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[Music] hello everyone and welcome to today's episode of 5-minute machine learning today we plot individual conditional expectation in python if you like the content please subscribe and hit the bell icon this episode is based on the partial dependence plot episode so if you haven't checked out that i highly recommend you check it out link in the description below like pdp to use ice you have to have a trained model take the same example from pdp to plot the relation between feature 1 and the target variable for observation 3 keep feature 1 unchanged change all the other observations to observation three use the trained model to score each new observation three do this to each and every observation you get the ice plot we bring in the module here there are the same module from the pdp episode the only difference this time is that we need this paste box module if you still recall the california housing data set we're going to use the same data set for consistency notice here the y is d mean meaning the ice plot will also be centralized around zero a quick refresh of the independent variables we have medium income house age etc and the target variable is the house price now we've seen this last time again we see long tails meaning outliers for certain variables and again we see two clusters for los angeles and san francisco for housing again we train a model first a gradient boosting regressor first now we've seen this last time this is for plotting the pdp notice here that the relationship between medium income and the housing price is positive we're going to do the ice plot on this relationship later now this is new for ice plot we use this ice function from the module and then we just bring in the data and then specify the column to be medium income predict we're going to say it's going to be the predict from the fed it model which we call est and then the number of grid points we say it's 10. and then let's look at it each column is a observation so for example if we look at here this is a 10 year old house it has some average rooms average bedrooms etc but for the medium income which is the variable of interest we have 10 values for each value of the medium income we have the target variable for example if we have medium income as 2 then the target variable will be negative 1.25 if we have medium income for 2.5 then we have the target variable be at negative 1.08 and so on and so forth so in fact for each column we will be able to plot a line for each observation now the second column is the next observation where we do the same thing to our medium income the number of bins can be specified so before we specify the number of bins to be 10 then we have we're going to have 10 different bins here you can specify any number you like now the fitted data set has 10 rules and more than 18 000 columns meaning we have more than 18 000 observations and then for each observations we are plotting 10 values to have the ice plot we need the ice plot function in which we call the ice data frame which we fit earlier and then the line width is going to be very thin color is going to be very colorful and alpha is going to be 0.1 meaning it's almost transparent because we have so many lines and there we go that's the ice plot of medium income on housing price as we can see here as medium income increases the housing price also increases notice here each single line represents a observation let's look at the data side-by-side along with the eyes plot here we're just using map lib plotting both the data set and the ice plot first thing the data is capped secondly there are many outliers in the medium income which stretches the right part of the ice plot so that we observe many long lines in the right portion of the ice plot now let's look at the ice plot of medium income on housing price here the thick black line is simply the pdp plot which is the average of the ice plot like pdp the individual conditional expectation or ice is also a model agnostic tool to explain various types of machine learning models it's basically a pdp on each single observation it does not depend on the model type unlike pdp which can only be used for global explainability between model inputs and model outputs the eyes can be used for local explainability since it depicts for each observation i hope you enjoyed today's episode and as always have a nice day you