Insurance cost prediction using linear regression

In this assignment we're going to use information like a person's age, sex, BMI, no. of children and smoking habit to predict the price of yearly medical bills. This kind of model is useful for insurance companies to determine the yearly insurance premium for a person. The dataset for this problem is taken from: https://www.kaggle.com/mirichoi0218/insurance

We will create a model with the following steps:

1. Download and explore the dataset
2. Prepare the dataset for training
3. Create a linear regression model
4. Train the model to fit the data
5. Make predictions using the trained model

This assignment builds upon the concepts from the first 2 lectures. It will help to review these Jupyter notebooks:

• PyTorch basics: https://jovian.ml/aakashns/01-pytorch-basics
• Linear Regression: https://jovian.ml/aakashns/02-linear-regression
• Logistic Regression: https://jovian.ml/aakashns/03-logistic-regression
• Linear regression (minimal): https://jovian.ml/aakashns/housing-linear-minimal
• Logistic regression (minimal): https://jovian.ml/aakashns/mnist-logistic-minimal

As you go through this notebook, you will find a ??? in certain places. Your job is to replace the ??? with appropriate code or values, to ensure that the notebook runs properly end-to-end . In some cases, you'll be required to choose some hyperparameters (learning rate, batch size etc.). Try to experiment with the hypeparameters to get the lowest loss.

Step 1: Download and explore the data

Let us begin by downloading the data. We'll use the download_url function from PyTorch to get the data as a CSV (comma-separated values) file.

To load the dataset into memory, we'll use the read_csv function from the pandas library. The data will be loaded as a Pandas dataframe. See this short tutorial to learn more: https://data36.com/pandas-tutorial-1-basics-reading-data-files-dataframes-data-selection/

We're going to do a slight customization of the data, so that you every participant receives a slightly different version of the dataset. Fill in your name below as a string (enter at least 5 characters)

The customize_dataset function will customize the dataset slightly using your name as a source of random numbers.

Let us answer some basic questions about the dataset.

Q: How many rows does the dataset have?

Q: How many columns doe the dataset have

Q: What are the column titles of the input variables?

Q: Which of the input columns are non-numeric or categorial variables ?

Hint: sex is one of them. List the columns that are not numbers.

Q: What are the column titles of output/target variable(s)?

Q: (Optional) What is the minimum, maximum and average value of the charges column? Can you show the distribution of values in a graph? Use this data visualization cheatsheet for referece: https://jovian.ml/aakashns/dataviz-cheatsheet

Note: There are multiple ways to visualize the min, avg and max values. I have commented the second method in above cell to check it's output uncomment and run the previous cell. I have commented that method because it gave somewhat ambigous looking graph but you can try and refine it or play around with it.

Remember to commit your notebook to Jovian after every step, so that you don't lose your work.

Step 2: Prepare the dataset for training

We need to convert the data from the Pandas dataframe into a PyTorch tensors for training. To do this, the first step is to convert it numpy arrays. If you've filled out input_cols, categorial_cols and output_cols correctly, this following function will perform the conversion to numpy arrays.

Read through the Pandas documentation to understand how we're converting categorical variables into numbers.

Q: Convert the numpy arrays inputs_array and targets_array into PyTorch tensors. Make sure that the data type is torch.float32.

1st trial inputs = torch.from_numpy(inputs_array)

2nd trial inputs = torch.from_numpy(inputs_array, dtype=torch.float32)

Other failed trials

• type_as(torch.float32)
• inputs.astype(np.float32)
• inputs.float()
• inputs.to(dtype=torch.float32)
• inputs.to(torch.float32)

Note - inputs can be replaced with targets

Successful Alternative -

inputs = torch.from_numpy(inputs_array.astype(np.float32))

Next, we need to create PyTorch datasets & data loaders for training & validation. We'll start by creating a TensorDataset.

**Q: Pick a number between 0.1 and 0.2 to determine the fraction of data that will be used for creating the validation set. Then use random_split to create training & validation datasets. **

Failed attempts and errors I got-

val_percent = torch.rand([0.1, 0.2])

TypeError: rand(): argument 'size' must be tuple of ints, but found element of type float at pos 1

train_ds, val_ds = torch.utils.data.random_split(dataset, train_size)

val_ds = torch.utils.data.random_split(dataset, val_size)

TypeError: 'int' object is not iterable

Finally, we can create data loaders for training & validation.

Q: Pick a batch size for the data loader.

Let's look at a batch of data to verify everything is working fine so far.

Let's save our work by committing to Jovian.

Step 3: Create a Linear Regression Model

Our model itself is a fairly straightforward linear regression (we'll build more complex models in the next assignment).

Q: Complete the class definition below by filling out the constructor (__init__), forward, training_step and validation_step methods.

Hint: Think carefully about picking a good loss fuction (it's not cross entropy). Maybe try 2-3 of them and see which one works best. See https://pytorch.org/docs/stable/nn.functional.html#loss-functions

References:

https://medium.com/udacity-pytorch-challengers/a-brief-overview-of-loss-functions-in-pytorch-c0ddb78068f7

https://towardsdatascience.com/pytorch-basics-intro-to-dataloaders-and-loss-functions-868e86450047

Loss functions to be used while doing linear regression and their loss values

loss = F.l1_loss(out, targets)                                   # {'val_loss': 15876.384765625}
loss= F.mse_loss(out, targets)                                   # {'val_loss': 462317440.0}

Other loss functions(not recommended to be used while dealing with linear regression)

Different loss values

loss = F.binary_cross_entropy_with_logits(out, targets)          # {'val_loss': 6555.9228515625}
loss = F.poisson_nll_loss(out, targets)                          # {'val_loss': 29691.9609375}
loss = F.hinge_embedding_loss(out, targets)                      # {'val_loss': 1.0}
loss= F.multilabel_soft_margin_loss(out, targets)                # {'val_loss': -160699.9375}
loss = F.soft_margin_loss(out, targets)                          # {'val_loss': inf}

Warning

loss = F.kl_div(out, targets)                                    # {'val_loss': 472210.84375}

UserWarning: reduction: 'mean' divides the total loss by both the batch size and the support size.'batchmean' divides only by the batch size, and aligns with the KL div math definition.'mean' will be changed to behave the same as 'batchmean' in the next major release. warnings.warn("reduction: 'mean' divides the total loss by both the batch size and the support size."

Errors

loss = F.binary_cross_entropy(out, targets)         # RuntimeError: all elements of input should be between 0 and 1
loss = F.cross_entropy(out, targets)          # RuntimeError: 1D target tensor expected, multi-target not supported
loss = F.nll_loss(out, targets)               # RuntimeError: 1D target tensor expected, multi-target not supported

Let us create a model using the InsuranceModel class. You may need to come back later and re-run the next cell to reinitialize the model, in case the loss becomes nan or infinity.

Let's check out the weights and biases of the model using model.parameters.

One final commit before we train the model.

Step 4: Train the model to fit the data

To train our model, we'll use the same fit function explained in the lecture. That's the benefit of defining a generic training loop - you can use it for any problem.

Q: Use the evaluate function to calculate the loss on the validation set before training.

We are now ready to train the model. You may need to run the training loop many times, for different number of epochs and with different learning rates, to get a good result. Also, if your loss becomes too large (or nan), you may have to re-initialize the model by running the cell model = InsuranceModel(). Experiment with this for a while, and try to get to as low a loss as possible.

Q: Train the model 4-5 times with different learning rates & for different number of epochs.

Hint: Vary learning rates by orders of 10 (e.g. 1e-2, 1e-3, 1e-4, 1e-5, 1e-6) to figure out what works.

Observations

no. of epochs and learning rate should be higher for better efficiency and less loss value

Q: What is the final validation loss of your model?

Let's log the final validation loss to Jovian and commit the notebook

Now scroll back up, re-initialize the model, and try different set of values for batch size, number of epochs, learning rate etc. Commit each experiment and use the "Compare" and "View Diff" options on Jovian to compare the different results.

Step 5: Make predictions using the trained model

Q: Complete the following function definition to make predictions on a single input

Are you happy with your model's predictions? Try to improve them further.

(Optional) Step 6: Try another dataset & blog about it

While this last step is optional for the submission of your assignment, we highly recommend that you do it. Try to clean up & replicate this notebook (or this one, or this one ) for a different linear regression or logistic regression problem. This will help solidify your understanding, and give you a chance to differentiate the generic patters in machine learning from problem-specific details.

Here are some sources to find good datasets:

• https://lionbridge.ai/datasets/10-open-datasets-for-linear-regression/
• https://www.kaggle.com/rtatman/datasets-for-regression-analysis
• https://archive.ics.uci.edu/ml/datasets.php?format=&task=reg&att=&area=&numAtt=&numIns=&type=&sort=nameUp&view=table
• https://people.sc.fsu.edu/~jburkardt/datasets/regression/regression.html
• https://archive.ics.uci.edu/ml/datasets/wine+quality
• https://pytorch.org/docs/stable/torchvision/datasets.html

We also recommend that you write a blog about your approach to the problem. Here is a suggested structure for your post (feel free to experiment with it):

• Interesting title & subtitle
• Overview of what the blog covers (which dataset, linear regression or logistic regression, intro to PyTorch)
• Downloading & exploring the data
• Preparing the data for training
• Creating a model using PyTorch
• Training the model to fit the data
• Your thoughts on how to experiment with different hyperparmeters to reduce loss
• Making predictions using the model

As with the previous assignment, you can embed Juptyer notebook cells & outputs from Jovian into your blog.

Don't forget to share your work on the forum: https://jovian.ml/forum/t/share-your-work-here-assignment-2/4931