mocchi but it's not so complicated stack quest hello I'm Josh stormer and welcome to stack quest today we're gonna cover adaboost and it's gonna be clearly explained note this stack quest shows how to combine adaboost with decision trees because that is the most common way to use adaboost so if you're not familiar with decision trees check out the quest we will also mention random forests so if you don't know about them check out the quest we'll start by using decision trees and random forests to explain the three concepts behind adaboost then we'll get into the nitty-gritty details of how adaboost creates a forest of trees from scratch and how it's used to make classifications so let's start by using decision trees and random forests to explain the three main concepts behind adaboost in a random forest each time you make a tree you make a full-sized tree some trees might be bigger than others but there's no predetermined maximum depth in contrast in a forest of trees made with adaboost the trees are usually just a node and two leaves oh no it's the dreaded terminology alert a tree with just one node and two leaves is called a stump so this is really a forest of stumps rather than trees stumps are not great at making accurate classifications for example if we were using this data to determine if someone had heart disease or not then a full-size decision tree would take advantage of all four variables that we measured chest pain blood circulation blocked arteries and weight to make a decision but a stump can only use one variable to make a decision thus stumps are technically weak learners however that's the way adaboost likes it and it's one of the reasons why they are so commonly combined now back to the random forest in a random forest each tree has an equal vote on the final classification this trees vote is worth just as much as this trees vote or this trees vote in contrast in a forest of stumps made with adaboost some stumps get more say in the final classification than others in this illustration the larger stumps get more say in the final classification than the smaller stumps lastly in a random forest each decision tree is made independently of the others in other words it doesn't matter if this tree was made first or this one in contrast in a forest of stumps made with adaboost order is important the errors that the first stump makes influence how the second stump is made and the air is that the second stone makes influence how the third stump is made etc etc etc to review the three ideas behind adaboost our one adaboost combines a lot of week learners to make classifications the week learners are almost always stumps to some stumps get more say in the classification than others three each stump is made by taking the previous stumps mistakes into account BAM into the nitty-gritty detail of how to create a forest of stumps using adaboost first we'll start with some data we create a forest of stumps with adaboost to predict if a patient has heart disease we will make these predictions based on a patient's chest pain and blocked artery status and their weight the first thing we do is give each sample a weight that indicates how important it is to be correctly classified note the sample weight is different from the patient weight and I'll do the best I can to be clear about which of the two I'm talking about at the start all samples get the same weight one divided by the total number of samples in this case that's 1/8 and that makes the samples all equally important however after we make the first stump these weights will change in order to guide how the next stump is created in other words we'll talk more about the sample weights later now we need to make the first stump in the forest this is done by finding the variable chest pain blocked arteries or patient weight that does the best job classifying the samples note because all of the weights are the same we can ignore them right now we start by seeing how well chest pain classifies the samples of the five samples with chest pain three were correctly classified as having heart disease and two were incorrectly classified of the three samples without chest pain two were correctly classified as not having heart disease and one was incorrectly classified now we do the same thing for blocked arteries and for patient wait note we used the techniques described in the decision tree stat quest to determine that 176 was the best weight to separate the patients now we calculate the Gini index for the three stumps the Gini index for patient weight is the lowest so this will be the first stump in the forest now we need to determine how much say this stump will have in the final classification remember some stumps get more say in the final classification than others we determine how much say a stump has in the final classification based on how well it classified the samples this stump made one error patient who weighs less than 176 has heart disease but the stump says they do not the total error for a stump is the sum of the weights associated with the incorrectly classified samples thus in this case the total error is 1/8 note because all of the sample weights add up to one total air will always be between zero for a perfect stump and one for a horrible stump we use the total error to determine the amount of say this stump has in the final classification with the following formula amount of say equals 1/2 times the log of 1 minus the total error divided by the total error we can draw a graph of the amount of say by plugging in a bunch of numbers between 0 & 1 for total error the blue line tells us the amount of safe for total error values between 0 & 1 when a stump does a good job and the total error is small then the amount of say is a relatively large positive value when a stump is no better at classification than flipping a coin ie half the stumps are correctly classified and half are incorrectly classified and the total error equals 0. 5 then the amount of say will be zero and when a stump does a terrible job and the total error is close to one in other words if the stump consistently gives you the opposite classification then the amount of say will be a large negative value so if a stump votes for heart disease the negative amount of say will turn that vote into not heart disease note if total error is 1 or 0 then this equation will freak out in practice a small error term is added to prevent this from happening with patient weight greater than 176 the total error is 1/8 so we just plug and chug booty today voodoo to pooh-poohed and the amount of say that this stump has in the final classification is zero point nine seven BAM now that we've worked out how much say this stump gets when classifying a sample let's work out how much say the chest pain stump would have if it had been the best stump note we don't need to do this but I think it helps illustrate the concepts we've covered so far chest pain made three errors and the total error equals the sum of the weights for the incorrectly classified samples be do do booty so the total error for chest pain is 3/8 we can get a sense of what the amount of say will be by looking at the graph when total error equals 3/8 so we are expecting the amount of say to be between 0 and 0. 5 now we plug 3/8 into the formula for the amount of say and do the math do t do pooty to do D pooh-coo pooh-coo and the amount of say that the chest pain stump would have had on the final classification is 0.
42 I'll leave the blocked artery stump as an exercise for the viewer now we know how the sample weights for the incorrectly classified samples are used to determine the amount of say each stump gets BAM now we need to learn how to modify the weights so that the next stump will take the errors that the current stump made into account let's go back to the first stump that we made when we created this stump all of the sample weights were the same and that meant we did not emphasize the importance of correctly classifying any particular sample but since this stumped incorrectly classified this sample we will emphasize the need for the next stump to correctly classify it by increasing its sample weight and decreasing all of the other sample weights let's start by increasing the sample wait for the incorrectly classified sample this is the formula we will use to increase the sample weight for the sample that was incorrectly classified we plug in the sample weight from the last stump and we scale one eighth with this term to get a better understanding of how this part will scale the previous sample wait let's draw a graph the blue line is equal to e raised to the amount of say when the amount of say is relatively large ie the last stump did a good job classifying samples then we will scale the previous sample weight with a large number this means that the new sample weight will be much larger than the old one and when the amount of say is relatively low ie the last stump did not do a very good job classifying samples then the previous sample weight is scaled by a relatively small number this means that the new sample weight will only be a little larger than the old one in this example the amount of say was zero point nine seven and E raised to the zero point nine seven equals two point six four that means the new sample weight is zero point three three which is more than the old one BAM now we need to decrease the sample weights for all of the correctly classified samples this is the formula we will use to decrease the sample weights the big difference is the negative sign in front of amount of say just like before we plug in the sample wait and just like before we can get a better understanding of how this will scale the sample weight by plotting a graph using different values for amount of say the blue line represents e raised to the negative amount of say when the amount of se is relatively large then we scale the sample weight by a value close to zero this will make the new sample weight very small if the amount of say for the last stump is relatively small then we will scale the sample weight by a value close to 1 this means that the new sample weight will be just a little smaller than the old one in this example the amount of say was 0. 97 and e raised to the negative zero point nine seven equals zero point three eight the new sample weight is zero point zero five which is less than the old one BAM we will keep track of the new sample weights in this column we plug in zero point three three for the sample that was incorrectly classified all of the other samples gets zero point zero five now we need to normalize the new sample weights so that they will add up to one right now if you add up the new sample weights you get zero point six eight so we divide each new sample weight by 0. 68 to get the normalized values now when we add up the new sample weights we get 1 plus or minus a little rounding error now we just transfer the normalized sample weights to the sample weights column since those are what we will use for the next stomp now we can use the modified sample weights to make the second stump in the forest BAM in theory we could use the sample weights to calculate weighted genie indexes to determine which variable should split the next stump the weighted genie index would put more emphasis on correctly classifying this sample the one that was miss classified by the last stump since this sample has the largest sample weight alternatively instead of using a weighted Gini index we can make a new collection of samples that contains duplicate copies of the samples with the largest sample weights so we start by making a new but empty data set that is the same size as the original then we pick a random number between 0 and 1 and we see where that number falls when you use the sample weights like a distribution if the number is between 0 and 0.
7 then we would put this sample into the new collection of samples and if the number is between 0. 7 and 0. 14 then we would put this sample into the new collection of samples and if the number is between 0.
14 and 0. 2 1 then we would put this sample into the new collection of samples and if the number is between zero point two one and zero point seven zero then we would put this sample into the new collection of samples etc etc for example imagine the first number I picked was 0. 72 then I would put this sample into my new collection of samples then I pick another random number and get 0.
42 and I would put this sample into my new collection of samples then I pick 0. 83 and I would put this sample into my new collection of samples then I pick 0.
