Browsing by Subject "Worst-case performance"

Now showing 1 - 3 of 3

Open Access
Comprehensive lower bounds on sequential prediction
(IEEE, 2014-09) Vanlı, N. Denizcan; Sayın, Muhammed O.; Ergüt, S.; Kozat, Süleyman S.
We study the problem of sequential prediction of real-valued sequences under the squared error loss function. While refraining from any statistical and structural assumptions on the underlying sequence, we introduce a competitive approach to this problem and compare the performance of a sequential algorithm with respect to the large and continuous class of parametric predictors. We define the performance difference between a sequential algorithm and the best parametric predictor as regret, and introduce a guaranteed worst-case lower bounds to this relative performance measure. In particular, we prove that for any sequential algorithm, there always exists a sequence for which this regret is lower bounded by zero. We then extend this result by showing that the prediction problem can be transformed into a parameter estimation problem if the class of parametric predictors satisfy a certain property, and provide a comprehensive lower bound to this case.
Open Access
Replacement problem in Web caching
(IEEE, 2003-06-07) Çakıroğlu, Seda; Arıkan, Erdal
Caching has been recognized as an effective scheme for avoiding service bottleneck and reducing network traffic in World Wide Web. Our work focuses on the replacement problem in Web caching, which arises due to limited storage. We seek the best configuration for a fully connected network of N caches. The problem is formulated as a discrete optimization problem. A number of low complexity heuristics are studied to obtain approximate solutions. Performances are tested under fictitious probabilistic request sequences access logs of real Web traffic. LFD (longest-forward-distance), the classical optimal off-line paging algorithm, is observed not to be optimal. Instead a window scheme should be used. Under an unchanging request pattern, a simple static placement algorithm achieves the maximum hit rates using the arrival probabilities. Otherwise, for quick adaptation to changing requests and for better worst-case performances a randomized algorithm should be chosen. We also give an analysis of Web data to propose best heuristics for its characteristics. © 2003 IEEE.
Open Access
A unified approach to universal prediction: Generalized upper and lower bounds
(Institute of Electrical and Electronics Engineers Inc., 2015) Vanli, N. D.; Kozat, S. S.
We study sequential prediction of real-valued, arbitrary, and unknown sequences under the squared error loss as well as the best parametric predictor out of a large, continuous class of predictors. Inspired by recent results from computational learning theory, we refrain from any statistical assumptions and define the performance with respect to the class of general parametric predictors. In particular, we present generic lower and upper bounds on this relative performance by transforming the prediction task into a parameter learning problem. We first introduce the lower bounds on this relative performance in the mixture of experts framework, where we show that for any sequential algorithm, there always exists a sequence for which the performance of the sequential algorithm is lower bounded by zero. We then introduce a sequential learning algorithm to predict such arbitrary and unknown sequences, and calculate upper bounds on its total squared prediction error for every bounded sequence. We further show that in some scenarios, we achieve matching lower and upper bounds, demonstrating that our algorithms are optimal in a strong minimax sense such that their performances cannot be improved further. As an interesting result, we also prove that for the worst case scenario, the performance of randomized output algorithms can be achieved by sequential algorithms so that randomized output algorithms do not improve the performance. © 2012 IEEE.