Probabilistic learning based decision making under uncertainty with application to biomedical process

Abstract

With the development of technology, humans are getting more and more understanding about biomedical process. Decision making in biomedical process becomes a hot topic. One serious challenge in biomedical decision making is the treatment of various uncertainties. At present, the mechanisms remain unknown for many critical diseases and the dynamics of cells, proteins and genes, which result in the structural uncertainty in the modeling of decision making. The difference of samples and the measurement noises will lead to the stochastic uncertainties in experimental data. When uncertainties are contained in high dimensional and limited data samples, which are the common characteristics of biomedical process, the decision making becomes especially difficult. In this thesis, probabilistic learning methods are proposed for decision making under uncertainties of biomedical process. The objectives of this thesis include 1) to develop a novel probabilistic support vector machine to reduce the effect of stochastic uncertainties; 2) to design a knowledge based probabilistic SVM learning system for pain diagnosis. 3) to propose a new entropy based learning method for feature selection under stochastic uncertainties; 4) to design an entropy based sequential learning methodology for gene selection. The significance and contributions of this thesis will be highlighted as follows. ● A probabilistic support vector machine (PSVM) is proposed for the classification of data with stochastic uncertainties. In most decision making, the data samples usually have large dimensions, thus conventional noise reduction methods are less effective. In PSVM, the uncertainties are modelled as the probability density function (PDF) of the separating margin in feature space. A principal component analysis (PCA) based distributed SVM system will be used to estimate the probabilistic distribution function of the separating margin. A new probabilistic optimization is proposed to determine the decision function. Furthermore, the confidence of the decision is estimated under uncertain circumstance and its correlation with sample uncertainties is demonstrated. ● A novel knowledge based probabilistic support vector learning system is proposed to deal with the diagnosis and treatment evaluation of LBP. The decision system consists of qualitative knowledge model and quantitative model. Expert knowledge and clinical experience are integrated into the design. To deal with the uncertainties in patients samples, PSVM is employed to learn the decision rules from data. ● A new entropy based feature selection method is propsed to selected informative features under uncertainties. The samples with different class labels are considered as the measurement from different systems. Due to the uncertainties and intrinsic dynamics, the different systems have different entropy. An importance sampling method is proposed to estimate the probability density function efficiently. ● An entropy based sequential learning methodology is proposed for gene selection. The spatial entropy is first defined to measure the uncertainties in genes. Genes are projected into the orthogonal space spanned by the orthogonal basis obtained by Proper Orthogonal Decomposition (POD). The spatial entropy is calculated by the approximation of variations on each orthogonal basis. To derive a low-dimensional classification model, the genes are projected into the feature space that will remove lots of gene redundancy. Then a neural network (NN) is employed to learn the parameter of the classification model. The proposed methodology is processed in a sequential manner until the classification performance is stable and satisfactory. This thesis proposed two probabilistic learning methods and two decision support systems for biomecial process. The methods are data driven and could explore the probability density function of features and integrate the PDF into the design of the decision making. In their applications to biomecial process, the expert knowledge and experience are extracted for the design, the probabilistic learning reduce the influence of various uncertainties. The methods have been applied to artificial data sets and many real life datasets and demonstrated the effectiveness.