7 2 3 loss function and cost function for logistic regression

Download 1M+ code from https://codegive.com/e4acdce understanding loss functions in logistic regression in logistic regression, we are interested in predicting the probability that a given input belongs to a certain class (e.g., class 0 or class 1). the most common loss function used for logistic regression is the **logistic loss function**, also known as the **binary cross-entropy loss**. this loss function quantifies the difference between the predicted probabilities and the actual class labels. key concepts 1. **logistic function (sigmoid function)**: the logistic function maps any real-valued number into a value between 0 and 1. this is crucial for classification tasks. the formula for the logistic function is: \[ \sigma(z) = \frac{1}{1 + e^{-z}} \] here, \(z\) is the linear combination of input features and weights. 2. **loss function**: in logistic regression, the loss function quantifies how well the model's predictions match the actual outcomes. the binary cross-entropy loss is defined as: \[ l(y, \hat{y}) = -y \log(\hat{y}) - (1 - y) \log(1 - \hat{y}) \] where: \(y\) is the actual label (0 or 1). \(\hat{y}\) is the predicted probability of the instance being class 1. 3. **cost function**: the cost function is the average of the loss function over all training examples: \[ j(\theta) = -\frac{1}{m} \sum_{i=1}^m \left[ y^{(i)} \log(\hat{y}^{(i)}) + (1 - y^{(i)}) \log(1 - \hat{y}^{(i)}) \right] \] where \(m\) is the number of training examples. python code example let's implement logistic regression using the logistic loss function. we'll use numpy for mathematical operations. explanation of the code 1. **class definition**: we define a `logisticregression` class that initializes learning rate and number of iterations. 2. **sigmoid function**: the `sigmoid` method applies the logistic function. 3. **fit method**: the `fit` method trains the model using gradient descent to minimize th ... #LogisticRegression #LossFunction #numpy 7 2 3 loss function cost function logistic regression binary classification gradient descent optimization algorithm model evaluation regularization techniques cross-entropy loss performance metrics loss minimization predictive modeling logistic model error analysis training convergence