How to calculate pairwise Mutual Information for entire pandas dataset? - python

I have 50 variables in my dataframe. 46 are dependant variables and 4 are independandt variables (precipitation, temperature, dew, snow). I want to calculate the mutual information of my dependant variables agaisnt my independant.
So in the end i want a dataframe like this
Right now i am calculating it using the following but it's taking so long because i have to change my y each time
X = df[['Temperature', 'Precipitation','Dew','Snow']] # Features
y = df[['N0037']] #target
from sklearn.feature_selection import mutual_info_regression
mi = mutual_info_regression(X, y)
mi /= np.max(mi)
mi = pd.Series(mi)
mi.index = X.columns
mi.sort_values(ascending=False)
mi

Using list comprehension:
indep_vars = ['Temperature', 'Precipitation', 'Dew', 'Snow'] # set independent vars
dep_vars = df.columns.difference(indep_vars).tolist() # set dependent vars
from sklearn.feature_selection import mutual_info_regression as mi_reg
df_mi = pd.DataFrame([mi_reg(df[indep_vars], df[dep_var]) for dep_var in dep_vars], index = dep_vars, columns = indep_vars).apply(lambda x: x / x.max(), axis = 1)

Another way is to pass a custom method to pandas.DataFrame.corr() function
from sklearn.feature_selection import mutual_info_regression
def custom_mi_reg(a, b):
a = a.reshape(-1, 1)
b = b.reshape(-1, 1)
return mutual_info_regression(a, b)[0] # should return a float value
df_mi = df.corr(method=custom_mi_reg)

Related

LinearRegression TypeError

The above screenshot is refereed to as: sample.xlsx. I've been having trouble getting the beta for each stock using the LinearRegression() function.
Input:
import numpy as np
import pandas as pd
from sklearn.linear_model import LinearRegression
df = pd.read_excel('sample.xlsx')
mean = df['ChangePercent'].mean()
for index, row in df.iterrows():
symbol = row['stock']
perc = row['ChangePercent']
x = np.array(perc).reshape((-1, 1))
y = np.array(mean)
model = LinearRegression().fit(x, y)
print(model.coef_)
Output:
Line 16: model = LinearRegression().fit(x, y)
"Singleton array %r cannot be considered a valid collection." % x
TypeError: Singleton array array(3.34) cannot be considered a valid collection.
How can I make the collection valid so that I can get a beta value(model.coef_) for each stock?
X and y must have same shape, so you need to reshape both x and y to 1 row and 1 column. In this case it is resumed to the following:
np.array(mean).reshape(-1,1) or np.array(mean).reshape(1,1)
Given that you are training 5 classifiers, each one with just one value, is not surprising that the 5 models will "learn" that the coefficient of the linear regression is 0 and the intercept is 3.37 (y).
import numpy as np
import pandas as pd
from sklearn.linear_model import LinearRegression
df = pd.DataFrame({
"stock": ["ABCD", "XYZ", "JK", "OPQ", "GHI"],
"ChangePercent": [-1.7, 30, 3.7, -15.3, 0]
})
mean = df['ChangePercent'].mean()
for index, row in df.iterrows():
symbol = row['stock']
perc = row['ChangePercent']
x = np.array(perc).reshape(-1,1)
y = np.array(mean).reshape(-1,1)
model = LinearRegression().fit(x, y)
print(f"{model.intercept_} + {model.coef_}*{x} = {y}")
Which is correct from an algorithmic point of view, but it doesn't make any practical sense given that you're only providing one example to train each model.

Why does it work when columns are larger than rows in Python Sklearn (Linear Regression) [duplicate]

it's known that when the number of variables (p) is larger than the number of samples (n) the least square estimator is not defined.
In sklearn I receive this values:
In [30]: lm = LinearRegression().fit(xx,y_train)
In [31]: lm.coef_
Out[31]:
array([[ 0.20092363, -0.14378298, -0.33504391, ..., -0.40695124,
0.08619906, -0.08108713]])
In [32]: xx.shape
Out[32]: (1097, 3419)
Call [30] should return an error. How does sklearn work when p>n like in this case?
EDIT:
It seems that the matrix is filled with some values
if n > m:
# need to extend b matrix as it will be filled with
# a larger solution matrix
if len(b1.shape) == 2:
b2 = np.zeros((n, nrhs), dtype=gelss.dtype)
b2[:m,:] = b1
else:
b2 = np.zeros(n, dtype=gelss.dtype)
b2[:m] = b1
b1 = b2
When the linear system is underdetermined, then the sklearn.linear_model.LinearRegression finds the minimum L2 norm solution, i.e.
argmin_w l2_norm(w) subject to Xw = y
This is always well defined and obtainable by applying the pseudoinverse of X to y, i.e.
w = np.linalg.pinv(X).dot(y)
The specific implementation of scipy.linalg.lstsq, which is used by LinearRegression uses get_lapack_funcs(('gelss',), ... which is precisely a solver that finds the minimum norm solution via singular value decomposition (provided by LAPACK).
Check out this example
import numpy as np
rng = np.random.RandomState(42)
X = rng.randn(5, 10)
y = rng.randn(5)
from sklearn.linear_model import LinearRegression
lr = LinearRegression(fit_intercept=False)
coef1 = lr.fit(X, y).coef_
coef2 = np.linalg.pinv(X).dot(y)
print(coef1)
print(coef2)
And you will see that coef1 == coef2. (Note that fit_intercept=False is specified in the constructor of the sklearn estimator, because otherwise it would subtract the mean of each feature before fitting the model, yielding different coefficients)

how to isolate data that are 2 and 3 sigma deviated from mean and then mark them in a plot in python?

I am reading from a dataset which looks like the following when plotted in matplotlib and then taken the best fit curve using linear regression.
The sample of data looks like following:
# ID X Y px py pz M R
1.04826492772e-05 1.04828050287e-05 1.048233088e-05 0.000107002791008 0.000106552433081 0.000108704469007 387.02 4.81947797625e+13
1.87380963036e-05 1.87370588085e-05 1.87372620448e-05 0.000121616280029 0.000151924707761 0.00012371156585 428.77 6.54636174067e+13
3.95579877816e-05 3.95603773653e-05 3.95610756809e-05 0.000163470663023 0.000265203868883 0.000228031803626 470.74 8.66961875758e+13
My code looks the following:
# Regression Function
def regress(x, y):
#Return a tuple of predicted y values and parameters for linear regression.
p = sp.stats.linregress(x, y)
b1, b0, r, p_val, stderr = p
y_pred = sp.polyval([b1, b0], x)
return y_pred, p
# plotting z
xz, yz = M, Y_z # data, non-transformed
y_pred, _ = regress(xz, np.log(yz)) # change here # transformed input
plt.semilogy(xz, yz, marker='o',color ='b', markersize=4,linestyle='None', label="l.o.s within R500")
plt.semilogy(xz, np.exp(y_pred), "b", label = 'best fit') # transformed output
However I can see a lot upward scatter in the data and the best fit curve is affected by those. So first I want to isolate the data points which are 2 and 3 sigma away from my mean data, and mark them with circle around them.
Then take the best fit curve considering only the points which fall within 1 sigma of my mean data
Is there a good function in python which can do that for me?
Also in addition to that may I also isolate the data from my actual dataset, like if the third row in the sample input represents 2 sigma deviation may I have that row as an output too to save later and investigate more?
Your help is most appreciated.
Here's some code that goes through the data in a given number of windows, calculates statistics in said windows, and separates data in well- and misbehaved lists.
Hope this helps.
from scipy import stats
from scipy import polyval
import numpy as np
import matplotlib.pyplot as plt
num_data = 10000
fake_data_x = np.sort(12.8+np.random.random(num_data))
fake_data_y = np.exp(fake_data_x) + np.random.normal(0,scale=50000,size=num_data)
# Regression Function
def regress(x, y):
#Return a tuple of predicted y values and parameters for linear regression.
p = stats.linregress(x, y)
b1, b0, r, p_val, stderr = p
y_pred = polyval([b1, b0], x)
return y_pred, p
# plotting z
xz, yz = fake_data_x, fake_data_y # data, non-transformed
y_pred, _ = regress(xz, np.log(yz)) # change here # transformed input
plt.figure()
plt.semilogy(xz, yz, marker='o',color ='b', markersize=4,linestyle='None', label="l.o.s within R500")
plt.semilogy(xz, np.exp(y_pred), "b", label = 'best fit') # transformed output
plt.show()
num_bin_intervals = 10 # approx number of averaging windows
window_boundaries = np.linspace(min(fake_data_x),max(fake_data_x),int(len(fake_data_x)/num_bin_intervals)) # window boundaries
y_good = [] # list to collect the "well-behaved" y-axis data
x_good = [] # list to collect the "well-behaved" x-axis data
y_outlier = []
x_outlier = []
for i in range(len(window_boundaries)-1):
# create a boolean mask to select the data within the averaging window
window_indices = (fake_data_x<=window_boundaries[i+1]) & (fake_data_x>window_boundaries[i])
# separate the pieces of data in the window
fake_data_x_slice = fake_data_x[window_indices]
fake_data_y_slice = fake_data_y[window_indices]
# calculate the mean y_value in the window
y_mean = np.mean(fake_data_y_slice)
y_std = np.std(fake_data_y_slice)
# choose and select the outliers
y_outliers = fake_data_y_slice[np.abs(fake_data_y_slice-y_mean)>=2*y_std]
x_outliers = fake_data_x_slice[np.abs(fake_data_y_slice-y_mean)>=2*y_std]
# choose and select the good ones
y_goodies = fake_data_y_slice[np.abs(fake_data_y_slice-y_mean)<2*y_std]
x_goodies = fake_data_x_slice[np.abs(fake_data_y_slice-y_mean)<2*y_std]
# extend the lists with all the good and the bad
y_good.extend(list(y_goodies))
y_outlier.extend(list(y_outliers))
x_good.extend(list(x_goodies))
x_outlier.extend(list(x_outliers))
plt.figure()
plt.semilogy(x_good,y_good,'o')
plt.semilogy(x_outlier,y_outlier,'r*')
plt.show()

How to remove outliers correctly and define predictors for linear model?

I am learning how to build a simple linear model to find a flat price based on its squared meters and the number of rooms. I have a .csv data set with several features and of course 'Price' is one of them, but it contains several suspicious values like '1' or '4000'. I want to remove these values based on mean and standard deviation, so I use the following function to remove outliers:
import numpy as np
import pandas as pd
def reject_outliers(data):
u = np.mean(data)
s = np.std(data)
data_filtered = [e for e in data if (u - 2 * s < e < u + 2 * s)]
return data_filtered
Then I construct function to build linear regression:
def linear_regression(data):
data_filtered = reject_outliers(data['Price'])
print(len(data)) # based on the lenght I see that several outliers have been removed
Next step is to define the data/predictors. I set my features:
features = data[['SqrMeters', 'Rooms']]
target = data_filtered
X = features
Y = target
And here is my question. How can I get the same set of observations for my X and Y? Now I have inconsistent numbers of samples (5000 for my X and 4995 for my Y after removing outliers). Thank you for any help in this topic.
The features and labels should have the same length
and you should pass the whole data object to reject_outliers:
def reject_outliers(data):
u = np.mean(data["Price"])
s = np.std(data["Price"])
data_filtered = data[(data["Price"]>(u-2*s)) & (data["Price"]<(u+2*s))]
return data_filtered
You can use it in this way:
data_filtered=reject_outliers(data)
features = data_filtered[['SqrMeters', 'Rooms']]
target = data_filtered['Price']
X=features
y=target
Following works for Pandas DataFrames (data):
def reject_outliers(data):
u = np.mean(data.Price)
s = np.std(data.Price)
data_filtered = data[(data.Price > u-2*s) & (data.Price < u+2*s)]
return data_filtered

Using multiple independent variables in Python lmfit

I am trying to fit a model to some data. The independent variables are called A and B, and they are columns in a Pandas DataFrame. I am trying to fit with two parameters against y in the data frame.
Previously, with curve_fit from Scipy, I could do:
def fun(X, p1, p2):
A, B = X
return np.exp(p1*A) + p2*B
X = (df['A'].tolist(), df['B'].tolist())
popt, pcov = curve_fit(fun, X, df['y'].tolist())
But now, I'm using lmfit, where I cannot simply "pack" the independent variables like with curve_fit:
def fun(A, B, p1 = 1, p2 = 1):
return np.exp(p1*A) + p2*B
model = Model(fun, independent_vars=['A', 'B'])
How do I run model.fit() here? The FAQ is not really helpful—what do I have to flatten in the first place?
I created a complete, working example with two independent variables:
import pandas as pd
import numpy as np
from lmfit import Model
df = pd.DataFrame({
'A' : pd.Series([1, 1, 1, 2, 2, 2, 2]),
'B' : pd.Series([5, 4, 6, 6, 5, 6, 5]),
'target' : pd.Series([87.79, 40.89, 215.30, 238.65, 111.15, 238.65, 111.15])
})
def fun(A, B, p1 = 1, p2 = 1):
return p1 * np.exp(A) + p2 * np.exp(B)
model = Model(fun, independent_vars=['A', 'B'])
fit = model.fit(df['target'], A = df['A'], B = df['B'])
The trick is to specify all variables as keyword arguments in fit().
Firstly, creat a model with this function of multiple independent variables.
for example,
def random_func(x,y,a,b,c):
return a*x**3+b*y**2+c
Secondly, specify which ones are the independent variables in the formula.
for example,
from lmfit import Model
model = Model(random_func,independent_vars=['x','y'])
Thirdly, set params for the model
for example,
model.set_param_hint('a',value=2)
model.set_param_hint('b',value=3)
model.set_param_hint('c',value=4)
finally, set your x-axis values, as well as y-axis. And do the fit
Like this,
x = np.arange(0,2,0.1)
y = np.arange(0,2,0.1)
z = np.loadtxt('filename')
A direct fit actually does not work well. The 2D data array has to be flattened into 1D array, as well as the coordinates. For example, let's leave the model as it is. We need to create new 1D coordinates arrays.
x1d = []
y1d = []
for i in x:
for j in y:
x1d = x1d.append(i)
y1d = y1d.append(j)
z1d = z.flatten_data()
result = model.fit(z1d, x = x1d, y = y1d)

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