I shared this not because I'm done, I just want yall to see my journey on making this. It is going to be a tough to make. Wish me luck.
Sigmoid function: The sigmoid function is a non-linear function that maps a real number to a value between 0 and 1. It is often used in machine learning to represent the probability of an event. Here is the mathematical formula for the sigmoid function: sigmoid(x) = 1 / (1 + e^(-x)) The sigmoid function has the following properties: It is monotonically increasing, meaning that as the input value increases, the output value also increases. It is symmetric around the value 0.5, meaning that sigmoid(-x) = 1 - sigmoid(x). It saturates at the values 0 and 1, meaning that as the input value approaches positive or negative infinity, the output value approaches 1 or 0, respectively. Binary cross-entropy loss: Binary cross-entropy loss is a measure of how different the predicted probabilities are from the actual labels. It is commonly used in machine learning for binary classification problems, where the goal is to predict whether a given input belongs to one of two classes. Here is the mathematical formula for binary cross-entropy loss: binary_crossentropy(y, y_pred) = -mean(y * log(y_pred) + (1 - y) * log(1 - y_pred)) where: y is the actual label y_pred is the predicted probability Binary cross-entropy loss is minimized when the predicted probabilities are exactly equal to the actual labels. How sigmoid and binary cross-entropy are used together: In machine learning, sigmoid and binary cross-entropy are often used together for binary classification problems. The sigmoid function is used to map the outputs of the neural network to probabilities, and the binary cross-entropy loss function is used to measure how different the predicted probabilities are from the actual labels. The goal of training a neural network for binary classification is to minimize the binary cross-entropy loss function. This can be done using an optimization algorithm such as gradient descent. Binary cross-entropy: 0.6931471805599456 This is the binary cross-entropy loss between the actual label y and the predicted probability y_hat. To train the neural network, we can adjust the weights of the neural network and then calculate the binary cross-entropy loss again. We can repeat this process until the binary cross-entropy loss is minimized. Once the neural network is trained, we can use it to predict the probability that a given input belongs to one of the two classes. To do this, we simply feed the input to the neural network and then calculate the output. The output will be a probability between 0 and 1, where a higher probability indicates that the input is more likely to belong to the first class.
