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Yayın VC-dimension of univariate decision trees(IEEE-INST Electrical Electronics Engineers Inc, 2015-02-25) Yıldız, Olcay TanerIn this paper, we give and prove the lower bounds of the Vapnik-Chervonenkis (VC)-dimension of the univariate decision tree hypothesis class. The VC-dimension of the univariate decision tree depends on the VC-dimension values of its subtrees and the number of inputs. Via a search algorithm that calculates the VC-dimension of univariate decision trees exhaustively, we show that our VC-dimension bounds are tight for simple trees. To verify that the VC-dimension bounds are useful, we also use them to get VC-generalization bounds for complexity control using structural risk minimization in decision trees, i.e., pruning. Our simulation results show that structural risk minimization pruning using the VC-dimension bounds finds trees that are more accurate as those pruned using cross validation.Yayın Modeling and simulation support to the defense planning process(Sage Publications Inc, 2017-04-01) Çayırcı, Erdal; Özçakır, LütfüDefense planning is a crucial part of the defense process. It identifies the capabilities required for the future defense environment, analyzes the capability shortfalls, prioritizes them, and provides the fundamental inputs for their development. Modeling and simulation may significantly contribute to the success of defense planning. However, neither the theory nor the tools are mature enough to fulfill the defense planning requirements. Various types of simulation tools, such as static, dynamic, deterministic, stochastic, closed, discrete, continuous, and symbiotic, in multiple levels of resolution and fidelity are needed to support the different stages and phases. The verification and validation of the models and the analysis of the input and output data are critical. Yet another challenge is that the uncertainties related to the contemporary defense scenarios are mostly not in aleatory but in the epistemic domain. In this paper, we briefly present a new computer-assisted defense planning process. Then, we introduce the service-oriented cloud approach for the modeling and simulation support to the process.Yayın On the online coalition structure generation problem(AI Access Foundationusc Information Sciences Inst, 2021) Flammini, Michele; Monaco, Gianpiero; Moscardelli, Luca; Shalom, Mordechai; Zaks, ShmuelWe consider the online version of the coalition structure generation problem, in which agents, corresponding to the vertices of a graph, appear in an online fashion and have to be partitioned into coalitions by an authority (i.e., an online algorithm). When an agent appears, the algorithm has to decide whether to put the agent into an existing coalition or to create a new one containing, at this moment, only her. The decision is irrevocable. The objective is partitioning agents into coalitions so as to maximize the resulting social welfare that is the sum of all coalition values. We consider two cases for the value of a coalition: (1) the sum of the weights of its edges, and (2) the sum of the weights of its edges divided by its size. Coalition structures appear in a variety of application in AI, multi-agent systems, networks, as well as in social networks, data analysis, computational biology, game theory, and scheduling. For each of the coalition value functions we consider the bounded and unbounded cases depending on whether or not the size of a coalition can exceed a given value alpha. Furthermore, we consider the case of a limited number of coalitions and various weight functions for the edges, i.e., unrestricted, positive and constant weights. We show tight or nearly tight bounds for the competitive ratio in each case.
