A stochastic approach to handle knapsack problems in the creation of ensembles

Ensemble-based methods are highly popular approaches that increase the accuracy of a decision by aggregating the opinions of individual voters. The common point is to maximize accuracy; however, a natural limitation occurs if incremental costs are also assigned to the individual voters. Consequently, we investigate creating ensembles under an additional constraint on the total cost of the members. This task can be formulated as a knapsack problem, where the energy is the ensemble accuracy formed by some aggregation rules. However, the generally applied aggregation rules lead to a nonseparable energy function, which takes the common solution tools -- such as dynamic programming -- out of action. We introduce a novel stochastic approach that considers the energy as the joint probability function of the member accuracies. This type of knowledge can be efficiently incorporated in a stochastic search process as a stopping rule, since we have the information on the expected accuracy or, alternatively, the probability of finding more accurate ensembles. Experimental analyses of the created ensembles of pattern classifiers and object detectors confirm the efficiency of our approach. Moreover, we propose a novel stochastic search strategy that better fits the energy, compared with general approaches such as simulated annealing.

Optimizing Majority Voting Based Systems Under a Resource Constraint for Multiclass Problems

Ensemble-based approaches are very effective in various fields in raising the accuracy of its individual members, when some voting rule is applied for aggregating the individual decisions. In this paper, we investigate how to find and characterize the ensembles having the highest accuracy if the total cost of the ensemble members is bounded. This question leads to Knapsack problem with non-linear and non-separable objective function in binary and multiclass classification if the majority voting is chosen for the aggregation. As the conventional solving methods cannot be applied for this task, a novel stochastic approach was introduced in the binary case where the energy function is discussed as the joint probability function of the member accuracy. We show some theoretical results with respect to the expected ensemble accuracy and its variance in the multiclass classification problem which can help us to solve the Knapsack problem.