Logistic Regression is a linear model for classificiation rather than regression. Also known as logit expression, maximum-entropy classfication (MaxEnt) or the log-linear classifier.

In `scikit-learn`

, the implementation of Logistic Regression can be accessed from class `LogisticRegression`

.

Binary class L2 penalized logistic regression minimizes the following cost function:

$min_{w,c} \frac{1}{2}w^T w + C \sum _{i=1}^{n}log(exp(-y_i(X_i^T w + c)) + 1)$

L1 regularized logistic regression solves the following optimization problem:

$min_{w,c} ||w||_1 + C \sum _{i=1}^{n}log(exp(-y_i(X_i^T w + c)) + 1)$

The solver implemented in the class `LogisticRegression`

are "liblinear", "newton-cg", "lbfgs", and "sag"

One way to choose solver:

```
Case Solver
Small dataset or L1 penalty "liblinear"
Multinomial loss "lbfgs" or "newton-cg"
Large dataset "sag"
```

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