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againdoing that from first principleswe can take the correlation between two sets of attributescompute the standard deviation of eachthen compute the covariance between these two thingsand divide by the standard deviations of each dataset that gives us the correlation valuewhich is normalized to - to we end up with val...
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now we could force perfect correlation by fabricating totally linear relationshipso let' take look at an example of thatqvsdibtf"npvou qbhf qffet tdbuufs qbhf qffetqvsdibtf"npvou dpssfmbujpo qbhf qffetqvsdibtf"npvou and againhere we would expect the correlation to come out to - for perfect negative correlationand...
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correlation activity so get your hands dirtyroll up your sleevesi want you to use the ovnqzdpw function that' actually way to get numpy to compute covariance for you we saw how to compute correlation using the dpssdpfg function so go back and rerun these examples just using the ovnqzdpw function and see if you get th...
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the probability of given is equal to the probability of and occurring over the probability of alone occurringso this teases out the probability of being dependent on the probability of it'll make more sense with an example hereso bear with me let' say that give youmy readerstwo testsand of you pass both tests now the f...
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what ' going to do is write little bit of python code that creates some fake datagspnovnqzjnqpsusboepn sboepntffe upubmt \qvsdibtft \upubm vsdibtft gps@josbohf bhf%fdbef sboepndipjdf qvsdibtf spcbcjmjuz gmpbu bhf%fdbef upubmt jg sboepnsboepn qvsdibtf spcbcjmjuz upubm vsdib...
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our upubmt dictionary is telling us how many people are in each age bracketand it' pretty evenly distributedjust like we expected the amount purchased by each age group is in fact increasing by ageso -year-olds only bought about , things and -year-olds bought about , thingsand overall the entire population bought about...
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know the probability of being in your  is about we'll now find out ( )which just represents the overall probability of buying something irrespective of your age gmpbu upubm vsdibtft qsjou  vsdibtf  vsdibtf that works out to bein this exampleabout can just take the total number of things purchased by ...
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now because of the random distribution of datait doesn' work out to be exactly the same thing we're talking about probabilities hererememberbut they're in the same ballparkso that makes senseabout versus %close enough now that is different again from ( | )so the probability of both being in your  and buying something...
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upubmt jg sboepnsboepn qvsdibtf spcbcjmjuz upubm vsdibtft qvsdibtft modify it to actually not have dependency between purchases and age make that an evenly distributed chance as well see what that does to your results do you end up with very different conditional probability of being in your  and purchasing somethin...
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what 've done here is 've taken the original snippet of code for creating our dictionary of age groups and how much was purchased by each age group for set of , random people instead of making purchase probability dependent on agei've made it constant probability of now we just have people randomly being assigned to an...
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bayestheorem now that you understand conditional probabilityyou can understand how to apply bayestheoremwhich is based on conditional probability it' very important conceptespecially if you're going into the medical fieldbut it is broadly applicable tooand you'll see why in minute you'll hear about this lotbut not many...
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let' nail that example home little bit more againa drug test can be common example of applying bayestheorem to prove point even highly accurate drug test can produce more false positives than true positives so in our example herewe're going to come up with drug test that can accurately identify users of drug of the tim...
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even though ( |ais high ( %)it doesn' mean ( |bis high people overlook this all the timeso if there' one lesson to be learned from bayestheoremit is to always take these sorts of things with grain of salt apply bayestheorem to these actual problems and you'll often find that what sounds like high accuracy rate can actu...
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predictive models in this we're going to look at what predictive modeling is and how it uses statistics to predict outcomes from existing data we'll cover real world examples to understand the concepts better we'll see what regression analysis means and analyze some of its forms in detail we'll also look at an example ...
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solinear regression is fitting straight line to set of observations for examplelet' say that have bunch of people that measured and the two features that measured of these people are their weight and their heighti' showing the weight on the -axis and the height on the -axisand can plot all these data pointsas in the pe...
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the ordinary least squares technique how does linear regression workwell internallyit uses technique called ordinary least squaresit' also known asols you might see that term tossed around as well the way it works is it tries to minimize the squared error between each point and the linewhere the error is just the dista...
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the intercept can then be computed as the mean of the minus the slope times the mean of againeven though that' really not that difficultpython will do it all for youbut the point is that these aren' complicated things to run they can actually be done very efficiently remember that least squares minimize the sum of squa...
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the co-efficient of determination or -squared so how do know how good my regression ishow well does my line fit my datathat' where -squared comes inand -squared is also known as the coefficient of determination againsomeone trying to sound smart might call it thatbut usually it' called -squared it is the fraction of th...
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computing linear regression and -squared using python let' now play with linear regression and actually compute some linear regression and rsquared we can start by creating little bit of python code here that generates some random-ish data that is in fact linearly correlated in this example ' going to fake some data ab...
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you can see just by eyeballing it that there' definitely linear relationship going on thereand that' because we did hardcode real linear relationship in our source data now let' see if we can tease that out and find the best fit line using ordinary least squares we talked about how to do ordinary least squares and line...
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the following is the output to the preceding codethis little bit of code will create function to draw the best fit line alongside the data there' little bit more matplotlib magic going on here we're going to make gju-jof list and we're going to use the qsfejdu function we wrote to take the qbhf qffetwhich is our -axisa...
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you can see that our line is in fact great fit for our datait goes right smack down the middleand all you need to predict new values is this predict function given new previously unseen page speedwe could predict the amount spent just using the slope times the page speed plus the intercept that' all there is to itand t...
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polynomial regression we've talked about linear regression where we fit straight line to set of observations polynomial regression is our next topicand that' using higher order polynomials to fit your data sosometimes your data might not really be appropriate for straight line that' where polynomial regression comes in...
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if you have data that' kind of all over the place and has lot of varianceyou can go crazy and create line that just like goes up and down to try to fit that data as closely as it canbut in fact that doesn' represent the intrinsic relationship of that data it doesn' do good job of predicting new values so always start b...
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if we do scatter plotwe end up with the followingby the wayif you're wondering what the oqsboepntffe line doesit creates random seed valueand it means that when we do subsequent random operations they will be deterministic by doing this we can make sure thatevery time we run this bit of codewe end up with the same ex...
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let' go ahead and run that it runs pretty quicklyand we can then plot that sowe're going to create little graph here that plots our scatter plot of original points versus our predicted points jnqpsunbuqmpumjcqzqmpubtqmu yq oqmjotqbdf qmutdbuufs  qmuqmpu yqqyq  qmutipx the output looks like the following g...
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imagine have some curve that swoops way up and then back down again to fit outliers my prediction for something in between there isn' going to be accurate the curve really should be in the middle later in this book we'll talk about the main ways of detecting such overfittingbut for nowplease just observe it and know we...
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just keep hitting run to go through each step and you can see the it' effect as our third-degree polynomial is definitely not as good fit as the fourth-degree polynomial if you actually measure the -squared errorit would actually turn out worsequantitativelybut if go too highyou might start to see overfitting so just h...
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let' talk about multivariate regressionwhich is little bit more complicated the idea of multivariate regression is thiswhat if there' more than one factor that influences the thing you're trying to predictin our previous exampleswe looked at linear regression we talked about predicting people' heights based on their we...
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now we can still measure the quality of fit with multivariate regression using -squared it works the same wayalthough one thing you need to assume when you're doing multivariate regression is that the factors themselves are not dependent on each other and that' not always true so sometimes you need to keep that little ...
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the following is the output for the preceding codethe actual dataset is much larger this is just the first few samples sothis is real data of mileagemakemodeltrimtypedoorscruisesound and leather oknow we're going to use qboebt to split that up into the features that we care about we're going to create model that tries ...
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the next two lines of the code just create model that ' calling ftu that uses ordinary least squaresolsand fits that using the columns that give itjmfbhfpefm@pseand %ppst then can use the summary call to print out what my model looks likeyou can see here that the -squared is pretty low it' not that good of modelreallyb...
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now have said before that the coefficient is way of determining which items matterand that' only true though if your input data is normalized that isif everything' on the same scale of to if it' notthen these coefficients are kind of compensating for the scale of the data that it' seeing if you're not dealing with norm...
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we introduced pandas and the way to work with pandas and dataframe objects pandas very powerful tool we'll use it more in future sectionsbut make sure you're starting to take notice of these things because these are going to be important techniques in your python skills for managing large amounts of data and organizing...
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the challenge here is to identify the factors in each level that actually affect the thing you're trying to predict if ' trying to predict overall sat scoresfor examplei know that depends in part on the individual child that' taking the testbut what is it about the child that matterswellit might be the geneticsit might...
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there you have the concepts of multi-level models it' very advanced topicbut you need to understand what the concept isat leastand the concept itself is pretty simple you just are looking at the effects at different levelsdifferent hierarchies when you're trying to make prediction so maybe there are different layers of...
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machine learning with python in this we get into machine learning and how to actually implement machine learning models in python we'll examine what supervised and unsupervised learning meansand how they're different from each other we'll see techniques to prevent overfittingand then look at an interesting example wher...
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machine learning and train/test so what is machine learningwellif you look it up on wikipedia or whateverit'll say that it is algorithms that can learn from observational data and can make predictions based on it it sounds really fancyrightlike artificial intelligence stufflike you have throbbing brain inside of your c...
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now haven' told the machine learning algorithmahead of timewhat categories certain objects belong to don' have cheat sheet that it can learn from where have set of existing objects and my correct categorization of it the machine learning algorithm must infer those categories on its own this is an example of unsupervise...
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supervised learning now in contrastsupervised learning is case where we have set of answers that the model can learn from we give it set of training datathat the model learns from it can then infer relationships between the features and the categories that we wantand apply that to unseen new values and predict informat...
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there are some caveats to supervised learning need to make sure that both your training and test datasets are large enough to actually be representative of your data you also need to make sure that you're catching all the different categories and outliers that you care aboutin both training and testingto get good measu...
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-fold cross validation now there is way around this problemcalled -fold cross-validationand we'll look at an example of this later in the bookbut the basic concept is you train/test many times so you actually split your data not into just one training set and one test setbut into multiple randomly assigned segmentsk se...
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just like in our previous examplewe're going to set up little fake dataset of randomly generated page speeds and purchase amountsand ' going to create quirky little relationship between them that' exponential in nature nbuqmpumjcjomjof jnqpsuovnqzbtoq gspnqzmbcjnqpsu oqsboepntffe qbhf qffet oqsboepnopsnbm ...
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we'll use python' syntax here for splitting the list the first points are going to go to the training setand the last everything after is going to go to test set you may remember this from our python basics earlier onwhere we covered the syntax to do thisand we'll do the same thing for purchase amounts hereusbjo qbhf q...
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basically points that were selected at random from the original complete dataset have been plotted it has basically the same shapeso that' good thing it' representative of our data that' importantnow let' plot the remaining points that we reserved as test data tdbuufs uftu uftuherewe see our remaining for testing also...
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now we'll plot the polynomial this came up with against the training data we can scatter our original data for the training data setand then we can plot our predicted values against themjnqpsunbuqmpumjcqzqmpubtqmu yq oqmjotqbdf byft qmubyft byfttfu@ymjn byfttfu@zmjn qmutdbuufs  qmuqmpu yqqyq  qmutipx y...
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byfttfu@ymjn byfttfu@zmjn qmutdbuufs uftuyuftuz qmuqmpu yqqyq  qmutipx indeedif we plot our test data against that same functionwellit doesn' actually look that bad we got lucky and none of our test is actually out here to begin withbut you can see that it' reasonable fitbut far from perfect and in factif you a...
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the -squared value turns out to be which isn' too surprisingbecause we trained it on the training data the test data is sort of its unknownits testand it did fail the testquite frankly %that' an fso this has been an example where we've used train/test to evaluate supervised learning algorithmand like said beforepand...
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so just refresher on bayestheorem -rememberthe probability of given is equal to the overall probability of times the probability of given over the overall probability of bhow can we use that in machine learningi can actually build spam classifier for thatan algorithm that can analyze set of known spam -mails and known ...
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now it' called naive bayes for reason it' naive is because we're assuming that there' no relationships between the words themselves we're just looking at each word in isolationindividually within messageand basically combining all the probabilities of each word' contribution to it being spam or not we're not looking at...
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dmptf nfttbhf = kpjo mjoft zjfmeqbuinfttbhf efgebub'sbnf'spn%jsfdupsz qbuidmbttjgjdbujpo spxt joefy gpsgjmfobnfnfttbhfjosfbe'jmft qbui spxtbqqfoe nfttbhf nfttbhfdmbtt dmbttjgjdbujpojoefybqqfoe gjmfobnf sfuvso%bub'sbnf spxtjoefy joefy ebub %bub'sbnf nfttbhf dmbtt ebub ebubbqqfoe ebub'sbnf'spn%jsfdupsz tvoephd...
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if you are playing along heremake sure you modify the path passed to the ebub'sbnf'spn%jsfdupsz function to match wherever you installed the book materials in your systemand againif you're on mac or linuxplease pay attention to backslashes and forward slashes and all that stuff in this caseit doesn' matterbut you won' ...
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alrightnow for the fun partwe're going to use the vmujopnjbm/scikit-learn to actually perform naive bayes on the data that we have function from wfdupsj[fs $pvou fdupsj[fs dpvout wfdupsj[fsgju@usbotgpsn ebubwbmvft dmbttjgjfs vmujopnjbm/ubshfut ebubwbmvft dmbttjgjfsgju dpvoutubshfut this is what your output should ...
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let' go ahead and run that it runs pretty quicklyi' going to use couple of examples here let' try message body that just says 'sff pofzopxwhich is pretty clearly spamand more innocent message that just says ) #pcipxbcpvubhbnfpg hpmgupnpsspxso we're going to pass these in fybnqmft 'sff pofzopx) #pcipxbcpvubhbn...
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how cool is thatwe just wrote our own spam classifier just using few lines of code in python it' pretty easy using scikit-learn and python that' naive bayes in actionand you can actually go and classify some spam or ham messages now that you have that under your belt pretty cool stuff let' talk about clustering next -m...
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this is showing an example of -means clustering with of threeand the squares represent data points in scatter plot the circles represent the centroids that the -means clustering algorithm came up withand each point is assigned cluster based on which centroid it' closest to so that' all there is to itreally it' an examp...
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let' look at graphical example to make little bit more sense we'll call the first figure in the following image as asecond as bthird as and the fourth as the gray squares in image represent data points in our scatter plot the axes represent some different features of something maybe it' age and incomeit' an example kee...
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limitations to -means clustering so there are some limitations to -means clustering here they are choosing kfirst of allwe need to choose the right value of kand that' not straightforward thing to do at all the principal way of choosing is to just start low and keep increasing the value of depending on how many groups ...
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clustering people based on income and age let' see just how easy it is to do -means clustering using scikit-learn and python the first thing we're going to do is create some random data that we want to try to cluster just to make it easierwe'll actually build some clusters into our fake test data so let' pretend there'...
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what we're doing here is creating fake scatter plot that will show income versus age for people and clusters so for each random centroid that we createdi' then going to create normally distributed set of random data with standard deviation of , in income and standard deviation of in age that will give us back bunch of ...
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now the scale alluded to earlierthat' normalizing the data one important thing with kmeans is that it works best if your data is all normalized that means everything is at the same scale so problem that have here is that my ages range from to but my incomes range all the way up to , so these values are not really compa...
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it didn' take that long you see the results are basically what clusters assigned everything into we know that our fake data is already pre-clusteredso it seems that it identified the first and second clusters pretty easily it got little bit confused beyond that pointthoughbecause our clusters in the middle are actually...
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so entropyjust like it is in physics and thermodynamicsis measure of dataset' disorderof how same or different the dataset is so imagine we have dataset of different classificationsfor exampleanimals let' say have bunch of animals that have classified by species nowif all of the animals in my dataset are an iguanai hav...
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you add these up for each individual class for exampleif the proportion of the datathat isfor given class is then the contribution to the overall entropy is and if everything is that classthen again the contribution to the overall entropy is because in either caseif nothing is this class or everything is this classthat...
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the way it would work in this example would be as follows would have some sort of dataset of historical weatherand data about whether or not people went outside to play on particular day would feed the model this data of whether it was sunny or not on each daywhat the humidity wasand if it was windy or notand whether o...
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decision tree example let' say want to build system that will automatically filter out resumes based on the information in them big problem that technology companies have is that we get tons and tons of resumes for our positions we have to decide who we actually bring in for an interviewbecause it can be expensive to f...
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so it just turns out that in my totally fabricated dataanyone that did an internship in college actually ended up getting job offer so my first decision point is "did this person do an internship or not?if yesgo ahead and bring them in in my experienceinternships are actually pretty good predictor of how good person is...
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walking through decision tree so that' how you walk through the results of decision tree it' just like going through flowchartand it' kind of awesome that an algorithm can produce this for you the algorithm itself is actually very simple let me explain how the algorithm works at each step of the decision tree flowchart...
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now that technique of randomly resampling our data with the same model is term called bootstrap aggregatingor bagging this is form of what we call ensemble learningwhich we'll cover in more detail shortly but the basic idea is that we have multiple treesa forest of trees if you willeach that uses random subsample of th...
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you'll want to please immediately change that path used here for my own system ( tqbsl%bub djfodf btu)jsftdtwto wherever you have installed the materials for this book ' not sure where you put itbut it' almost certainly not there we will use qboebt to read our csv inand create dataframe object out of it let' go ahe...
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basicallywe're making dictionary in python that maps the letter to the number and the letter to the value sowe want to convert all our ys to and ns to so will mean yes and will mean no what we do is just take the hired column from the dataframeand call nbq on itusing dictionary this will go through the entire hired col...
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we get the following outputabove are the column names that contain our feature informationyears experienceemployed?previous employerslevel of educationtop-tier schooland interned these are the attributes of candidates that we want to predict hiring on nextwe construct our vector which is assigned what we're trying to p...
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hsbqi qzepuhsbqi@gspn@epu@ebub epu@ebubhfuwbmvf *nbhf hsbqidsfbuf@qoh so let' go ahead and run this this is what your output should now look likethere we have ithow cool is that?we have an actual flow chart here
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nowlet me show you how to read it at each stagewe have decision remember most of our data which is yes or nois going to be or sothe first decision point becomesis employedless than meaning that if we have an employment value of that is nowe're going to go left if employment is that is yeswe're going to go right sowere ...
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soyou can see we just keep going until we reach an entropy of if at all possiblefor every case ensemble learning using random forest nowlet' say we want to use random forestyou knowwe're worried that we might be over fitting our training data it' actually very easy to create random forest classifier of multiple decisio...
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soin this particular casewe ended up with hire decision on both butwhat' interesting is there is random component to that you don' actually get the same result every timemore often than notthe unemployed person does not get job offerand if you keep running this you'll see that' usually the case butthe random nature of ...
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basicallythe idea is that you have more than one modeland they might be the same kind of model or it might be different kinds of modelsbut you run them allon your set of training dataand they all vote on the final result for whatever it is you're trying to predict and oftentimesyou'll find that this ensemble of differe...
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stackingstacking has the same idea soyou run multiple models on the datacombine the results together somehow the subtle difference here between bucket of models and stackingis that you pick the model that wins soyou' run train/testyou find the model that works best for your dataand you use that model by contraststackin...
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it' always good idea to try ensemble learning out it' been proven time and time again that it will produce better results than any single modelso definitely consider itsupport vector machine overview finallywe're going to talk about support vector machines (svm)which is very advanced way of clustering or classifying hi...
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want to point out that svm is supervised learning technique sowe're actually going to train it on set of training dataand we can use that to make predictions for future unseen data or test data it' little bit different than -means clustering and that -means was completely unsupervisedwith support vector machineby contr...
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with different kernels you might get different results svc with linear kernel will produce something very much as you see in the preceding image you can use polynomial kernels or fancier kernels that might project down to curves in two dimensions as shown in the image you can do some pretty fancy classification this wa...
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oqbssbz oqbssbz sfuvso  please note that because we're using supervised learning herewe not only need the feature data againbut we also need the actual answers for our training dataset what the dsfbuf$mvtufsfe%bub function does hereis to create bunch of random data for people that are clustered around pointsbased on...
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now we can use linear svc (svc is form of svm)to actually partition that into clusters we're going to use svm with linear kerneland with value of  is just an error penalty term that you can adjustit' by default normallyyou won' want to mess with thatbut if you're doing some sort of convergence on the right model usin...
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it helps us visualize where different classifications come out basicallyit' creating mesh across the entire gridand it will plot different classifications from the svc models as different colors on that gridand then we're going to plot our original data on top of thatefgqmpu sfejdujpot dmg yyzz oqnftihsje oqbsbohf ...
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you can see here that it did its best given that it had to draw straight linesand polygonal shapesit did decent job of fitting to the data that we had soyou knowit did miss few but by and largethe results are pretty good svc is actually very powerful techniqueit' real strength is in higher dimensional feature data go a...
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this is little exercisenot just in playing with svm and different kinds of svcbut also in familiarizing yourself with how to learn more on your own about svc andhonestlya very important trait of any data scientist or engineer is going to be the ability to go and look up information yourself when you don' know the answe...
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recommender systems let' talk about my personal area of expertise--recommender systemsso systems that can recommend stuff to people based on what everybody else did we'll look at some examples of this and couple of ways to do it specificallytwo techniques called user-based and item-based collaborative filtering solet' ...
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what are recommender systemswelllike said amazon is great exampleand one ' very familiar with soif you go to their recommendations sectionas shown in the following imageyou can see that it will recommend things that you might be interested in purchasing based on your past behavior on the site the recommender system mig...
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another example is from netflixas shown in the following image (the following image is screenshot from netflix)they have various features that try to recommend new movies or other movies you haven' seen yetbased on the movies that you liked or watched in the past as welland they break that down by genre they have kind ...
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the whole point of it is to help you discover things you might not know about beforeso it' pretty cool you knowit gives individual moviesor booksor musicor whatevera chance to be discovered by people who might not have heard about them before soyou knownot only is it cool technologyit also kind of levels the playing fi...
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let' look at real exampleand it'll make little bit more senselet' say that this nice lady in the preceding image watched star wars and the empire strikes back and she loved them both sowe have user vectorof this ladygiving -star rating to star wars and the empire strikes back let' also say mr edgy mohawk man comes alon...
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limitations of user-based collaborative filtering nowunfortunatelyuser-based collaborative filtering has some limitations when we think about relationships and recommending things based on relationships between items and people and whatnotour mind tends to go on relationships between people sowe want to find people tha...
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there is research around how to detect and avoid these shilling attacks in user-based collaborative filteringbut an even better approach would be to use totally different approach entirely that' not so susceptible to gaming the system that' user-based collaborative filtering againit' simple concept-you look at similari...
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the other advantage is that there are generally fewer things that you're trying to recommend than there are people you're recommending to so again billion people in the worldyou're probably not offering billion things on your website to recommend to themso you can save lot of computational resources by evaluating relat...
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solet' presume have movie pairokaymaybe star wars and the empire strikes back find list of everyone who watched both of those moviesthen compare their ratings to each otherand if they're similar then can say these two movies are similarbecause they were rated similarly by people who watched both of them that' the gener...
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for examplelet' say that our nice young lady in the preceding image watched star wars and the empire strikes back and liked both of themso rated them both five stars or something nowalong comes mr edgy mohawk man who also watched star wars and the empire strikes back and also liked both of them soat this point we can s...
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well that' finewe computed relationship between the empire strikes back and star wars based on the behavior of these two peopleso we know that these two movies are similar to each other sogiven that mr hipster man liked the empire strikes backwe can say with good confidence that he would also like star warsand we can t...
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collaborative filtering using python alrightso let' do itwe have some python code that will use pandasand all the various other tools at our disposalto create movie recommendations with surprisingly little amount of code the first thing we're going to do is show you item-based collaborative filtering in practice sowe'l...
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okay solet' go ahead and compute the first half of item-based collaborative filteringwhich is finding similarities between items download and open the jnjmbs pwjftjqzoc file in this casewe're going to be looking at similarities between moviesbased on user behavior andwe're going to be using some real movie rating data...
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understanding the code the first thing we're going to do is import the ebub file as part of the movielens datasetand that is tab-delimited file that contains every rating in the dataset jnqpsuqboebtbtqe @dpmt sbujoht qesfbe@dtw tvoephdpotvmuqbdluebubtdjfodfnm  ebub tfq == obnft @dpmtvtfdpmt sbohf note th...