PMC:4996407 / 23934-25322 JSONTXT

{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/4996407","sourcedb":"PMC","sourceid":"4996407","source_url":"https://www.ncbi.nlm.nih.gov/pmc/4996407","text":"2.3.6. Search Speed Optimization\nHowever, the solution proposed above has the consequence of increasing both the size of the data set and the number of potential combinations to be evaluated to the point that it becomes too time-consuming to conduct a systematic search. Since the goal is only to find some combinations of genes that predict disease well enough to be useful, we used a Monte-Carlo approach to accelerate the search.\nThe efficiency of a random Monte-Carlo evaluation can be illustrated by comparing the numerical estimation of the value of π with and without Monte-Carlo acceleration. The mathematical constant, π, represents the ratio of the area within a circle to the square of its radius. For a circle of unit radius with an enclosed area of π units squared, the enclosing square has sides of 2 units with an area of 4 units squared. A systematic evaluation would divide the enclosing square into a grid with regularly spaced points and determine whether each of these points is within the circle or outside it. The ratio of the number of points within the circle to the number of points inside the square is an approximation of π/4. A random search would select points at random rather than systematically march along the grid. As illustrated in Figure 3, the Monte-Carlo estimate comes within 5% of the correct value much more rapidly than the systematic evaluation.","divisions":[{"label":"Title","span":{"begin":0,"end":32}}],"tracks":[]}