? Build Linear Neural Network for Regression

Build Linear Neural Network for Regression - explained in simple terms with code implementation

A linear neural network for regression consists of an input layer, one or more hidden layers, and an output layer. The key characteristic of this type of network is that the activation function used in the output layer is typically a linear function.

A linear neural network for regression is a type of NN that is specifically designed for solving regression problems. Regression is a type of supervised learning task where the goal is to predict a continuous numerical value.

Imagine you have a magic box that can tell you how much something costs based on its features. For example, it can tell you how much a toy car costs based on its color, size, and wheels.

A linear neural network for regression is like a special machine that tries to figure out how much things cost based on their features. It has different layers inside, just like different parts of the machine.

The first layer is where you put in the features of the toy car, like its color, size, and wheels. Then, the machine does some calculations using special numbers called weights, which are like the machine's magic power.

These weights are like little helpers that help the machine understand the importance of each feature. Next, the machine goes through some more layers, and at the end, it gives you the predicted cost of the toy car.

It does this by adding up all the features of the car multiplied by their weights. So if big cars are usually more expensive, the weight for the "size" feature will be bigger, and the machine will multiply it with the size of the car to get the predicted cost.

The machine learns how to find the right weights by looking at many examples of toy cars and their actual costs. It compares its predicted cost with the real cost and adjusts the weights to get better and better at guessing the right cost.

So, a linear neural network for regression is like a magic box that uses features of things to guess how much they cost. It learns from examples and gets better at its guessing by adjusting its weights.

It consists of - Input Features: The network takes in a set of input features that describe the object or phenomenon we want to predict something about. For example, if we want to predict price of a house, input features could include number of rooms, size of the house etc

Weights and Bias: Each input feature is assigned a weight, which represents its importance in the prediction. Think of weights as network's way of deciding how much each feature contributes to final prediction. Additionally, there is bias that is added to the calculation.

Linear Combination: The input features are multiplied by their corresponding weights and then summed together, along with the bias term. This calculation is a linear combination of the input features and weights.

Activation Function: The linear combination is then passed through an activation function, which introduces non-linearity into the network. In the case of a linear neural network for regression, the activation function used in the output layer is typically a linear function.

Output: The output of the activation function is the predicted value, which represents the network's estimation of the target variable. In the case of regression, this predicted value is a continuous numerical value.

Training: To make accurate predictions, network needs to learn the appropriate weights and bias values. This is done through a process called training. During training, network is presented with a set of labeled examples.

The network compares its predicted values with the true values and adjusts the weights and bias to minimize the difference between them. This optimization process is typically performed using techniques such as gradient descent.

Prediction: Once the network has been trained, it can be used to make predictions on new, unseen data. It takes input features of a new instance, performs same calculations as during training using the learned weights and bias, and produces a prediction for the target value.

When to use it?

Small Dataset: Linear models tend to work well with smaller datasets, as they have fewer parameters to estimate. If the available dataset is limited, a linear neural network can provide reasonable predictions without overfitting.

Feature Importance: Linear models explicitly assign weights to each feature, indicating their relative importance in predicting the target variable. This can be valuable when you want to understand which features are more influential in the prediction.

Speed and Efficiency: Linear models are computationally efficient and can be trained and evaluated relatively quickly, especially compared to more complex models. If there are constraints on time or computational resources, a linear neural network can be a suitable choice.

Simplicity and Interpretability: Linear models are relatively simple and easier to interpret compared to more complex models like deep NN. Linear neural networks provide a balance between simplicity and performance, making them useful when a simpler model is desired.

Linear Relationships: If there is a clear, linear relationship between the input features and the target variable, a linear neural network can be effective.

Implementation

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