# Effect Of Alpha On Lasso Regression

Often we want conduct a process called regularization, wherein we penalize the number of features in a model in order to only keep the most important features. This can be particularly important when you have a dataset with 100,000+ features.

Lasso regression is a common modeling technique to do regularization. The math behind it is pretty interesting, but practically, what you need to know is that Lasso regression comes with a parameter, `alpha`

, and the higher the `alpha`

, the most feature coefficients are zero.

That is, when `alpha`

is `0`

, Lasso regression produces the same coefficients as a linear regression. When `alpha`

is very very large, all coefficients are zero.

In this tutorial, I run three lasso regressions, with varying levels of alpha, and show the resulting effect on the coefficients.

## Preliminaries

```
from sklearn.linear_model import Lasso
from sklearn.preprocessing import StandardScaler
from sklearn.datasets import load_boston
import pandas as pd
```

## Load Data

```
boston = load_boston()
scaler = StandardScaler()
X = scaler.fit_transform(boston["data"])
Y = boston["target"]
names = boston["feature_names"]
```

## Run Three Lasso Regressions, Varying Alpha Levels

```
/* Create a function called lasso */
def lasso(alphas):
'''
Takes in a list of alphas. Outputs a dataframe containing the coefficients of lasso regressions from each alpha.
'''
/* Create an empty data frame */
df = pd.DataFrame()
/* Create a column of feature names */
df['Feature Name'] = names
/* For each alpha value in the list of alpha values */
for alpha in alphas:
/* Create a lasso regression with that alpha value */
lasso = Lasso(alpha=alpha)
/* Fit the lasso regression */
lasso.fit(X, Y)
/* Create a column name for that alpha value */
column_name = 'Alpha = %f' % alpha
/* Create a column of coefficient values */
df[column_name] = lasso.coef_
/* Return the datafram */
return df
```

```
/* Run the function called, Lasso */
lasso([.0001, .5, 10])
```

Feature Name | Alpha = 0.000100 | Alpha = 0.500000 | Alpha = 10.000000 | |
---|---|---|---|---|

0 | CRIM | -0.920130 | -0.106977 | -0.0 |

1 | ZN | 1.080498 | 0.000000 | 0.0 |

2 | INDUS | 0.142027 | -0.000000 | -0.0 |

3 | CHAS | 0.682235 | 0.397399 | 0.0 |

4 | NOX | -2.059250 | -0.000000 | -0.0 |

5 | RM | 2.670814 | 2.973323 | 0.0 |

6 | AGE | 0.020680 | -0.000000 | -0.0 |

7 | DIS | -3.104070 | -0.169378 | 0.0 |

8 | RAD | 2.656950 | -0.000000 | -0.0 |

9 | TAX | -2.074110 | -0.000000 | -0.0 |

10 | PTRATIO | -2.061921 | -1.599574 | -0.0 |

11 | B | 0.856553 | 0.545715 | 0.0 |

12 | LSTAT | -3.748470 | -3.668884 | -0.0 |

Notice that as the alpha value increases, more features have a coefficient of 0.

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