Generate predictions that are orthogonal to another variable
$begingroup$
I have an X matrix, a y variable, and another variable ORTHO_VAR. I need to predict the y variable using X, however, the predictions from that model need to be orthogonal to ORTHO_VAR while being as correlated with y as possible.
I would prefer that the predictions are generated with a non-parametric method such as xgboost.XGBRegressor but I could use a linear method if absolutely necessary.
This code:
import numpy as np
import pandas as pd
from sklearn.datasets import make_regression
from xgboost import XGBRegressor
ORTHO_VAR = 'ortho_var'
IND_VARNM = 'indep_var'
TARGET = 'target'
CORRECTED_VARNM = 'indep_var_fixed'
# Create regression dataset with two correlated targets
X, y = make_regression(n_features=20, random_state=245, n_targets=2)
indep_vars = ['var{}'.format(i) for i in range(X.shape[1])]
# Pull into dataframe
df = pd.DataFrame(X, columns=indep_vars)
df[TARGET] = y[:, 0]
df[ORTHO_VAR] = y[:, 1]
# Fit a model to predict TARGET
xgb = XGBRegressor(n_estimators=10)
xgb.fit(df[indep_vars], df[TARGET])
df['yhat'] = xgb.predict(df[indep_vars])
# Correlation should be low or preferably zero
pred_corr_w_ortho = df.corr().abs()['yhat']['ortho_var']
assert pred_corr_w_ortho < 0.01, pred_corr_w_ortho
Returns this:
---------------------------------------------------------------------------
AssertionError
1 pred_corr_w_ortho = df.corr().abs()['yhat']['ortho_var']
----> 2 assert pred_corr_w_ortho < 0.05, pred_corr_w_ortho
AssertionError: 0.5895885756753665
...and I would like something that maintains as much predictive accuracy as possible while remaining orthogonal to ORTHO_VAR
correlation
asked 11 mins ago
ChrisChris
1627
$endgroup$
add a comment |
$begingroup$
I have an X matrix, a y variable, and another variable ORTHO_VAR. I need to predict the y variable using X, however, the predictions from that model need to be orthogonal to ORTHO_VAR while being as correlated with y as possible.
I would prefer that the predictions are generated with a non-parametric method such as xgboost.XGBRegressor but I could use a linear method if absolutely necessary.
This code:
import numpy as np
import pandas as pd
from sklearn.datasets import make_regression
from xgboost import XGBRegressor
ORTHO_VAR = 'ortho_var'
IND_VARNM = 'indep_var'
TARGET = 'target'
CORRECTED_VARNM = 'indep_var_fixed'
# Create regression dataset with two correlated targets
X, y = make_regression(n_features=20, random_state=245, n_targets=2)
indep_vars = ['var{}'.format(i) for i in range(X.shape[1])]
# Pull into dataframe
df = pd.DataFrame(X, columns=indep_vars)
df[TARGET] = y[:, 0]
df[ORTHO_VAR] = y[:, 1]
# Fit a model to predict TARGET
xgb = XGBRegressor(n_estimators=10)
xgb.fit(df[indep_vars], df[TARGET])
df['yhat'] = xgb.predict(df[indep_vars])
# Correlation should be low or preferably zero
pred_corr_w_ortho = df.corr().abs()['yhat']['ortho_var']
assert pred_corr_w_ortho < 0.01, pred_corr_w_ortho
Returns this:
---------------------------------------------------------------------------
AssertionError
1 pred_corr_w_ortho = df.corr().abs()['yhat']['ortho_var']
----> 2 assert pred_corr_w_ortho < 0.05, pred_corr_w_ortho
AssertionError: 0.5895885756753665
...and I would like something that maintains as much predictive accuracy as possible while remaining orthogonal to ORTHO_VAR
correlation
asked 11 mins ago
ChrisChris
1627
$endgroup$
add a comment |
$begingroup$
I have an X matrix, a y variable, and another variable ORTHO_VAR. I need to predict the y variable using X, however, the predictions from that model need to be orthogonal to ORTHO_VAR while being as correlated with y as possible.
I would prefer that the predictions are generated with a non-parametric method such as xgboost.XGBRegressor but I could use a linear method if absolutely necessary.
This code:
import numpy as np
import pandas as pd
from sklearn.datasets import make_regression
from xgboost import XGBRegressor
ORTHO_VAR = 'ortho_var'
IND_VARNM = 'indep_var'
TARGET = 'target'
CORRECTED_VARNM = 'indep_var_fixed'
# Create regression dataset with two correlated targets
X, y = make_regression(n_features=20, random_state=245, n_targets=2)
indep_vars = ['var{}'.format(i) for i in range(X.shape[1])]
# Pull into dataframe
df = pd.DataFrame(X, columns=indep_vars)
df[TARGET] = y[:, 0]
df[ORTHO_VAR] = y[:, 1]
# Fit a model to predict TARGET
xgb = XGBRegressor(n_estimators=10)
xgb.fit(df[indep_vars], df[TARGET])
df['yhat'] = xgb.predict(df[indep_vars])
# Correlation should be low or preferably zero
pred_corr_w_ortho = df.corr().abs()['yhat']['ortho_var']
assert pred_corr_w_ortho < 0.01, pred_corr_w_ortho
Returns this:
---------------------------------------------------------------------------
AssertionError
1 pred_corr_w_ortho = df.corr().abs()['yhat']['ortho_var']
----> 2 assert pred_corr_w_ortho < 0.05, pred_corr_w_ortho
AssertionError: 0.5895885756753665
...and I would like something that maintains as much predictive accuracy as possible while remaining orthogonal to ORTHO_VAR
correlation
asked 11 mins ago
ChrisChris
1627
$endgroup$
I have an X matrix, a y variable, and another variable ORTHO_VAR. I need to predict the y variable using X, however, the predictions from that model need to be orthogonal to ORTHO_VAR while being as correlated with y as possible.
I would prefer that the predictions are generated with a non-parametric method such as xgboost.XGBRegressor but I could use a linear method if absolutely necessary.
This code:
import numpy as np
import pandas as pd
from sklearn.datasets import make_regression
from xgboost import XGBRegressor
ORTHO_VAR = 'ortho_var'
IND_VARNM = 'indep_var'
TARGET = 'target'
CORRECTED_VARNM = 'indep_var_fixed'
# Create regression dataset with two correlated targets
X, y = make_regression(n_features=20, random_state=245, n_targets=2)
indep_vars = ['var{}'.format(i) for i in range(X.shape[1])]
# Pull into dataframe
df = pd.DataFrame(X, columns=indep_vars)
df[TARGET] = y[:, 0]
df[ORTHO_VAR] = y[:, 1]
# Fit a model to predict TARGET
xgb = XGBRegressor(n_estimators=10)
xgb.fit(df[indep_vars], df[TARGET])
df['yhat'] = xgb.predict(df[indep_vars])
# Correlation should be low or preferably zero
pred_corr_w_ortho = df.corr().abs()['yhat']['ortho_var']
assert pred_corr_w_ortho < 0.01, pred_corr_w_ortho
Returns this:
---------------------------------------------------------------------------
AssertionError
1 pred_corr_w_ortho = df.corr().abs()['yhat']['ortho_var']
----> 2 assert pred_corr_w_ortho < 0.05, pred_corr_w_ortho
AssertionError: 0.5895885756753665
...and I would like something that maintains as much predictive accuracy as possible while remaining orthogonal to ORTHO_VAR
correlation
correlation
asked 11 mins ago
ChrisChris
1627
asked 11 mins ago
ChrisChris
1627
asked 11 mins ago
ChrisChris
1627
asked 11 mins ago
ChrisChris
1627
asked 11 mins ago
ChrisChris
1627
1627
add a comment |
add a comment |
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