Using upper bounds on attainable discrimination to select discrete valued features

Selection of features that will permit accurate pattern classification is a difficult task. However, if a particular data set is represented by discrete valued features, it becomes possible to determine empirically the contribution that each feature makes to the discrimination between classes. This paper extends the discrimination bound method so that both the maximum and average discrimination expected on unseen test data can be estimated. These estimation techniques are the basis of a backwards elimination algorithm that can be use to rank features in order of their discriminative power. Two problems are used to demonstrate this feature selection process: classification of the Mushroom Database, and a real-world, pregnancy related medical risk prediction task - assessment of risk of perinatal death.

Upper Bounds on the Size of Grain-Correcting Codes

In this paper, we revisit the combinatorial error model of Mazumdar et al. that models errors in high-density magnetic recording caused by lack of knowledge of grain boundaries in the recording medium. We present new upper bounds on the cardinality/rate of binary block codes that correct errors within this model. All our bounds, except for one, are obtained using combinatorial arguments based on hypergraph fractional coverings. The exception is a bound derived via an information-theoretic argument. Our bounds significantly improve upon existing bounds from the prior literature.

Upper bounds on the photon mass

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Error Upper Bounds for a Computational Method for Nonlinear Boundary and Initial-Value Problems

This work develops a computational approach for boundary and initial-value problems by using operational matrices, in order to run an evolutive process in a Hilbert space. Besides, upper bounds for errors in the solutions and in their derivatives can be estimated providing accuracy measures.

Safe upper-bounds inference of energy consumption for java bytecode applications

Abstract is not available.

Two upper bounds for the weighted path length of binary trees.

Thesis (M.S.)--University of Illinois at Urbana-Champaign.

New Upper Bounds for Some Spherical Codes

The maximal cardinality of a code W on the unit sphere in n dimensions with (x, y) ≤ s whenever x, y ∈ W, x 6= y, is denoted by A(n, s). We use two methods for obtaining new upper bounds on A(n, s) for some values of n and s. We find new linear programming bounds by suitable polynomials of degrees which are higher than the degrees of the previously known good polynomials due to Levenshtein [11, 12]. Also we investigate the possibilities for attaining the Levenshtein bounds [11, 12]. In such cases we find the distance distributions of the corresponding feasible maximal spherical codes. Usually this leads to a contradiction showing that such codes do not exist.

Convexity, Classification, and Risk Bounds

Many of the classification algorithms developed in the machine learning literature, including the support vector machine and boosting, can be viewed as minimum contrast methods that minimize a convex surrogate of the 0–1 loss function. The convexity makes these algorithms computationally efficient. The use of a surrogate, however, has statistical consequences that must be balanced against the computational virtues of convexity. To study these issues, we provide a general quantitative relationship between the risk as assessed using the 0–1 loss and the risk as assessed using any nonnegative surrogate loss function. We show that this relationship gives nontrivial upper bounds on excess risk under the weakest possible condition on the loss function—that it satisfies a pointwise form of Fisher consistency for classification. The relationship is based on a simple variational transformation of the loss function that is easy to compute in many applications. We also present a refined version of this result in the case of low noise, and show that in this case, strictly convex loss functions lead to faster rates of convergence of the risk than would be implied by standard uniform convergence arguments. Finally, we present applications of our results to the estimation of convergence rates in function classes that are scaled convex hulls of a finite-dimensional base class, with a variety of commonly used loss functions.

Bounds on the Lifetime of Wireless Sensor Networks Employing Multiple Data Sinks

Employing multiple base stations is an attractive approach to enhance the lifetime of wireless sensor networks. In this paper, we address the fundamental question concerning the limits on the network lifetime in sensor networks when multiple base stations are deployed as data sinks. Specifically, we derive upper bounds on the network lifetime when multiple base stations are employed, and obtain optimum locations of the base stations (BSs) that maximize these lifetime bounds. For the case of two BSs, we jointly optimize the BS locations by maximizing the lifetime bound using a genetic algorithm based optimization. Joint optimization for more number of BSs is complex. Hence, for the case of three BSs, we optimize the third BS location using the previously obtained optimum locations of the first two BSs. We also provide simulation results that validate the lifetime bounds and the optimum locations of the BSs.

Bounds on Probability of Error Due to Co-Channel Interference

Upper bounds on the probability of error due to co-channel interference are proposed in this correspondence. The bounds are easy to compute and can be fairly tight.

Estimation of Probabilistic Bounds on Phase CPI and Relevance in WCET Analysis

Estimating program worst case execution time(WCET) accurately and efficiently is a challenging task. Several programs exhibit phase behavior wherein cycles per instruction (CPI) varies in phases during execution. Recent work has suggested the use of phases in such programs to estimate WCET with minimal instrumentation. However the suggested model uses a function of mean CPI that has no probabilistic guarantees. We propose to use Chebyshev's inequality that can be applied to any arbitrary distribution of CPI samples, to probabilistically bound CPI of a phase. Applying Chebyshev's inequality to phases that exhibit high CPI variation leads to pessimistic upper bounds. We propose a mechanism that refines such phases into sub-phases based on program counter(PC) signatures collected using profiling and also allows the user to control variance of CPI within a sub-phase. We describe a WCET analyzer built on these lines and evaluate it with standard WCET and embedded benchmark suites on two different architectures for three chosen probabilities, p={0.9, 0.95 and 0.99}. For p= 0.99, refinement based on PC signatures alone, reduces average pessimism of WCET estimate by 36%(77%) on Arch1 (Arch2). Compared to Chronos, an open source static WCET analyzer, the average improvement in estimates obtained by refinement is 5%(125%) on Arch1 (Arch2). On limiting variance of CPI within a sub-phase to {50%, 10%, 5% and 1%} of its original value, average accuracy of WCET estimate improves further to {9%, 11%, 12% and 13%} respectively, on Arch1. On Arch2, average accuracy of WCET improves to 159% when CPI variance is limited to 50% of its original value and improvement is marginal beyond that point.