哈尔滨工业大学深圳-模式识别-2017-考试重要知识点word

1(i | j) be the loss incurred for taking action i when the state of nature is j.action i assign the sample into any class-Conditional risk for i = 1,a cjjii xPxR1 )|()|(Select the action i for which R(i | x) is minimumR is minimum and R in this case is called the Bayes risk = best reasonable result that can be achieved!ij :loss incurred for deciding i when the true state of nature is jgi(x) = - R(i | x)max. discriminant corresponds to min. riskgi(x) = P(i | x)max. discrimination corresponds to max. posteriorgi(x) p(x | i) P(i) gi(x) = ln p(x | i) + ln P(i)问题由估计似然概率变为估计正态分布的参数问题极大似然估计和贝叶斯估计结果接近相同，但方法概念不同1Please present the basic ideas of the maximum likelihood estimation method and Bayesian estimation method. When do these two methods have similar results ?请描述最大似然估计方法和贝叶斯估计方法的基本概念。什么情况下两个方法有类似的结果？IMaximum-likelihood view the parameters as quantities whose values are fixed but unknown. The best estimate of their value is defined to be the one that maximizes the probability of obtaining the samples actually observed.IIBayesian methods view the parameters as random variables having some known prior distribution. Observation of the samples converts this to a posterior density, thereby revising our opinion about the true values of the parameters.IIIUnder the condition that the number of the training samples approaches to the infinity, the estimation of the mean obtained using Bayesian estimation method is almost identical to that obtained using the maximum likelihood estimation method.111最小风险决策通常有一个更低的分类准确度相比于最小错误率贝叶斯决策。然而，最小风险决策能够避免可能的高风险和损失。贝叶斯参数估计方法。Vectorize the samples.Calculation of the mean of all training samples.Calculation of the covariance matrixCalculation of eigenvectors and eigenvalue of the covariance matrix. Build the feature space.Feature extraction of all samples. Calculation the feature value of every sample.Calculation of the test sample feature value.Calculation of the samples of training samples like the above step.Find the nearest training sample as the result.1Exercises1. How to use the prior and likehood to calculate the posterior ? What is the formula ?怎么用先验概率和似然函数计算后验概率？公式是什么？P(j | x) = p(x | j) . P(j) / p(x), 1)(jP1)|(xj2. Whats the difference in the ideas of the minimum error Bayesian decision and minimum risk Bayesian decision? Whats the condition that makes the minimum error Bayesian decision identical to the minimum risk Bayesian decision?最小误差贝叶斯决策和最小风险贝叶斯决策的概念的差别是什么？什么情况下最小误差贝叶斯决策和最小风险贝叶斯决策是一致的（相同的）？答：在两类问题中，若有 ，即所谓对称损失函数的情况，则这时最小风1221险的贝叶斯决策和最小误差的贝叶斯决策方法显然是一致的。theminimumerrorB2(|()(jj jjxp1ayesiandecision: tominimizetheclassificati1onerroroftheBayesiandecision. themini1mumriskBayesiandecision: tominimizetheri1skoftheBayesiandecision. if R(1 | x) R(2 | x) action 1: “decide 1” is takenR(1 | x) = 11P(1 | x) + 12P(2 | x)R(2 | x) = 21P(1 | x) + 22P(2 | x) 3. A person takes a lab test of nuclear radiation and the result is positive. The test returns a correct positive result in 99% of the cases in which the nuclear radiation is actually present, and a correct negative result in 95% of the cases in which the nuclear ra