Statistical Optimization Techniques

Abstract

QSAR studies can be broadly divided into two types-regression and classification. The development of QSAR models essentially consists of the application of statistical methods to chemical datasets. As such, the statistical and machine learning literature provides a number of useful techniques. Some techniques are specifically designed to build classification models whereas others can carry out both classification as well as regression. In addition to these techniques, a number of methods are available for the optimization of various parameters and selection of variables required in the model building process. These can be deterministic methods such as the BFGS algorithm 1-4 and the Nelder-Mead simplex algorithm 5 or stochastic methods such as genetic algorithms 6-8 and simulated annealing. 9 This chapter discusses the underlying details of the various modeling and optimization techniques used in this work. 2.1 Linear Methods As the title of this section indicates linear methods employ a linear relationship between the predictor variables and the observed response to develop a predictive model. In many QSAR problems, structure property trends can be modeled reasonably well by linear approximations. In general it is observed that physical properties are well modeled by these types of methods. In the case of biological properties linear models do not always exhibit good predictive performance. The poorer behavior of linear models when faced with biological structure property trends is understandable when we consider the fact that biological properties in general are the result of a number of interactions that might include absorption, metabolic degradation, excretion and so on. Clearly the relationship between molecular structure and these factors is complex and in general nonlinear. However, linear methods are useful as a first step in the modeling process and, though not always very accurate, the simple interpretation methods that can be applied to linear models makes up, to some extent, for the lack of predictive ability for these methods. Though linear methods can be applied to both classification and regression we focus on the latter application in this section.