing methods such as support vector machines and random forests, but has the advantage of not requiring separate variable selection steps. It is also works for data types which these methods were not designed to handle. The method usually produces very sparse models which make biological interpretation simpler and more focused.</p

Simple but Not Simplistic: Reducing the Complexity of Machine Learning Methods

Programa Oficial de Doutoramento en Computación . 5009V01[Resumo] A chegada do Big Data e a explosión do Internet das cousas supuxeron un gran reto para os investigadores en Aprendizaxe Automática, facendo que o proceso de aprendizaxe sexa mesmo roáis complexo. No mundo real, os problemas da aprendizaxe automática xeralmente teñen complexidades inherentes, como poden ser as características intrínsecas dos datos, o gran número de mostras, a alta dimensión dos datos de entrada, os cambios na distribución entre o conxunto de adestramento e test, etc. Todos estes aspectos son importantes, e requiren novoS modelos que poi dan facer fronte a estas situacións. Nesta tese, abordáronse todos estes problemas, tratando de simplificar o proceso de aprendizaxe automática no escenario actual. En primeiro lugar, realízase unha análise de complexidade para observar como inflúe esta na tarefa de clasificación, e se é posible que a aplicación dun proceso previo de selección de características reduza esta complexidade. Logo, abórdase o proceso de simplificación da fase de aprendizaxe automática mediante a filosofía divide e vencerás, usando un enfoque distribuído. Seguidamente, aplicamos esa mesma filosofía sobre o proceso de selección de características. Finalmente, optamos por un enfoque diferente seguindo a filosofía do Edge Computing, a cal permite que os datos producidos polos dispositivos do Internet das cousas se procesen máis preto de onde se crearon. Os enfoques propostos demostraron a súa capacidade para reducir a complexidade dos métodos de aprendizaxe automática tradicionais e, polo tanto, espérase que a contribución desta tese abra as portas ao desenvolvemento de novos métodos de aprendizaxe máquina máis simples, máis robustos, e máis eficientes computacionalmente.[Resumen] La llegada del Big Data y la explosión del Internet de las cosas han supuesto un gran reto para los investigadores en Aprendizaje Automático, haciendo que el proceso de aprendizaje sea incluso más complejo. En el mundo real, los problemas de aprendizaje automático generalmente tienen complejidades inherentes) como pueden ser las características intrínsecas de los datos, el gran número de muestras, la alta dimensión de los datos de entrada, los cambios en la distribución entre el conjunto de entrenamiento y test, etc. Todos estos aspectos son importantes, y requieren nuevos modelos que puedan hacer frente a estas situaciones. En esta tesis, se han abordado todos estos problemas, tratando de simplificar el proceso de aprendizaje automático en el escenario actual. En primer lugar, se realiza un análisis de complejidad para observar cómo influye ésta en la tarea de clasificación1 y si es posible que la aplicación de un proceso previo de selección de características reduzca esta complejidad. Luego, se aborda el proceso de simplificación de la fase de aprendizaje automático mediante la filosofía divide y vencerás, usando un enfoque distribuido. A continuación, aplicamos esa misma filosofía sobre el proceso de selección de características. Finalmente, optamos por un enfoque diferente siguiendo la filosofía del Edge Computing, la cual permite que los datos producidos por los dispositivos del Internet de las cosas se procesen más cerca de donde se crearon. Los enfoques propuestos han demostrado su capacidad para reducir la complejidad de los métodos de aprendizaje automático tnidicionales y, por lo tanto, se espera que la contribución de esta tesis abra las puertas al desarrollo de nuevos métodos de aprendizaje máquina más simples, más robustos, y más eficientes computacionalmente.[Abstract] The advent of Big Data and the explosion of the Internet of Things, has brought unprecedented challenges to Machine Learning researchers, making the learning task more complexo Real-world machine learning problems usually have inherent complexities, such as the intrinsic characteristics of the data, large number of instauces, high input dimensionality, dataset shift, etc. AH these aspects matter, and can fOI new models that can confront these situations. Thus, in this thesis, we have addressed aH these issues) simplifying the machine learning process in the current scenario. First, we carry out a complexity analysis to see how it inftuences the classification models, and if it is possible that feature selection might result in a deerease of that eomplexity. Then, we address the proeess of simplifying learning with the divide-and-conquer philosophy of the distributed approaeh. Later, we aim to reduce the complexity of the feature seleetion preprocessing through the same philosophy. FinallYl we opt for a different approaeh following the eurrent philosophy Edge eomputing, whieh allows the data produeed by Internet of Things deviees to be proeessed closer to where they were ereated. The proposed approaehes have demonstrated their eapability to reduce the complexity of traditional maehine learning algorithms, and thus it is expeeted that the eontribution of this thesis will open the doors to the development of new maehine learning methods that are simpler, more robust, and more eomputationally efficient