Subset selection, optimization

Direct sampling methods, which try to obtain a subset of optimally diverse compounds from an available pool by directly analyzing the diversity of the selected molecules [75,76]. 

The nature of combinatorial chemistry can present a considerable challenge because these libraries are generally produced as arrays of compounds and it is often inconvenient to synthesize individual compounds in order to achieve an optimal design. Two methods have been described that attempt to select optimal subset of reagents from a virtual library that has been partitioned into favorable and unfavorable compounds by some method of filtering. The PLUMS algorithm [97] was designed to simultaneously optimize the size of the library based on effectiveness and efEciency . 

The compound selection methods described thus far can be used to select compounds for screening from an in-house collection, or to select which compounds to purchase from an external supplier. In combinatorial library design, however, it is necessary to select subsets of reactants for actual synthesis. The two main strategies for combinatorial library design are reactant-based selection and product-based selection. In reactant-based selection, optimized subsets of reactants are selected without consideration of the products that will result and any of the compound selection methods already identified can be used. An early example of reactant-based design is that already described by Martin and colleagues which is based on experimental design and where diverse subsets of reactants were selected for the synthesis of peptoid libraries [1]. 

A requirement for any subset selection method is the ability to accommodate a set of previously selected molecules, where augmentation of the pre-existing set is desired. For example, when purchasing compounds, the goal is to augment what is already owned so that the current corporate collection would be used in the analysis as the pre-existing set of molecules. The goal then is to select a subset of the candidate molecules that optimizes a specified criterion with reference to the molecules in both the candidate set and the previously selected set. 

A promising new use of prior distributions for subset selection is in the formulation of optimality criteria for the construction of designs that allow model discrimination. This technique is discussed in Section 6. The chapter concludes with a discussion, including possible extensions of the techniques to generalized linear models. 

Phase II and phase III randomized trials with subset selection and disease documentation are ongoing to evaluate the efficacy of various combinations of chemotherapy, radiation, and surgery. Clinicians must refrain from extrapolating the results from early clinical trials into their general daily practice and should continue, whenever possible, to refer patients to carefully designed randomized trials to define the optimal therapy for the various subsets of NSCLC. 

Generating Optimal Linear PLS Estimations = GOLPE variable selection > genetic algorithm - variable subset selection variable selection... 

The chapter begins with a discussion of similarity and diversity measures and how they can be applied in a virtual screening context. The various computational filters in use are also discussed. The rest of the chapter is concerned with different approaches to combinatorial library design, beginning with reagent-based methods followed by product-based approaches of cherry picking and combinatorial subset selection. Finally, approaches to designing libraries optimized on multiple properties simultaneously are discussed. 

The final category of subset selection algorithms is termed optimization techniques and it includes a number of different approaches. For example, Martin et al. [41] have described a subset selection technique based on Z)-optimal design, which is a... 

Taking account of the combinatorial constraint requires methods that are able to select a combinatorial subset directly from within product space, as illustrated in Fig. 4b. Combinatorial subset selection represents an enormous search space and is typically implemented using an optimization technique such as a GA or SA. For example, there are ... 

Figure 4. The substituents Rl, R2 and R3 can be selected using D-optimal design. All the interesting compounds were collected in a pool of candidates. We can remove from this pool some compounds that are difficult to synthesize, toxic, etc.. .. The D-optimal algorithm extracts from the pool the subset that optimizes the D criterion. Seven points are enough to test the six variables used in the design of the ...

For any synthetic scheme, the key issue in combinatorial library design is monomer selection, the objective of which is to identify those monomers which when combined together provide the optimal combinatorial library. By optimal we mean that Uhrary which best meets the prescribed objectives it might be the most diverse, have the maximum number of molecules that could fit a 3D pharmacophore or a protein binding site, best match a particular distribution of some physicochemical property, or some combination of these or other criteria. An important consideration when designing a combinatorial Uhrary is the subset selection constraint. In a true combinatorial Ubrary of the form A x B x C, every molecule from the set of reagents A reacts with every molecule from B and every molecule from C to generate n xn x c product structures, where are the numbers of... 

If the selection problem "select c V " is solved optimally, then the algorithm will obviously supply an optimum result. Since the problem of an optimal subset selection is NP-hard, an efflcient solution is only possible by using heuristics. The following heuristics are used ... 

Perhaps the best idea is to compute as many descriptors as possible and then to select an optimal subset by applying sophisticated techniques, discussed below. 

Once the quality of the dataset is defined, the next task is to improve it. Again, one has to remove outliers, find out and remove redundant objects (as they deliver no additional information), and finally, select the optimal subset of descriptors. 

Factorial design methods cannot always be applied to QSAR-type studies. For example, i may not be practically possible to make any compounds at all with certain combination of factor values (in contrast to the situation where the factojs are physical properties sucl as temperature or pH, which can be easily varied). Under these circumstances, one woul( like to know which compounds from those that are available should be chosen to give well-balanced set with a wide spread of values in the variable space. D-optimal design i one technique that can be used for such a selection. This technique chooses subsets o... 

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