Tadayoshi Fushiki | Search PubMed

PubMed2006

Identification of biomarkers from mass spectrometry data using a "common" peak approach.

BACKGROUND: Proteomic data obtained from mass spectrometry have attracted great interest for the detection of early-stage cancer. However, as mass spectrometry data are high-dimensional, identification of biomarkers is a key problem. RESULTS: This paper proposes the use of "common" peaks in data as biomarkers. Analysis is conducted as follows: data preprocessing, identification of biomarkers, and application of AdaBoost to construct a classification function. Informative "common" peaks are selected by AdaBoost. AsymBoost is also examined to balance false negatives and false positives. The effectiveness of the approach is demonstrated using an ovarian cancer dataset. CONCLUSION: Continuous covariates and discrete covariates can be used in the present approach. The difference between the result for the continuous covariates and that for the discrete covariates was investigated in detail. In the example considered here, both covariates provide a good prediction, but it seems that they provide different kinds of information. We can obtain more information on the structure of the data by integrating both results.

Algorithms↗

PubMed2006

A maximum likelihood approach to density estimation with semidefinite programming.

Density estimation plays an important and fundamental role in pattern recognition, machine learning, and statistics. In this article, we develop a parametric approach to univariate (or low-dimensional) density estimation based on semidefinite programming (SDP). Our density model is expressed as the product of a nonnegative polynomial and a base density such as normal distribution, exponential distribution, and uniform distribution. When the base density is specified, the maximum likelihood estimation of the polynomial is formulated as a variant of SDP that is solved in polynomial time with the interior point methods. Since the base density typically contains just one or two parameters, computation of the maximum likelihood estimate reduces to a one- or two-dimensional easy optimization problem with this use of SDP. Thus, the rigorous maximum likelihood estimate can be computed in our approach. Furthermore, such conditions as symmetry and unimodality of the density function can be easily handled within this framework. AIC is used to choose the best model. Through applications to several instances, we demonstrate flexibility of the model and performance of the proposed procedure. Combination with a mixture approach is also presented. The proposed approach has possible other applications beyond density estimation. This point is clarified through an application to the maximum likelihood estimation of the intensity function of a nonstationary Poisson process.

Data Interpretation, Statistical↗