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Total = 10 Heads = 8 Tails = 2 Odds of head = 8/2 Odds of tails = 2/8 prob of head = 8/10 prob of tails = 2/10

Odds of head 8/2 = = prob of head/1- prob of head = (8/10)/(2/10) = 8/2 Odds of Tail 2/8 = = prob of tail/1- prob of tail = (2/10)/(8/10) = 2/8

p value : https://www.youtube.com/watch?v=5Z9OIYA8He8 : see StatQuest: P Values, clearly explained

p valus is sum of all probablities of similar probablity or rarer probablity. example lets say probablity of 5 times Head HHHHH = 1/32 then p valis for 5H = 5H + 5T + rarere than 5h which is 0 so p value is = 1/32 + /32 = 1/16.

many people misunderstand confidence intervals but that's only because they didn't learn about bootstrapping first.

bootstrap refresher imagine we wait a bunch of female mice in this case we weighed 12 of them we didn't weigh every single female Mouse on the planet just 12 now we can take these 12 measurements and we can use them to calculate the sample mean now the sample mean is not the mean for all mice the entire planet it's just the mean of the mice that we sampled however we can use bootstrapping and the data that we have here to determine what values would be reasonable for the global worldwide mean of all female mice on the planet now that we've calculated the sample mean we can bootstrap the sample to bootstrap the sample we randomly select 12 weights from the original sample and duplicates are okay here's an example of a bootstrap sample we can see that this measurement on the far left. was sampled twice in our bootstrap sample and the measurement to its right wasn't included in our bootstrap sample this is called sampling with replacement now we calculate the mean of the random sample after we've calculated the mean of our first random sample all we have to do is repeat steps 1 and 2 until we've calculated a lot of means sometimes more than 10,000 . that's all there is to bootstrapping now.

let's talk about confidence intervals usually when you see a confidence interval out in the wild it's called a 95% confidence interval a 95% confidence interval is just an interval that covers 95% of the means

https://www.youtube.com/watch?v=LsK-xG1cLYA

So let's start by using decision trees and random forests to explain the three main concepts behind adaboost.

1. Tree size RF : Trees has no size limit 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. ADAboost: The trees are usually just a node and two leaves. 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 technically weak learners however that's the way adaboost likes it.

2. Equal votes RF: random forest in a random forest each tree has an equal vote on the final classification. Adaboost: Some stumps get more say in the final classification than others in this illustration the larger stumps get more say in the final.

3. RF 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

Adaboost :stumps made with adaboost order is important. the errors that the first stump makes influence how the second stump is made and the error is that the second stone makes influence how the third stump is made etc etc etc.

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. Predictors : chest_pain, artery_status and weight 1] give each sample a weight that indicates how important it is to be correctly classified. 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.

2] calculate gini index of all features. 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 calculate the Gini index for the three stumps. the Gini index for patient weight is the lowest so this will be the first stump.

3] 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. The total error for a stump is the sum of the weights associated with the incorrectly classified samples. in this case the total error is 1/8 note because all of the sample weights add up to one. total error 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) = 1/2 * log( (1 - total_error)/ total error).

we can draw a graph of the amount of say by plugging in a bunch of numbers 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 than flipping a coin ie 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.

4] After 1st tree/stun calculate new sample weights for each data point

sample with wrong class = (e^(Amount of say))/N sample with correct class = (e^-(Amount of say))/N

**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.

to review the three ideas behind adaboost our one adaboost combines a lot 
of weak learners to make classifications the weak learners are almost always 
stumps to some stumps get more say in the classification than others and three 
each stump is made by taking the previous stumps mistakes into account if we 
have a way to Gini function then we use it with the sample weights otherwise 
we use the sample weights to make a new dataset that reflects those weights