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4141Generative Threshold from Equal-Variance Gaussians 1A discriminative model was trained at class prior P(Y=1)=0.5 and outputs posterior probability 0.7 for a case x. Overnight the base rate shifts to P(Y=1)=0.2, while the class-conditional evidence for x is assumed unchanged. What posterior probability should you use after this pure prior shift?机器学习中等数值题未尝试面试订阅4146Naive Bayes Posterior 1A generative regime model assigns posterior probability P(trend|x)=0.7 to the trend regime. If the next-day expected payoff is 12 bps in trend and -4 bps in mean reversion, what conditional expected payoff E[r|x] does the model imply?机器学习中等数值题未尝试面试订阅4148Naive Bayes Posterior 3A generative regime model assigns posterior probability P(trend|x)=0.6 to the trend regime. If the next-day expected payoff is 0.015 return units in trend and -0.01 return units in mean reversion, what conditional expected payoff E[r|x] does the model imply?机器学习中等数值题未尝试面试订阅4149Naive Bayes Posterior 4A generative regime model assigns posterior probability P(trend|x)=0.4 to the trend regime. If the next-day expected payoff is 3 return units in trend and 1 return units in mean reversion, what conditional expected payoff E[r|x] does the model imply?机器学习中等数值题未尝试面试订阅4150Naive Bayes Posterior 5A generative regime model assigns posterior probability P(trend|x)=0.8 to the trend regime. If the next-day expected payoff is -2 bps in trend and 5 bps in mean reversion, what conditional expected payoff E[r|x] does the model imply?机器学习中等数值题未尝试面试订阅4151Generative Classification with a Missing Feature 1A two-feature naive Bayes model was trained generatively, but at prediction time X2 is missing. Prior P(Y=1)=0.5, P(X1=1|Y=1)=0.8, P(X1=1|Y=0)=0.3, P(X2=1|Y=1)=0.75, P(X2=1|Y=0)=0.4. You only observe X1=1. What posterior P(Y=1|X1) should the generative model use?机器学习中等数值题未尝试面试订阅4156Small Labeled Sample with Plausible StructureFor an observation x, a generative model summarizes the evidence as likelihood ratio p(x|Y=1)/p(x|Y=0) = 5. If the prior probability of class 1 is 0.2, what posterior probability P(Y=1|x) follows, and what 0.5-threshold decision does that imply?机器学习中等derivation未尝试面试订阅4157Lots of Labels but Misspecified Density StoryFor an observation x, a generative model summarizes the evidence as likelihood ratio p(x|Y=1)/p(x|Y=0) = 0.5. If the prior probability of class 1 is 0.4, what posterior probability P(Y=1|x) follows, and what 0.5-threshold decision does that imply?机器学习中等derivation未尝试面试订阅4161Why Naive Bayes Can Work Despite Wrong IndependenceYou have only a few hundred labeled observations, but domain knowledge gives a plausible class-conditional structure and you also have many unlabeled feature vectors. Would you start with a generative or a discriminative model first?机器学习中等essay未尝试面试订阅4162Why Discriminative Models Often Win AsymptoticallyA classifier was trained last quarter, and now only the class prevalence has shifted while the conditional shape of features given class appears stable. Which side, generative or discriminative, is easier to adjust quickly?机器学习中等essay未尝试面试订阅4163Why Generative Models Handle Missingness More NaturallyYou have millions of labeled examples and care only about predictive accuracy on the deployed label, not about simulating x. Which side usually deserves the first try?机器学习中等essay未尝试面试订阅4164Why Generative and Discriminative Can Share a BoundaryA production system frequently has one sensor missing at test time, but your model family can factor the joint feature likelihood cleanly. Which side gets a practical advantage?机器学习中等essay未尝试面试订阅4165A Fast Sanity Check for Gen-vs-Disc QuestionsThe research desk wants not only labels but also synthetic feature draws conditional on each class for stress testing. Which side is the more natural starting point?机器学习中等essay未尝试面试订阅5891Who Owns the Class PriorTwo teams ship classifiers trained on a balanced 50/50 dataset, but the live population is 90% class 0. Team A used Gaussian discriminant analysis; Team B used logistic regression. Which model explicitly contains an estimate of the class prior P(y), and explain why that distinction makes one team's fix to the prevalence mismatch cleaner than the other's.机器学习中等essay未尝试面试订阅5892Posterior from a Generative Gaussian ModelA generative classifier models one feature as Gaussian within each class with equal variance: x|Y=0 ~ N(0,1), x|Y=1 ~ N(2,1), and class prior P(Y=1)=0.5. Using Bayes' rule to convert this generative description into the discriminative posterior, compute P(Y=1|x=1.5).机器学习中等数值题未尝试面试订阅