1. Naïve Bayes Consider the following dataset: Shape Circle Color Label Blue 1 Circle Blue Green Circle Diamond Blue Green Green Diamond Diamond Diamond Red 1 Square Square Square Blue 1 Red 1 Red 1 (a) What are the parameters of the Naïve Bayes model estimated using maximum likelihood estima- tion? (b) What is a testing example (Shape, Color) for which the maximum likelihood Naïve Bayes model provides an undefined posterior label probability (i.e., 0/0)? (c) What are the parameters of the Naïve Bayes model using Laplacian smoothing with a pseudo- count of 1? (d) What is the posterior label probability for your example from part (b) under the Laplacian- smoothed Naiïve Bayes model?

1. Naïve Bayes Consider the following dataset: Shape Circle Color Label Blue 1 Circle Blue Green Circle Diamond Blue Green Green Diamond Diamond Diamond Red 1 Square Square Square Blue 1 Red 1 Red 1 (a) What are the parameters of the Naïve Bayes model estimated using maximum likelihood estima- tion? (b) What is a testing example (Shape, Color) for which the maximum likelihood Naïve Bayes model provides an undefined posterior label probability (i.e., 0/0)? (c) What are the parameters of the Naïve Bayes model using Laplacian smoothing with a pseudo- count of 1? (d) What is the posterior label probability for your example from part (b) under the Laplacian- smoothed Naiïve Bayes model?

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

See similar textbooks

Similar questions

Question: Using Naive Bayes classification method (m-estimate of probability), classify the testing data and calculate Accuracy, Precision, and Recall from confusion matrix. Training Dataset Target Attribute Age Income Student Credit Buys computer high high high P1 40 medium fair yes no P5 fair >40 low yes yes P6 >40 low yes excellent no P7 31..40 low yes excellent yes P8 40 medium yes fair yes 40 medium excellent no no Testing Data: Age 40 low no fair no R6 >40 high yes excellent yes Subject: Machine Learning 2 2 2 重

For a HMM, the hidden states are {bull, bear}, the observation variables are {rise, fall}, the initial state probability distribution is [0.5 0.5]¹, the transition probability distribution A is [0.4 0.7; 0.6 0.3], and the observation probability distribution B is [0.8 0.1;0.2 0.9]. If the observation sequence is {fall fall rise}, please show the computation procedure for estimating the most likely state sequence?
2. Take a bivariate normal distribution with two random variables X and Y, with mean value = (1, -1), var(X) = 3, var(Y) = 6, and cor(X,Y) = -0.5. %3! (a) create a contour plot for this data (b) plot 1,000 simulations of this distribution (c) Using 1,000,000 simulations, find (1) the expected value of Y (ii) the expected value of Y, given that X> 2 (ii) the expected value of Y, given that X = 2
give the steps by steps answer
dont reject the questions give the steps by steps
Consider the graph of a Bayesian Network shown below showing 7 binary random variables. Age Gender Exposure to Toxics Serum Calcium Cancer Smoking Lung tumor How many probabilities will be needed to complete the conditional probability table of variable "Cancer"? How many probabilities will be needed to complete the conditional probability table of variable "Lung tumor"? How many probabilities will be needed in total to complete all the conditional probability tables of this BN? How many probabilities will be needed to complete the joint probability table of all variables? Give the answers for each question as a number (e.g., 4)
Explain how we perform maximum likelihood
2. Can you design a binary classification experiment with 100 total population (TP+TN+FP+ FN), with precision (TP/(TP+FP)) of 1/2, with sensitivity (TP/(TP+FN)) of 2/3, and specificity (TN/(FP+TN)) of 3/5? (Please consider the population to consist of 100 individuals.)
Question 1: Suppose that a Naive Bayesian classifier is created using a given training data set. Then, predictions are made on several testing points using this classifier. The predicted positive class probabilities and the actual class labels for these testing points are shown as follows. Please draw the ROC curve for the above prediction. Please clearly denote your splitting values and show the TP, FP, TN, FN, TPR, FPR values at each splitting value. Sample ID Actual Class Label Predicted Positive Class Probability 1 - 0.1 2 + 0.3 3 - 0.4 4 + 0.4 5 + 0.6 6 + 0.8