11522481
New approaches to support vector ordinal regression
In this paper, we propose two new support vector approaches for ordinal regression, which optimize multiple thresholds to define parallel discriminant hyperplanes for the ordinal scales. Both approaches guarantee that the thresholds are properly ordered at the optimal solution. The size of these optimization problems is linear in the number of training samples. The SMO algorithm is adapted for the resulting optimization problems; it is extremely easy to implement and scales efficiently as a quadratic function of the number of examples. The results of numerical experiments on benchmark datasets verify the usefulness of these approaches.
2788778
Gaussian Processes for Ordinal Regression
We present a probabilistic kernel approach to ordinal regression based on Gaussian processes. A threshold model that generalizes the probit function is used as the likelihood function for ordinal variables. Two inference techniques, based on the Laplace approximation and the expectation propagation algorithm respectively, are derived for hyperparameter learning and model selection. We compare these two Gaussian process approaches with a previous ordinal regression method based on support vector machines on some benchmark and real-world data sets, including applications of ordinal regression to collaborative filtering and gene expression analysis. Experimental results on these data sets verify the usefulness of our approach.
8243953
Bayesian segmental models with multiple sequence alignment profiles for protein secondary structure and contact map prediction
In this paper, we develop a segmental semi-Markov model (SSMM) for protein secondary structure prediction which incorporates multiple sequence alignment profiles with the purpose of improving the predictive performance. The segmental model is a generalization of the hidden Markov model where a hidden state generates segments of various length and secondary structure type. A novel parameterized model is proposed for the likelihood function that explicitly represents multiple sequence alignment profiles to capture the segmental conformation. Numerical results on benchmark data sets show that incorporating the profiles results in substantial improvements and the generalization performance is promising. By incorporating the information from long range interactions in beta-sheets, this model is also capable of carrying out inference on contact maps. This is an important advantage of probabilistic generative models over the traditional discriminative approach to protein secondary structure prediction. The Web server of our algorithm and supplementary materials are available at http://public.kgi.edu/-wild/bsm.html
820844
Identifying Protein Complexes in High-Throughput Protein Interaction Screens Using an Infinite Latent Feature Model
We propose a Bayesian approach to identify protein complexes and their constituents from high-throughput protein-protein interaction screens. An infinite latent feature model that allows for multi-complex membership by individual proteins is coupled with a graph diffusion kernel that evaluates the likelihood of two proteins belonging to the same complex. Gibbs sampling is then used to infer a catalog of protein complexes from the interaction screen data. An advantage of this model is that it places no prior constraints on the number of complexes and automatically infers the number of significant complexes from the data. Validation results using affinity purification/mass spectrometry experimental data from yeast RNA-processing complexes indicate that our method is capable of partitioning the data in a biologically meaningful way. A supplementary web site containing larger versions of the figures is available at http://public.kgi.edu/wild/PSBO6/index.html.
5337232
A Unified Loss Function in Bayesian Framework for Support Vector Regression
In this paper, we propose a unified non-quadratic loss function for regression known as soft insensitive loss function (SILF). SILF is a flexible model and possesses most of the desirable characteristics of popular non-quadratic loss functions, such as Laplacian, Huber’s and Vapnik’s e-insensitive loss function. We describe the properties of SILF and illustrate our assumption on the underlying noise model in detail. Moreover, the introduction of SILF in regression makes it possible to apply Bayesian techniques on Support Vector methods. Experimental results on simulated and real-world datasets indicate the feasibility of the approach.
523115
Biomarker discovery in microarray gene expression data with Gaussian processes
MOTIVATION
In clinical practice, pathological phenotypes are often labelled with ordinal scales rather than binary, e.g. the Gleason grading system for tumour cell differentiation. However, in the literature of microarray analysis, these ordinal labels have been rarely treated in a principled way. This paper describes a gene selection algorithm based on Gaussian processes to discover consistent gene expression patterns associated with ordinal clinical phenotypes. The technique of automatic relevance determination is applied to represent the significance level of the genes in a Bayesian inference framework.


RESULTS
The usefulness of the proposed algorithm for ordinal labels is demonstrated by the gene expression signature associated with the Gleason score for prostate cancer data. Our results demonstrate how multi-gene markers that may be initially developed with a diagnostic or prognostic application in mind are also useful as an investigative tool to reveal associations between specific molecular and cellular events and features of tumour physiology. Our algorithm can also be applied to microarray data with binary labels with results comparable to other methods in the literature.
8326709
Randomized Carrier PWM With Exponential Frequency Mapping
Pulsewidth modulation (PWM) and sigma-delta modulation (SDM) have been used in several high linearity, high accuracy power delivery applications such as dc-dc power converters, audio, and radio frequency power amplifiers and data converters. While PWM can generate high linearity signals with high efficiency, it suffers from discrete tonal output spectrums. SDM, on the other hand, can generate high linearity output spectrums with shaped quantization noise spectrums and lower efficiencies due to oversampling requirements. In this paper we present a particular class of carrier frequency modulated PWM (CFMPWM), which spreads the tonal content of regular PWM uniformly in frequency and reduces the baseband noise with respect to SDM by up to 15 dB. The new modulation scheme preserves the high efficiency properties of PWM. An approximate method to estimate the spectrum of CFMPWM signals with both deterministic and random modulation is also presented. Simulation results and experimental data are reported to analyze the spectral spreading properties of the proposed CFMPWM scheme