Model building optimization

The model building step deals with the development of mathematical models to relate the optimized set of descriptors with the target property. Two statistical measures indicate the quality of a model, the regression coefficient, r, or its square, r, and the standard deviation, a (see Chapter 9). 

Figure 3 Model building by Modeller [31], First, spatial restraints in the form of atomic distances and dihedral angles are extracted from the template stmcture(s). The alignment is used to determine equivalent residues between the target and the template. The restraints are combined into an objective function. Finally, the model for the target is optimized until a model that best satisfies the spatial restraints is obtained. This procedure is technically similar to the one used in structure determination by NMR.

For many proteins, it is possible to generate structures of protein-ligand complexes quite rapidly. It is therefore not uncommon for many hundreds of structures to be determined in support of a drug discovery and optimization project. The major challenge for this level of throughput is informatics support. It is also this type of crystallography that is most in need of semiautomated procedures for structure solution and model building (see Section 12.6). 

As will be seen later, these techniques will prove to be useful when solving design problems in general-purpose software, such as spreadsheets. Many of the numerical problems associated with optimization can be avoided by appropriate formulation of the model. Further details of model building can be found elsewhere12. 

Part I comprises three chapters that motivate the study of optimization by giving examples of different types of problems that may be encountered in chemical engineering. After discussing the three components in the previous list, we describe six steps that must be used in solving an optimization problem. A potential user of optimization must be able to translate a verbal description of the problem into the appropriate mathematical description. He or she should also understand how the problem formulation influences its solvability. We show how problem simplification, sensitivity analysis, and estimating the unknown parameters in models are important steps in model building. Chapter 3 discusses how the objective function should be developed. We focus on economic factors in this chapter and present several alternative methods of evaluating profitability. 

In PAT, one is often faced with the task of building, optimizing, evaluating, and deploying a model based on a limited set of calibration data. In such a situation, one can use model validation and cross-validation techniques to perform two of these functions namely to optimize the model by determining the optimal model complexity and to perform preliminary evaluation of the model s performance before it is deployed. There are several validation methods that are commonly used in PAT applications, and some of these are discussed below. 

Model building is an interpretation of the currently available electron density. Refinement is the adjustment of the built model to fit better to the experimental data. A crucial point here is that a density map computed from the refined model is generally better than the map obtained from the same model before the refinement. This then allows for an even better model to be built. Thus, refinement is needed to improve the outcome of model building by generating a better electron density map and model building is needed to provide a model in the first place and to provide stereochemical restraints for the subsequent refinement to proceed smoothly. This viewpoint merges these two steps into one model optimization process. 

Yasri, A. and Hartsough, D. (2001) Toward an optimal procedure for variable selection and QSAR model building. J. Chem. Inf. Comput. Sci. 41, 1218-1227. 

The software requires the following information the concentration and spectral data, the preprocessing selections, the maximum number of factors to estimate, and the validation approach used to choose the optimal number of factors. The maximum rank selected is 10 for constructing the model to predict the caustic concentration. The validation technique is leave-one-out cross-validation where an entire design point is left out. Tliat is, there are 12 cross validation steps and all spectra for each standard (at various temperatures) are left out of the model building phase at each step. 

Perform a correct and extensive validation of models, in order to properly evaluate their prediction ability and thus their actual applicability. In particular, mind that if model building involves optimization steps, a three-set validation strategy should be applied. 

Building Product Models. The next step in product optimization deals with model building. A model summarizes the relations between formula variables in a succinct, quantitative way. 

Reducing the dimensionality of the descriptor space not only facilitates model building with molecular descriptors but also makes data visualization and identification of key variables in various models possible. Notice that while a low dimension mathematically simplifies a problem such as model development or data visualization, it is usually more difficult to correlate trends directly with physical descriptors, and hence the data become less interpretable, after the dimension transformation. Trends directly linked with physical descriptors provide simple guidance for molecular modifications during potency/property optimizations. 

A. Dijkstra, and L. Kaufman, Evaluation and Optimization of Laboratory Methods and Analytical Procedures (Amsterdam Elsevier, 1978) G. E. P. Box, W. G. Hunter, and J. S. Hunter, Statistics for Experimenters An Introduction to Design Data Analysis and Model Building (New York Wiley, 1978) R. S. Strange, Introduction to Experimental Design for Chemists, J. Chem. Ed. 1990,67. 113. 

Probably the most common internal validation method, cross-validation, involves the execution of one or more internal validation procedures (hereby called sub-validations), where each procedure involves the removal of a part of the calibration data, use of the remaining calibration data to build a subset calibration model, and subsequent application of the removed data to the subset calibration model. Unlike the Model fit evaluation method discussed earlier, the same data are not used for model building and model testing for each of the sub-validations. As a result, they can provide more realistic estimates of a model s prediction performance, as well as better assessments of the optimal complexity of a model. 

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