Results 1  10
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22
Computing Variance for Interval Data is NPHard
, 2002
"... When we have only interval ranges [x i ; x i ] of sample values x 1 ; : : : ; xn , what is the interval [V ; V ] of possible values for the variance V of these values? We prove that the problem of computing the upper bound V is NPhard. We provide a feasible (quadratic time) algorithm for computi ..."
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Cited by 66 (48 self)
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When we have only interval ranges [x i ; x i ] of sample values x 1 ; : : : ; xn , what is the interval [V ; V ] of possible values for the variance V of these values? We prove that the problem of computing the upper bound V is NPhard. We provide a feasible (quadratic time) algorithm for computing the lower bound V on the variance of interval data. We also provide a feasible algorithm that computes V under reasonable easily verifiable conditions.
Experimental Uncertainty Estimation and Statistics for Data Having Interval Uncertainty
 11733, SAND20070939. hal00839639, version 1  28 Jun 2013
"... Sandia is a multiprogram laboratory operated by Sandia Corporation, ..."
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Cited by 39 (20 self)
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Sandia is a multiprogram laboratory operated by Sandia Corporation,
Outlier Detection Under Interval Uncertainty: Algorithmic Solvability and Computational Complexity
 LargeScale Scientific Computing, Proceedings of the 4th International Conference LSSC’2003, Sozopol, Bulgaria, June 4–8, 2003, Springer Lecture Notes in Computer Science
"... In many application areas, it is important to detect outliers. The traditional engineering approach to outlier detection is that we start with some “normal ” values x1,..., xn, compute the sample average E, the sample standard variation σ, and then mark a value x as an outlier if x is outside the k0 ..."
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Cited by 19 (11 self)
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In many application areas, it is important to detect outliers. The traditional engineering approach to outlier detection is that we start with some “normal ” values x1,..., xn, compute the sample average E, the sample standard variation σ, and then mark a value x as an outlier if x is outside the k0sigma interval [E − k0 · σ,E + k0 · σ] (for some preselected parameter k0). In real life, we often have only interval ranges [xi, xi] for the normal values x1,..., xn. In this case, we only have intervals of
Exact bounds on finite populations of interval data
 Reliable Computing
, 2001
"... In this paper, we start research into using intervals to bound the impact of bounded measurement errors on the computation of bounds on finite population parameters (“descriptive statistics”). Specifically, we provide a feasible (quadratic time) algorithm for computing the lower bound σ 2 on the fin ..."
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Cited by 15 (10 self)
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In this paper, we start research into using intervals to bound the impact of bounded measurement errors on the computation of bounds on finite population parameters (“descriptive statistics”). Specifically, we provide a feasible (quadratic time) algorithm for computing the lower bound σ 2 on the finite population variance function of interval data. We prove that the problem of computing the upper bound σ 2 is, in general, NPhard. We provide a feasible algorithm that computes σ 2 under reasonable easily verifiable conditions, and provide preliminary results on computing other functions of finite populations. 1
Fast Algorithms for Computing Statistics under Interval Uncertainty, with Applications to Computer Science and to Electrical and Computer Engineering
, 2007
"... Computing statistics is important. In many engineering applications, we are interested in computing statistics. For example, in environmental analysis, we observe a pollution level x(t) in a lake at different moments of time t, and we would like to estimate standard statistical characteristics such ..."
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Cited by 11 (6 self)
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Computing statistics is important. In many engineering applications, we are interested in computing statistics. For example, in environmental analysis, we observe a pollution level x(t) in a lake at different moments of time t, and we would like to estimate standard statistical characteristics such as mean, variance, autocorrelation, correlation with other measurements. For each of these characteristics C, there is an expression C(x1,..., xn) that enables us to provide an estimate for C based on the observed values x1,..., xn. For example: a reasonable statistic for estimating the mean value of a probability distribution is the population average E(x1,..., xn) = 1 n · (x1 +... + xn); a reasonable statistic for estimating the variance V is the population variance V (x1,..., xn) = 1 n · n∑
Exact Bounds on Sample Variance of Interval Data
, 2002
"... We provide a feasible (quadratic time) algorithm for computing the lower bound V on the sample variance of interval data. The problem of computing the upper bound V is, in general, NPhard. We provide a feasible algorithm that computes V for many reasonable situations. ..."
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Cited by 11 (9 self)
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We provide a feasible (quadratic time) algorithm for computing the lower bound V on the sample variance of interval data. The problem of computing the upper bound V is, in general, NPhard. We provide a feasible algorithm that computes V for many reasonable situations.
Outlier Detection Under Interval and Fuzzy Uncertainty: Algorithmic Solvability and
 Computational Complexity, Proceedings of the 22nd International Conference of the North American Fuzzy Information Processing Society NAFIPS’2003
"... In many application areas, it is important to detect outliers. Traditional engineering approach to outlier detection is that we start with some “normal ” values compute the sample average , the sample standard variation, and then mark a value as an outlier if is outside ..."
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Cited by 7 (6 self)
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In many application areas, it is important to detect outliers. Traditional engineering approach to outlier detection is that we start with some “normal ” values compute the sample average , the sample standard variation, and then mark a value as an outlier if is outside
OnLine Algorithms for Computing Mean and Variance of Interval Data, and Their Use in Intelligent Systems
 OF INTERVAL DATA, AND THEIR USE IN INTELLIGENT SYSTEMS, INFORMATION SCIENCES
, 2003
"... When we have only interval ranges [x i ; x i ] of sample values x1 ; : : : ; xn , what is the interval [V ; V ] of possible values for the variance V of these values? There are quadratic time algorithms for computing the exact lower bound V on the variance of interval data, and for computing V und ..."
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Cited by 6 (3 self)
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When we have only interval ranges [x i ; x i ] of sample values x1 ; : : : ; xn , what is the interval [V ; V ] of possible values for the variance V of these values? There are quadratic time algorithms for computing the exact lower bound V on the variance of interval data, and for computing V under reasonable easily verifiable conditions. The problem is that in real life, we often make additional measurements. In traditional statistics, if we have a new measurement result, we can modify the value of variance in constant time. In contrast, previously known algorithms for processing interval data required that, once a new data point is added, we start from the very beginning.
Realtime algorithms for statistical analysis of interval data
 Proceedings of the International Conference on Information Technology InTech’03, Chiang Mai
, 2003
"... When we have only interval ranges [x i, xi] of sample values x1,..., xn, what is the interval [V, V] of possible values for the variance V of these values? There are quadratic time algorithms for computing the exact lower bound V on the variance of interval data, and for computing V under reasonable ..."
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Cited by 6 (4 self)
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When we have only interval ranges [x i, xi] of sample values x1,..., xn, what is the interval [V, V] of possible values for the variance V of these values? There are quadratic time algorithms for computing the exact lower bound V on the variance of interval data, and for computing V under reasonable easily verifiable conditions. The problem is that in real life, we often make additional measurements. In traditional statistics, if we have a new measurement result, we can modify the value of variance in constant time. In contrast, previously known algorithms for processing interval data required that, once a new data point is added, we start from the very beginning. In this paper, we describe new algorithms for statistical processing of interval data, algorithms in which adding a data point requires only O(n) computational steps.
Estimating covariance for privacy case under interval (and fuzzy) uncertainty
 Proceedings of the 2011 World Conference on Soft Computing
, 2011
"... Abstract—One of the main objectives of collecting data in statistical databases (medical databases, census databases) is to find important correlations between different quantities. To enable researchers to looks for such correlations, we should allow them them to ask queries testing different combi ..."
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Cited by 4 (4 self)
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Abstract—One of the main objectives of collecting data in statistical databases (medical databases, census databases) is to find important correlations between different quantities. To enable researchers to looks for such correlations, we should allow them them to ask queries testing different combinations of such quantities. However, when we receive answers to many such questions, we may inadvertently disclose information about individual patients, information that should be private. One way to preserve privacy in statistical databases is to store ranges instead of the original values. For example, instead of an exact age of a patient in a medical database, we only store the information that this age is, e.g., between 60 and 70. This idea solves the privacy problem, but it make statistical analysis more complex. Different possible values from the corresponding ranges lead, in general, to different values of the corresponding