Choosing the best of the current crop

1981 ◽  
Vol 13 (3) ◽  
pp. 510-532 ◽  
Author(s):  
Gregory Campbell ◽  
Stephen M. Samuels

A best choice problem is presented which is intermediate between the constraints of the ‘no-information’ problem (observe only the sequence of relative ranks) and the demands of the ‘full-information’ problem (observations from a known continuous distribution). In the intermediate problem prior information is available in the form of a ‘training sample’ of size m and observations are the successive ranks of the n current items relative to their predecessors in both the current and training samples.Optimal stopping rules for this problem depend on m and n essentially only through m + n; and, as m/(m + n) → t, their success probabilities, P*(m, n), converge rapidly to explicitly derived limits p*(t) which are the optimal success probabilities in an infinite version of the problem. For fixed n, P*(m, n) increases with m from the ‘no-information’ optimal success probability to the ‘full-information’ value for sample size n. And as t increases from 0 to 1, p*(t) increases from the ‘no-information’ limit e–1 ≍ 0·37 to the ‘full-information’ limit ≍0·58. In particular p*(0·5) ≍ 0·50.

1981 ◽  
Vol 13 (03) ◽  
pp. 510-532 ◽  
Author(s):  
Gregory Campbell ◽  
Stephen M. Samuels

A best choice problem is presented which is intermediate between the constraints of the ‘no-information’ problem (observe only the sequence of relative ranks) and the demands of the ‘full-information’ problem (observations from a known continuous distribution). In the intermediate problem prior information is available in the form of a ‘training sample’ of size m and observations are the successive ranks of the n current items relative to their predecessors in both the current and training samples. Optimal stopping rules for this problem depend on m and n essentially only through m + n; and, as m/(m + n) → t, their success probabilities, P*(m, n), converge rapidly to explicitly derived limits p*(t) which are the optimal success probabilities in an infinite version of the problem. For fixed n, P*(m, n) increases with m from the ‘no-information’ optimal success probability to the ‘full-information’ value for sample size n. And as t increases from 0 to 1, p*(t) increases from the ‘no-information’ limit e –1 ≍ 0·37 to the ‘full-information’ limit ≍0·58. In particular p*(0·5) ≍ 0·50.


2004 ◽  
Vol 36 (2) ◽  
pp. 398-416 ◽  
Author(s):  
Stephen M. Samuels

The full-information best-choice problem, as posed by Gilbert and Mosteller in 1966, asks us to find a stopping rule which maximizes the probability of selecting the largest of a sequence of n i.i.d. standard uniform random variables. Porosiński, in 1987, replaced a fixed n by a random N, uniform on {1,2,…,n} and independent of the observations. A partial-information problem, imbedded in a 1980 paper of Petruccelli, keeps n fixed but allows us to observe only the sequence of ranges (max - min), as well as whether or not the current observation is largest so far. Recently, Porosiński compared the solutions to his and Petruccelli's problems and found that the two problems have identical optimal rules as well as risks that are asymptotically equal. His discovery prompts the question: why? This paper gives a good explanation of the equivalence of the optimal rules. But even under the lens of a planar Poisson process model, it leaves the equivalence of the asymptotic risks as somewhat of a mystery. Meanwhile, two other problems have been shown to have the same limiting risks: the full-information problem with the (suboptimal) Porosiński-Petruccelli stopping rule, and the full-information ‘duration of holding the best’ problem of Ferguson, Hardwick and Tamaki, which turns out to be nothing but the Porosiński problem in disguise.


1986 ◽  
Vol 23 (3) ◽  
pp. 718-735 ◽  
Author(s):  
Mitsushi Tamaki

n i.i.d. random variables with known continuous distribution are observed sequentially with the objective of selecting the largest. This paper considers the finite-memory case which, at each stage, allows a solicitation of anyone of the last m observations as well as of the present one. If the (k – t)th observation with value x is solicited at the k th stage, the probability of successful solicitation is p1(x) or p2(x) according to whether t = 0 or 1 ≦ t ≦ m. The optimal procedure is shown to be characterized by the double sequences of decision numbers. A simple algorithm for calculating the decision numbers and the probability of selecting the largest is obtained in a special case.


1996 ◽  
Vol 10 (1) ◽  
pp. 41-56 ◽  
Author(s):  
Mitsushi Tamaki ◽  
J. George Shanthikumar

This paper considers a variation of the classical full-information best-choice problem. The problem allows success to be obtained even when the best item is not selected, provided the item that is selected is within the allowance of the best item. Under certain regularity conditions on the allowance function, the general nature of the optimal strategy is given as well as an algorithm to determine it exactly. It is also examined how the success probability depends on the allowance function and the underlying distribution of the observed values of the items.


2004 ◽  
Vol 36 (02) ◽  
pp. 398-416 ◽  
Author(s):  
Stephen M. Samuels

The full-information best-choice problem, as posed by Gilbert and Mosteller in 1966, asks us to find a stopping rule which maximizes the probability of selecting the largest of a sequence of n i.i.d. standard uniform random variables. Porosiński, in 1987, replaced a fixed n by a random N, uniform on {1,2,…,n} and independent of the observations. A partial-information problem, imbedded in a 1980 paper of Petruccelli, keeps n fixed but allows us to observe only the sequence of ranges (max - min), as well as whether or not the current observation is largest so far. Recently, Porosiński compared the solutions to his and Petruccelli's problems and found that the two problems have identical optimal rules as well as risks that are asymptotically equal. His discovery prompts the question: why? This paper gives a good explanation of the equivalence of the optimal rules. But even under the lens of a planar Poisson process model, it leaves the equivalence of the asymptotic risks as somewhat of a mystery. Meanwhile, two other problems have been shown to have the same limiting risks: the full-information problem with the (suboptimal) Porosiński-Petruccelli stopping rule, and the full-information ‘duration of holding the best’ problem of Ferguson, Hardwick and Tamaki, which turns out to be nothing but the Porosiński problem in disguise.


1986 ◽  
Vol 23 (03) ◽  
pp. 718-735 ◽  
Author(s):  
Mitsushi Tamaki

n i.i.d. random variables with known continuous distribution are observed sequentially with the objective of selecting the largest. This paper considers the finite-memory case which, at each stage, allows a solicitation of anyone of the last m observations as well as of the present one. If the (k – t)th observation with value x is solicited at the k th stage, the probability of successful solicitation is p 1(x) or p 2(x) according to whether t = 0 or 1 ≦ t ≦ m. The optimal procedure is shown to be characterized by the double sequences of decision numbers. A simple algorithm for calculating the decision numbers and the probability of selecting the largest is obtained in a special case.


Author(s):  
P. Burai ◽  
T. Tomor ◽  
L. Bekő ◽  
B. Deák

In our study we classified grassland vegetation types of an alkali landscape (Eastern Hungary), using different image classification methods for hyperspectral data. Our aim was to test the applicability of hyperspectral data in this complex system using various image classification methods. To reach the highest classification accuracy, we compared the performance of traditional image classifiers, machine learning algorithm, feature extraction (MNF-transformation) and various sizes of training dataset. Hyperspectral images were acquired by an AISA EAGLE II hyperspectral sensor of 128 contiguous bands (400–1000 nm), a spectral sampling of 5 nm bandwidth and a ground pixel size of 1 m. We used twenty vegetation classes which were compiled based on the characteristic dominant species, canopy height, and total vegetation cover. Image classification was applied to the original and MNF (minimum noise fraction) transformed dataset using various training sample sizes between 10 and 30 pixels. In the case of the original bands, both SVM and RF classifiers provided high accuracy for almost all classes irrespectively of the number of the training pixels. We found that SVM and RF produced the best accuracy with the first nine MNF transformed bands. Our results suggest that in complex open landscapes, application of SVM can be a feasible solution, as this method provides higher accuracies compared to RF and MLC. SVM was not sensitive for the size of the training samples, which makes it an adequate tool for cases when the available number of training pixels are limited for some classes.


2021 ◽  
pp. 1-9
Author(s):  
Yibin Deng ◽  
Xiaogang Yang ◽  
Shidong Fan ◽  
Hao Jin ◽  
Tao Su ◽  
...  

Because of the long propulsion shafting of special ships, the number of bearings is large and the number of measured bearing reaction data is small, which makes the installation of shafting difficult. To apply a small amount of measured data to the process of ship installation so as to accurately calculate the displacement value in the actual installation, this article proposes a method to calculate the displacement value of shafting intermediate bearing based on different confidence-level training samples. Taking a ro-ro ship as the research object, this research simulates the actual installation process, gives a higher confidence level to a small amount of measured data, constructs a new training sample set for machine learning, and finally obtains the genetic algorithm-backpropagation(GABP) neural network reflecting the actual installation process. At the same time, this research compares the accuracy between different confidence-level training sample shafting neural network and the shafting neural network without measured data, and the results show that the accuracy of shafting neural network with different confidence-level training samples is higher. Although as the adjustment times and the number of measured data increase, the network accuracy is significantly improved. After adding four measured data, the maximum error is within 1%, which can play a guiding role in the ship propulsion shafting alignment. Introduction With the rapid development of science and technology in the world, special ships such as engineering ships, official ships, and warships play an important role (Carrasco et al. 2020; Prill et al. 2020). Some ships of this special type are limited by various factors such as the stern line of engine room, hull stability, and operation requirements. They usually adopt the layout of middle or front engine room, which causes the propulsion system to have a longer shaft and the number of intermediate shafts and intermediate bearings exceeds two. This forms a so-called multisupport shafting (Lee et al. 2019) and it increases the difficulty of shafting alignment because of the force-coupling between the bearings (Lai et al. 2018a, 2018b). The process of the existing methods for calculating the displacement value is complex, and because of the influence of installation error and other factors, it is necessary to adjust the bearing height several times to make the bearing reaction meet the specification requirements(Kim et al. 2017, Ko et al. 2017). So how to predict the accurate displacement value of each intermediate bearing is the key to solving the problem of multisupport shafting intermediate bearing installation and calibration (Zhou et al. 2005, Xiao-fei et al. 2017).


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