Browsing by Subject "Equivalence classes"

Now showing 1 - 5 of 5

Open Access
Energy consumption forecasting via order preserving pattern matching
(IEEE, 2014-12) Vanlı, N. Denizcan; Sayın, Muhammed O.; Yıldız, Hikmet; Göze, Tolga; Kozat, Süleyman S.
We study sequential prediction of energy consumption of actual users under a generic loss/utility function. Particularly, we try to determine whether the energy usage of the consumer will increase or decrease in the future, which can be subsequently used to optimize energy consumption. To this end, we use the energy consumption history of the users and define finite state (FS) predictors according to the relative ordering patterns of these past observations. In order to alleviate the overfitting problems, we generate equivalence classes by tying several states in a nested manner. Using the resulting equivalence classes, we obtain a doubly exponential number of different FS predictors, one among which achieves the smallest accumulated loss, hence is optimal for the prediction task. We then introduce an algorithm to achieve the performance of this FS predictor among all doubly exponential number of FS predictors with a significantly reduced computational complexity. Our approach is generic in the sense that different tying configurations and loss functions can be incorporated into our framework in a straightforward manner. We illustrate the merits of the proposed algorithm using the real life energy usage data. © 2014 IEEE.
Open Access
Multi-criteria analysis using latent class cluster ranking: An investigation into corporate resiliency
(Elsevier, 2014) Mistry, J.; Sarkis, J.; Dhavale, D. G.
In this paper, we introduce a multi-stage multiple criteria latent class model within a Bayesian framework that can be used to evaluate and rank-order objects based on multiple performance criteria. The latent variable extraction in our methodology relies on Bayesian analysis and Monte Carlo simulation, which uses a Gibbs sampler. Ranking of clusters of objects is completed using the extracted latent variables. We apply the methodology to evaluate the resiliency of e-commerce companies using balanced scorecard performance dimensions. Cross-validation of the latent class model confirms a superior fit for classifying the e-commerce companies. Specifically, using the methodology we determine the ability of different perspectives of the balanced scorecard method to predict the continued viability and eventual survival of e-commerce companies. The novel methodology may also be useful for performance evaluation and decision making in other contexts. In general, this methodology is useful where a ranking of elements within a set, based on multiple objectives, is desired. A significant advantage of this methodology is that it develops weighting scheme for the multiple objective based on intrinsic characteristics of the set with minimal subjective input from decision makers. © 2013 Elsevier B.V.
Open Access
Reward-rate maximization in sequential identification under a stochastic deadline
(2013) Dayanık, S.; Yu, A. J.
Any intelligent system performing evidence-based decision making under time pressure must negotiate a speed-accuracy trade-off. In computer science and engineering, this is typically modeled as minimizing a Bayes-risk functional that is a linear combination of expected decision delay and expected terminal decision loss. In neuroscience and psychology, however, it is often modeled as maximizing the long-term reward rate, or the ratio of expected terminal reward and expected decision delay. The two approaches have opposing advantages and disadvantages. While Bayes-risk minimization can be solved with powerful dynamic programming techniques unlike reward-rate maximization, it also requires the explicit specification of the relative costs of decision delay and error, which is obviated by reward-rate maximization. Here, we demonstrate that, for a large class of sequential multihypothesis identification problems under a stochastic deadline, the reward-rate maximization is equivalent to a special case of Bayes-risk minimization, in which the optimal policy that attains the minimal risk when the unit sampling cost is exactly the maximal reward rate is also the policy that attains maximal reward rate. We show that the maximum reward rate is the unique unit sampling cost for which the expected total observation cost and expected terminal reward break even under every Bayes-risk optimal decision rule. This interplay between reward-rate maximization and Bayesrisk minimization formulations allows us to show that maximum reward rate is always attained. We can compute the policy that maximizes reward rate by solving an inverse Bayes-risk minimization problem, whereby we know the Bayes risk of the optimal policy and need to find the associated unit sampling cost parameter. Leveraging this equivalence, we derive an iterative dynamic programming procedure for solving the reward-rate maximization problem exponentially fast, thus incorporating the advantages of both the reward-rate maximization and Bayes-risk minimization formulations. As an illustration, we will apply the procedure to a two-hypothesis identification example.
Open Access
Scheduling to minimize the coefficient of variation
(Elsevier, 1996) De, P.; Ghosh, J. B.; Wells, C. E.
In this paper, we address the problem of uninterruptedly scheduling a set of independent jobs that are ready at time zero with the objective of minimizing the coefficient of variation (CV) of their completion times. We first show that, for high processing time values of the longest job, a variance (V) minimizing schedule also minimizes CV. Using this equivalence, we next demonstrate the invalidity of an earlier conjecture about the structure of a CV-optimal schedule and proceed to establish the NP-hardness of the CV problem. Finally, drawing from our prior work on the V problem, we provide a pseudo-polynomial dynamic programming algorithm for the solution of the CV problem.
Open Access
Simple functors of admissible linear categories
(Springer, 2016) Barker, L.; Demirel, M.
Generalizing an idea used by Bouc, ThÃ©venaz, Webb and others, we introduce the notion of an admissible R-linear category for a commutative unital ring R. Given an R-linear category (Formula presented.) , we define an (Formula presented.) -functor to be a functor from (Formula presented.) to the category of R-modules. In the case where (Formula presented.) is admissible, we establish a bijective correspondence between the isomorphism classes of simple functors and the equivalence classes of pairs (G, V) where G is an object and V is a module of a certain quotient of the endomorphism algebra of G. Here, two pairs (F, U) and (G, V) are equivalent provided there exists an isomorphism F ← G effecting transport to U from V. We apply this to the category of finite abelian p-groups and to a class of subcategories of the biset category. Â© 2015, Springer Science+Business Media Dordrecht.