Develop Reference

Getting feature importances out of an Adaboosted linear regression

I have the following code:
modelClf = AdaBoostRegressor(base_estimator=LinearRegression(), learning_rate=2, n_estimators=427, random_state=42)
modelClf.fit(X_train, y_train)
While trying to interpret and improve the results, I wanted to see the feature importances, however I get an error saying that linear regressions don't really do that kind of thing.
Alright, sounds reasonable, so I tried using .coef_ since it should work for linear regressions, but it, in place, turned out incompatible with the adaboost regressor.
Is there any way to find the feature importances or is it impossible when adaboost it used on a linear regression?

Issue12137 suggests to add support for this using the coefs_, although a choice needs to be made how to normalize negative coefficients. There's also the question of when coefficients are really good representatives of importance (you should at least scale your data first). And then there's the question of when adaptive boosting helps a linear model in the first place.
One way to do this quickly is to modify the LinearRegression class:
class MyLinReg(LinearRegression):
#property
def feature_importances_(self):
return self.coef_ # assuming one output
modelClf = AdaBoostRegressor(base_estimator=MyLinReg(), ...)

Checked with below code, there is an attribute for feature importance:
import pandas as pd
import random
from sklearn.ensemble import AdaBoostRegressor
df = pd.DataFrame({'x1':random.choices(range(0, 100), k=10), 'x2':random.choices(range(0, 100), k=10)})
df['y'] = df['x2'] * .5
X = df[['x1','x2']].values
y = df['y'].values
regr = AdaBoostRegressor(random_state=0, n_estimators=100)
regr.fit(X, y)
regr.feature_importances_
Output: You can see feature 2 is more important as Y is nothing but half of it (as the data is created in such way).

Getting probability values for random forest and Gradient Boosting in python

I have been learning about classification techniques and studied about random forest, gradient boosting etc.Based on some help from codes available online,i tried to write code in python3 for random forest and GBM. My objective is to get the probability values from the model and not just look at accuracy as i intend to use the probability values to create KS later on.
I used the readily available titanic data set to start practicing.
Following are some of the steps i did :
/**load train data**/
train_df=pd.read_csv('***/classification/titanic/train.csv')
/**load test data**/
test_df =pd.read_csv('***/Desktop/classification/titanic/test.csv')
/**drop some variables in train data**/
train_df = train_df.drop(['Ticket', 'Cabin'], axis=1)
/**drop some variables in test data**/
test_df = test_df.drop(['Ticket', 'Cabin'], axis=1)
/** i calculated the title variable (again based on multiple threads in kaggle**/
train_df=pd.get_dummies(train_df,columns=['Pclass','Sex','Title'],drop_first=True)
test_df=pd.get_dummies(test_df,columns=['Pclass','Sex','Title'],drop_first=True)
/**i checked for missing and IV values next (not including that code here***/
predictors=[x for x in train.columns if x not in ['Survived','PassengerID']]
predictors
# create classifier object (GBM)
from sklearn.ensemble import GradientBoostingClassifier
clf = GradientBoostingClassifier(random_state=10)
# fit the classifier with x and y data
clf.fit(train[predictors],train.Survived)
prob=pd.DataFrame({'prob':clf.predict_proba(train[predictors])[:,1]})
prob['prob'].value_counts()
# create classifier object (RF)
from sklearn.ensemble import RandomForestClassifier
clf = RandomForestClassifier(random_state=10)
# fit the classifier with x and y data
clf.fit(train[predictors],train.Survived)
prob=pd.DataFrame({'prob':clf.predict_proba(train[predictors])[:,1]})
prob['prob'].value_counts()
Now when i check the probability values from the two different models, i noticed that for the Random forest output, a significant chunk had a 0 probability score whereas that was not the case for the GBM model.
I understand that the techniques are different, but how can the results be so far off ? Am i missing out on something ?
With a large chunk of the population getting tagged with '0' as probability score, my KS table goes for a toss.

Welcome to SO! Since you don't seem to be having an issue with code execution in specific, or totally incorrect outputs, this looks like it is more appropriate for CrossValidated, where you can find answers to questions of statistical concerns.
In fact, I'd suggest that answers to this question might give you some good insights into why you are seeing very different values from the predict_proba method. In short: while both GradientBoostingClassifier and RandomForestClassifier both use tree methods, what they do is very different, so direct comparison of the model parameters is not necessarily appropriate.

Limitations of Regression in Machine Learning?

I've been learning some of the core concepts of ML lately and writing code using the Sklearn library. After some basic practice, I tried my hand at the AirBnb NYC dataset from kaggle (which has around 40000 samples) - https://www.kaggle.com/dgomonov/new-york-city-airbnb-open-data#New_York_City_.png
I tried to make a model that could predict the price of a room/apt given the various features of the dataset. I realised that this was a regression problem and using this sklearn cheat-sheet, I started trying the various regression models.
I used the sklearn.linear_model.Ridge as my baseline and after doing some basic data cleaning, I got an abysmal R^2 score of 0.12 on my test set. Then I thought, maybe the linear model is too simplistic so I tried the 'kernel trick' method adapted for regression (sklearn.kernel_ridge.Kernel_Ridge) but they would take too much time to fit (>1hr)! To counter that, I used the sklearn.kernel_approximation.Nystroem function to approximate the kernel map, applied the transformation to the features prior to training and then used a simple linear regression model. However, even that took a lot of time to transform and fit if I increased the n_components parameter which I had to to get any meaningful increase in the accuracy.
So I am thinking now, what happens when you want to do regression on a huge dataset? The kernel trick is extremely computationally expensive while the linear regression models are too simplistic as real data is seldom linear. So are neural nets the only answer or is there some clever solution that I am missing?
P.S. I am just starting on Overflow so please let me know what I can do to make my question better!

This is a great question but as it often happens there is no simple answer to complex problems. Regression is not a simple as it is often presented. It involves a number of assumptions and is not limited to linear least squares models. It takes couple university courses to fully understand it. Below I'll write a quick (and far from complete) memo about regressions:
Nothing will replace proper analysis. This might involve expert interviews to understand limits of your dataset.
Your model (any model, not limited to regressions) is only as good as your features. If home price depends on local tax rate or school rating, even a perfect model would not perform well without these features.
Some features cannot be included in the model by design, so never expect a perfect score in real world. For example, it is practically impossible to account for access to grocery stores, eateries, clubs etc. Many of these features are also moving targets, as they tend to change over time. Even 0.12 R2 might be great if human experts perform worse.
Models have their assumptions. Linear regression expects that dependent variable (price) is linearly related to independent ones (e.g. property size). By exploring residuals you can observe some non-linearities and cover them with non-linear features. However, some patterns are hard to spot, while still addressable by other models, like non-parametric regressions and neural networks.
So, why people still use (linear) regression?
it is the simplest and fastest model. There are a lot of implications for real-time systems and statistical analysis, so it does matter
often it is used as a baseline model. Before trying a fancy neural network architecture, it would be helpful to know how much we improve comparing to a naive method.
sometimes regressions are used to test certain assumptions, e.g. linearity of effects and relations between variables
To summarize, regression is definitely not the ultimate tool in most cases, but this is usually the cheapest solution to try first
UPD, to illustrate the point about non-linearity.
After building a regression you calculate residuals, i.e. regression error predicted_value - true_value. Then, for each feature you make a scatter plot, where horizontal axis is feature value and vertical axis is the error value. Ideally, residuals have normal distribution and do not depend on the feature value. Basically, errors are more often small than large, and similar across the plot.
This is how it should look:
This is still normal - it only reflects the difference in density of your samples, but errors have the same distribution:
This is an example of nonlinearity (a periodic pattern, add sin(x+b) as a feature):
Another example of non-linearity (adding squared feature should help):
The above two examples can be described as different residuals mean depending on feature value. Other problems include but not limited to:
different variance depending on feature value
non-normal distribution of residuals (error is either +1 or -1, clusters, etc)
Some of the pictures above are taken from here:
http://www.contrib.andrew.cmu.edu/~achoulde/94842/homework/regression_diagnostics.html
This is an great read on regression diagnostics for beginners.

I'll take a stab at this one. Look at my notes/comments embedded in the code. Keep in mind, this is just a few ideas that I tested. There are all kinds of other things you can try (get more data, test different models, etc.)
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
#%matplotlib inline
import sklearn
from sklearn.linear_model import RidgeCV, LassoCV, Ridge, Lasso
from sklearn.datasets import load_boston
#boston = load_boston()
# Predicting Continuous Target Variables with Regression Analysis
df = pd.read_csv('C:\\your_path_here\\AB_NYC_2019.csv')
df
# get only 2 fields and convert non-numerics to numerics
df_new = df[['neighbourhood']]
df_new = pd.get_dummies(df_new)
# print(df_new.columns.values)
# df_new.shape
# df.shape
# let's use a feature selection technique so we can see which features (independent variables) have the highest statistical influence on the target (dependent variable).
from sklearn.ensemble import RandomForestClassifier
features = df_new.columns.values
clf = RandomForestClassifier()
clf.fit(df_new[features], df['price'])
# from the calculated importances, order them from most to least important
# and make a barplot so we can visualize what is/isn't important
importances = clf.feature_importances_
sorted_idx = np.argsort(importances)
# what kind of object is this
# type(sorted_idx)
padding = np.arange(len(features)) + 0.5
plt.barh(padding, importances[sorted_idx], align='center')
plt.yticks(padding, features[sorted_idx])
plt.xlabel("Relative Importance")
plt.title("Variable Importance")
plt.show()
X = df_new[features]
y = df['price']
reg = LassoCV()
reg.fit(X, y)
print("Best alpha using built-in LassoCV: %f" % reg.alpha_)
print("Best score using built-in LassoCV: %f" %reg.score(X,y))
coef = pd.Series(reg.coef_, index = X.columns)
print("Lasso picked " + str(sum(coef != 0)) + " variables and eliminated the other " + str(sum(coef == 0)) + " variables")
Result:
Best alpha using built-in LassoCV: 0.040582
Best score using built-in LassoCV: 0.103947
Lasso picked 78 variables and eliminated the other 146 variables
Next step...
imp_coef = coef.sort_values()
import matplotlib
matplotlib.rcParams['figure.figsize'] = (8.0, 10.0)
imp_coef.plot(kind = "barh")
plt.title("Feature importance using Lasso Model")
# get the top 25; plotting fewer features so we can actually read the chart
type(imp_coef)
imp_coef = imp_coef.tail(25)
matplotlib.rcParams['figure.figsize'] = (8.0, 10.0)
imp_coef.plot(kind = "barh")
plt.title("Feature importance using Lasso Model")
X = df_new
y = df['price']
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 10)
# Training the Model
# We will now train our model using the LinearRegression function from the sklearn library.
from sklearn.linear_model import LinearRegression
lm = LinearRegression()
lm.fit(X_train, y_train)
# Prediction
# We will now make prediction on the test data using the LinearRegression function and plot a scatterplot between the test data and the predicted value.
prediction = lm.predict(X_test)
plt.scatter(y_test, prediction)
from sklearn import metrics
from sklearn.metrics import r2_score
print('MAE', metrics.mean_absolute_error(y_test, prediction))
print('MSE', metrics.mean_squared_error(y_test, prediction))
print('RMSE', np.sqrt(metrics.mean_squared_error(y_test, prediction)))
print('R squared error', r2_score(y_test, prediction))
Result:
MAE 1004799260.0756996
MSE 9.87308783180938e+21
RMSE 99363412943.64531
R squared error -2.603867717517002e+17
This is horrible! Well, we know this doesn't work. Let's try something else. We still need to rowk with numeric data so let's try lng and lat coordinates.
X = df[['longitude','latitude']]
y = df['price']
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 10)
# Training the Model
# We will now train our model using the LinearRegression function from the sklearn library.
from sklearn.linear_model import LinearRegression
lm = LinearRegression()
lm.fit(X_train, y_train)
# Prediction
# We will now make prediction on the test data using the LinearRegression function and plot a scatterplot between the test data and the predicted value.
prediction = lm.predict(X_test)
plt.scatter(y_test, prediction)
df1 = pd.DataFrame({'Actual': y_test, 'Predicted':prediction})
df2 = df1.head(10)
df2
df2.plot(kind = 'bar')
from sklearn import metrics
from sklearn.metrics import r2_score
print('MAE', metrics.mean_absolute_error(y_test, prediction))
print('MSE', metrics.mean_squared_error(y_test, prediction))
print('RMSE', np.sqrt(metrics.mean_squared_error(y_test, prediction)))
print('R squared error', r2_score(y_test, prediction))
# better but not awesome
Result:
MAE 85.35438165291622
MSE 36552.6244271195
RMSE 191.18740655994972
R squared error 0.03598346983552425
Let's look at OLS:
import statsmodels.api as sm
model = sm.OLS(y, X).fit()
# run the model and interpret the predictions
predictions = model.predict(X)
# Print out the statistics
model.summary()
I would hypothesize the following:
One hot encoding is doing exactly what it is supposed to do, but it is not helping you get the results you want. Using lng/lat, is performing slightly better, but this too, is not helping you achieve the results you want. As you know, you must work with numeric data for a regression problem, but none of the features is helping you to predict price, at least not very well. Of course, I could have made a mistake somewhere. If I did make a mistake, please let me know!
Check out the links below for a good example of using various features to predict housing prices. Notice: all variables are numeric, and the results are pretty decent (just around 70%, give or take, but still much better than what we're seeing with the Air BNB data set).
https://bigdata-madesimple.com/how-to-run-linear-regression-in-python-scikit-learn/
https://towardsdatascience.com/linear-regression-on-boston-housing-dataset-f409b7e4a155

Why do I get different results when I do a manual split of test and train data as opposed to using the Python splitting function

If I run a simple dtree regression model using data via the train_test_split function, I get nice r2 scores, and low mse values.
training_data = pandas.read_csv('data.csv',usecols=['y','x1','x2','x3'])
y = training_data.iloc[:,0]
x = training_data.iloc[:,1:]
X_train, X_test, y_train, y_test = train_test_split(x, y, test_size=0.33)
regressor = DecisionTreeRegressor(random_state = 0)
# fit the regressor with X and Y data
regressor.fit(X_train, y_train)
y_pred = regressor.predict(X_test)
yet if I split the data file manually into two files 2/3 train and 1/3 test. there is a column called human which gives a value 1 to 9 which human it is, i use human 1-6 for training, and 7-9 for test
i get negative r2 scores, and high mse
training_data = pandas.read_csv("train"+".csv",usecols=['y','x1','x2','x3'])
testing_data = pandas.read_csv("test"+".csv", usecols=['y','x1','x2','x3'])
y_train = training_data.iloc[:,training_data.columns.str.contains('y')]
X_train = training_data.iloc[:,training_data.columns.str.contains('|'.join(['x1','x2','x3']))]
y_test = testing_data.iloc[:,testing_data.columns.str.contains('y')]
X_test = testing_data.iloc[:,testing_data.columns.str.contains('|'.join(l_vars))]
y_train = pandas.Series(y_train['y'], index=y_train.index)
y_test = pandas.Series(y_test['y'], index=y_test.index)
regressor = DecisionTreeRegressor(random_state = 0)
regressor.fit(X_train, y_train)
y_pred = regressor.predict(X_test)
I was expecting more or less the same results, and all the data types seem the same for both calls.
What am I missing?

I'm assuming that both methods here actually do what you intend doing and the shapes of your X_train/test and y_train/tests are the same coming from both methods. You can either plot the underlying distributions of your datasets or compare your second implementation against a cross-validated model (for better rigour).
Plot the distributions (i.e. make bar charts/density plots) of the labels (y) in the initial train - test sets vs in the second ones (from the manual implementation). You can dive deeper and also plot your other columns in the data, see if anything about the distributions of your data is different between the resulting sets of the two implementations. If the distributions are different than it makes sense you get discrepancies between your two models. If your discrepancy is huge, it could be your labels (or other columns) are actually sorted for your manual implementation, so then you get very different distributions in the datasets you're comparing.
Also, if you want to make sure that your manual splitting results is a 'representative' set(that would generalise well) based on model results instead of underlying data distributions, I would compare it against the results of a cross-validated model, not one single set of results.
Essentially, although the probability is small and the train_test_split does some shuffling, you could essentially get a 'train/test' pair that is performing well just out of luck. (To reduce the chance of that without doing cross validation, I'd suggest making use of the stratify argument of the train_test_split function. then at least you're sure the first implementation 'tries harder' to get balanced train/test pairs.)
If you decide to cross validate (with test_train_split), you get an average model prediction for the folds and a confidence intervals around it and can check if your second model results fall within that interval. If it doesn't again, it just means your split is actually 'corrupted' somehow (e.g. by having sorted values).
P.S. I'd also add that Decision Trees are models that are known to overfit massively [1]. Maybe use a random forest instead? (you should get more stable results due to bootstraping/bagging which would act similarly to cross-validating to reduce the chance of overfitting.)
1 - http://cv.znu.ac.ir/afsharchim/AI/lectures/Decision%20Trees%203.pdf

The train_test_split function from scikit-learn uses sklearn.model_selection.ShuffleSplit as per the documentation and this means, this method randomize your data when splitting.
When you split manually, you didn't randomize it so if your labels is not spreaded evenly throughout your dataset, you'll of course have performance issue since your model won't be generalized enough due to train data not containing enough sample of other labels.
If my suspicion is correct, you should get similar result by passing shuffle=False into train_test_split.

suppose your dataset contains this data.
1 + 1 = 2
2 + 2 = 4
4 - 4 = 0
2 - 2 = 0
So suppose you want a 50% train split. train_test_split shuffles it like this so it genaralizes better
1+1=2
2-2= 0
So it knows what do to when it sees this data
2+2
4-4#since it learned both addition and subtraction
But when you manually shuffle it like this
1 + 1 = 2
2 + 2 =4#only learned addition
It doesn't know what do do when it sees this data
2 - 2
4 - 4#test data is subtraction
Hope this answers you question

It may sound like a simple check but..
In the first example you are reading data from 'data.csv', in the second example you are reading from 'train.csv' and 'test.csv'. Since you say you split the file manually, I have a question about how that was done. If you simply cut the file at the 2/3's mark and saved as 'train.csv' and the remaining as 'test.csv' then you have unknowingly made an assumption about the uniformity of the data in the file. Data files can have an ordered structure which would skew the training or testing, which is why the train_test_split randomizes the rows. If you haven't already done it, try to randomize the rows first and then write to your train and test csv file to ensure you have a homogeneous dataset.
The other line that might be out of place is line 6:
X_test = testing_data.iloc[:,testing_data.columns.str.contains('|'.join(l_vars))]
Perhaps the l_vars contains something other than what you expect. Maybe it should read the following to be more consistent.
X_test = testing_data.iloc[:,testing_data.columns.str.contains('|'.join(['x1','x2','x3']))]
good luck, let us know if this helps.

SVM regression ruined by adding polynomial features

I'm trying to get the feel for SVM regression with a toy example. I generated random numbers between 1 and 100 as the predictors, then took their log and added gaussian noise to create the target variables. Popping this data into sklearn's SVR module produces a reasonable looking model:
However, when I augment the training data by throwing in the squares of the original predictor variables, everything goes haywire:
I understand that the RBF kernel does something analogous to taking powers of the original features, so throwing in the second feature is mostly redundant. However, is it really the case the SVMs are this bad at handling feature redundancy? Or am I doing something wrong?
Here is the code I used to generate these graphs:
from sklearn.svm import SVR
import numpy as np
import matplotlib.pyplot as plt
# change to highest_power=2 to get the bad model
def create_design_matrix(x_array, highest_power=1):
return np.array([[x**k for k in range(1, highest_power + 1)] for x in x_array])
N = 1000
x_array = np.random.uniform(1, 100, N)
y_array = np.log(x_array) + np.random.normal(0,0.2,N)
model = SVR(C=1.0, epsilon=0.1)
print model
X = create_design_matrix(x_array)
#print X
#print y_array
model = model.fit(X, y_array)
test_x = np.linspace(1.0, 100.0, num=10000)
test_y = model.predict(create_design_matrix(test_x))
plt.plot(x_array, y_array, 'ro')
plt.plot(test_x, test_y)
plt.show()
I'd appreciate any help with this mystery!

It looks like your model's picking up on outliers too heavily, which is a symptom of error from variance. This makes sense, because adding polynomial features increases the variance of a model. You should try tweaking the bias-variance tradeoff via cross validation by tweaking parameters. The parameters to modify would be C, epsilon, and gamma. The gamma parameter's incredibly important when using an RBF kernel, so I'd start there.
Manually fiddling with these parameters (which is not recommended - see below) gave me the following model:
The parameters used here were C=5, epsilon=0.1, gamma=2**-15.
Choosing these parameters is really a task for a proper model selection framework. I prefer simulated annealing + cross validation. The best scikit-learn currently has is random grid search + crossval. Shameless plug for a simulated annealing module I helped with: https://github.com/skylergrammer/SimulatedAnnealing
Note: Polynomial features are actually products of all combinations of size d (with replacement), not just the squares of features. In the second degree case, since you only have a single feature, these are equivalent. Scikit-learn has a class that'll calculate these though: sklearn.preprocessing.PolynomialFeatures