| Classification is widely used in medicine,engineering,artificial intelligence and so on.Classification accuracy is an important index to measure the quality of classification methods.In some practical problems such as medical diagnosis,the cost of classification errors is quite high,even affecting the safety of human life.This paper introduces the conservative and exact classification methods based on confidence sets proposed by Liu et al.(2019).This classification method has "β-(1-α。)"property.The confidence sets constructed by any training data set(?)can guarantee with the probability of at least β that those confidence sets include the classes of future objects with the probability of at least 1-α.In this paper,the critical values of two kinds of confidence sets under some simple conditions are given,and the rule of the change of values is analyzed.The differ-ences between conservative and exact confidence sets in shape、recall、precision and Fβ are analyzed by practical example.The differences between the point estimation classifiers and the classification methods based on confidence sets in covering probabil-ity、complete risk and potential risk through simulation tests was studied.It is found that the classification methods based on confidence sets are“stable and high coverage probability、low complete risk、exist potential risk”,the point estimation classifiers are " unstable coverage probability、higher complete risk、no potential risk”.It is found that the exact confidence set is closer to 1-α than the conservative confidence set in the coverage probability,and the complete risk is closer to α.As far as potential risk is concerned,the exact confidence set can be reduced by 32%at most and 5%at least compared with the conservative confidence set.For the same conservative confidence set,critical constant of exact confidence sets with different assumptions is positively proportional to coverage probability and potential risk and inversely proportional to complete risk.When the proportion of(m1;m2:m3)and(ω1;ω2:ω3)approaches,the critical constant is more smaller and the confidence sets more"exact " than other conditions in the simulation of critical constant. |
