In a three-class classification problem, if the data model predicts the probability for a sample to belong to three classes respectively as (g;, g2. g3). Consider the following two ways to assess the model performance: 1. First make a decision from the predicted probabilities, e.g. when the prediction is g, =0.1, q2=0.5, g3 =0.4, then we call the model has predicted the class to be "2". Then we compare the class-prediction with the ground-truth, the cost is 0/1 for being correct and wrong. 2. First assume the model WAS right about the probabilities of the classes. Then compute the probability of observing the actual data in this a hypothetical world. E.g. for some sample, According some model h*, the probabilities of the three classes are q1=0.1, g2=0.5, g3 =04, While the actually observed class of that sample is 2. Then the probability of observing the class-2 according to h4 is g2=0.5. The value 0.5 is the likelihood of h* (Notice the value in this perspective is about the models, not the samples). The higher the likelihood is, the better the model prediction fits to the practical observation. The likelihood is slightly post-processed to suit the convention that when the model agrees with the data, we want the cost to be O, and when the model disagrees with the data, we want the cost to be high. The cost is defined as log(Likelihood). Note we take the negative of the log likelihood, so when the likelihood of the correct label is high (desired), the cost will be low, and vice versa. If your model has 100% confidence on the correct class, then the corresponding likelihood is 1.0 and the costis - log 1 = 0. This question is about the two types of costs of the following cases, chose the values for: Model Outputs: g1 =0.33, g2=0.33, g3 =0.34, True Class: 2 Cost-1 (#.Errors)is ___(1) __, Cost-2 (Negative-Log-Likelihood)is __ (2) Model Outputs: g1 =0.33, g2=0.34, q3=0.33, True Class: 2 Cost-1is ___(3) ,Cost-2is__ (4} . Remark-1: Facts: log 0.34 =~ 1.08 and log 0.33 =~ 1.11 Remark-2: Answers can be approximate to a precision of 0.01. \f