模式识别课后习题(英文)

1、Pattern Recognition Theory and Its ApplicationPROBLEMS2.5 (1) 对C类情况推广最小错误率贝叶斯决策规则； (2)指出此时使最小错误率最小等价于后验概率最大，即 对一切。2.5 (1) Generalize the minimum error Bayes decision rule in case of class C; (2) Show that the minimum error rate is equivalent to the maximum posterior probability, namely where and .2.

2、6 对两类问题，证明最小风险贝叶斯决策规则可表示为若 。2.6 In the two-category case, show that the minimum risk Bayes decision rule may be expressed as if .2.7 若，证明此时最小最大决策面是来自两类的错误率相等。2.7 Consider minimax criterion for and.Prove that in this case .2.22 似然比决策准则为若 则 付对数似然比为，当是均值向量为 和协方差矩阵为的正态分布时：（1） 试推导出，并指出其决策规则；推荐精选（2） 当时，推导

3、及其决策规则；（3） 分析（1），（2）两种情况下的决策面类型。2.22 Likelihood ratio decision rules can be expressed as if .minus-log-likelihood ratio can be expressed as ,where .(1) Deduce and find the decision rule;(2) Let .Find the decision rule;(3)Analyze the decision surface types in question(1) and question(2).2.23 二维正态分布，,

4、。试写出负对数似然比决策规则。2.23 Let ，,。Find the minus-log-likelihood ratio decision rule。2.24 在2.23中，若，写出负对数似然比规则。2.24 Let ， .Find the minus-log-likelihood ratio decision rule under the condition of exercise 5 习题2.24 的情况下，若考虑损失函数，画出似然比阈与错误率之间的关系。(1) 求出时完成Neyman-Pearson决策时总的错误率；推荐精选(2) 求出最小最大决策的阈值和总的错误率。2

5、.25 under the condition of exercise 3.3，let ，.(1) Consider the Neyman-Pearson criterion , what is the error rate for ;(2) Calculate the threshold of the minimax decision and overall error rate.3.1 Consider the sample set with the distribution density, , where the prior distribution of is . Respectiv

6、ely calculate the maximum likelihood estimate and the Bayesian estimation .3.2 Consider the sample set drawn from a multivariate normal population . Respectively calculate the maximum likelihood estimate of .3.3 Consider the sample set drawn from a binomial distribution , , , . Calculate the maximum

7、 likelihood estimate of the parameter.3.4 Suppose that the loss function is the quadratic function and the prior density of follows the uniform distribution , . Calculate the Bayesian estimation under the condition of exercise 4 Consider the sample set drawn from a multivariate normal distrib

8、ution where is known. Calculate the maximum likelihood estimate of .4.4 Consider a two-dimensional linear discriminant（判别） function 推荐精选Transform the discriminant function into the form of , and describe the geometric figure（几何图形） of ;Map the discriminant function to obtain the generalized(广义) homog

9、eneous（齐次） linear discriminant function .Show that the X-space is actually a subspace of the Y-space, and the partition of the X-space by is the same as the partition of the X-space by in the original space. Describe it by a figure. 8.1 Given three partitions as shown in the figure below.Calculate .

10、8.7 Given two sample sets 推荐精选 Calculate the transform to obtain the biggest expressed by.9.1 Given two sample sets Respectively reduce the feature space dimension to and , then describe the positions of the samples in the feature space.10.5 Let , , and , and consider the following three partitions:,Show that by t