# Multinomial Logistic Regression

In multinomial logistic regression (MLR) the logistic function we saw in Recipe 15.1 is replaced with a softmax function:

$$P(y_i=k \mid X)={\frac {e^{\beta_{k}x_{i}}}{{\sum_{j=1}^{K}}e^{\beta_{j}x_{i}}}}$$

where $P(y_i=k \mid X)$ is the probability the $i$th observation’s target value, $y_i$, is class $k$, and $K$ is the total number of classes. One practical advantage of the MLR is that its predicted probabilities using the `predict_proba`

method are more reliable (i.e. better calibrated).

## Preliminaries

```
# Load libraries
from sklearn.linear_model import LogisticRegression
from sklearn import datasets
from sklearn.preprocessing import StandardScaler
```

## Load Iris Flower Data

```
# Load data
iris = datasets.load_iris()
X = iris.data
y = iris.target
```

## Standardize Features

```
# Standarize features
scaler = StandardScaler()
X_std = scaler.fit_transform(X)
```

## Create Multinomial Logistic Regression

```
# Create one-vs-rest logistic regression object
clf = LogisticRegression(random_state=0, multi_class='multinomial', solver='newton-cg')
```

## Train Multinomial Logistic Regression

```
# Train model
model = clf.fit(X_std, y)
```

## Create Previously Unseen Observation

```
# Create new observation
new_observation = [[.5, .5, .5, .5]]
```

## Predict Observation’s Class

```
# Predict class
model.predict(new_observation)
```

```
array([1])
```

## View Probability Observation Is Each Class

```
# View predicted probabilities
model.predict_proba(new_observation)
```

```
array([[ 0.01944996, 0.74469584, 0.2358542 ]])
```