A Comprehensive Guide to Sequence Prediction Using the Compact Prediction Tree Algorithm in Python

Introduction

Sequence prediction is a common and important machine learning task with many practical applications. Given a sequence of events, the goal is to predict the most likely next event(s) in the sequence. Some real-world examples include:

• Predicting the next word a user will type based on their previous text input
• Recommending the next product a customer is likely to purchase based on their order history
• Forecasting a patient‘s future medical events based on their clinical history
• Predicting tomorrow‘s weather based on recent meteorological conditions

Traditionally, approaches like Markov chains, hidden Markov models, and recurrent neural networks have been used for sequence prediction. However, in 2015 a team at Microsoft Research introduced a new algorithm called the Compact Prediction Tree (CPT) that offers some compelling advantages.

In this post, we‘ll take a deep dive into how the CPT algorithm works under the hood. We‘ll walk through a detailed example and share Python code you can use to implement CPT yourself. Finally, we‘ll evaluate CPT‘s performance compared to other methods and discuss potential optimizations.

Whether you‘re a machine learning practitioner or just curious about the latest sequence prediction techniques, this post will give you a solid understanding of a powerful approach. Let‘s get started!

What is the Compact Prediction Tree Algorithm?

At a high level, the compact prediction tree algorithm works by:

1. Building a compressed trie data structure called a prediction tree that stores all the training sequences
2. Creating an inverted index that maps each unique item to the set of sequences that contain it
3. Generating a lookup table with pointers from each training sequence to its terminal node in the tree

To make a prediction for a new sequence, CPT finds all training sequences that are similar to it using the inverted index. It then finds the most common next item(s) that follow the similar sequences in the prediction tree.

The key advantages of CPT are:

• Fast training and prediction times compared to neural networks
• Ability to handle new items not seen during training without retraining the model
• Relatively simple to understand and implement
• Strong empirical performance on sequence prediction tasks

With that overview in mind, let‘s now walk through each of the major components of the CPT algorithm in more detail.

CPT Data Structures

There are three key data structures used in the CPT algorithm:

1. Prediction Tree

The prediction tree is a compressed trie that efficiently stores all the sequences in the training set. Each node in the tree represents a unique item and contains:

• Item – the item value
• Children – a list of child nodes
• Parent – a pointer to the parent node

For example, let‘s say we have the following two training sequences:

1. A, B, C
2. A, B, D

The prediction tree would look like:

        Root
        /  \
       A    B
      / \    \
     B   C    D
    /
   C

Sequences are added to the tree one item at a time, starting from the root. If the next item doesn‘t exist as a child of the current node, a new node is created and added as a child. This continues until the full sequence has been inserted.

The prediction tree allows us to efficiently store and query our training data to find sequences that share the same prefix.

2. Inverted Index

The inverted index is a dictionary that maps each unique item in the training set to the set of sequences that contain it. Continuing our example from before, the inverted index would be:

II = {
  ‘A‘: {1, 2},
  ‘B‘: {1, 2}, 
  ‘C‘: {1},
  ‘D‘: {2}
}

The inverted index allows us to quickly look up all sequences that contain a given item. This is useful during the prediction phase for finding sequences that are similar to our query sequence.

3. Lookup Table

The lookup table is a dictionary mapping each training sequence ID to the terminal node representing the last item in that sequence. For our running example, it would be:

LT = {
  1: Node(‘C‘), 
  2: Node(‘D‘)
}

The lookup table gives us a fast way to access the terminal node for a sequence so we can scan the prediction tree to find the most likely next events.

CPT Training Phase

Now that we understand the key data structures, let‘s walk through how CPT builds them during the training phase. We‘ll use this example training set:

1: A, B, C
2: A, B 
3: A, B, D, C
4: B, C

The training phase initializes an empty prediction tree, inverted index, and lookup table. Then for each training sequence:

1. Set the current node to the root of the tree
2. For each item in the sequence:
   • If the item is already a child of the current node, move to that child node
   • Else, create a new node for the item and add it as a child of the current node
   • Add the sequence ID to the inverted index entry for this item
   • Move to the new child node
3. Add the sequence ID and terminal node to the lookup table

After processing all 4 sequences, our final prediction tree would be:

     Root
     /  \
    A    B
   /    / \ 
  B    C   D
 / \       |
C   D      C
    |
    C

The final inverted index would be:

II = {
  ‘A‘: {1, 2, 3},
  ‘B‘: {1, 2, 3, 4},
  ‘C‘: {1, 3, 4},
  ‘D‘: {3}
}  

And the final lookup table would be:

  
LT = {
  1: Node(‘C‘),
  2: Node(‘B‘),
  3: Node(‘C‘),
  4: Node(‘C‘)
}

That covers the training phase. Next let‘s look at how CPT uses these data structures to make predictions.

CPT Prediction Phase

To make a prediction for a new query sequence, CPT:

1. Finds all training sequences that are similar to the query sequence
2. Scans the prediction tree to find the most common item(s) that follow the similar sequences
3. Returns the item(s) with the highest score

Let‘s walk through an example query:

Query sequence: A, B

Step 1: Find similar sequences

To find similar training sequences, CPT looks up each item from the query sequence in the inverted index and takes the intersection of the results.

For our query, that means finding the intersection of sequences containing A and sequences containing B:

Sequences containing A: {1, 2, 3}  
Sequences containing B: {1, 2, 3, 4}
Similar sequences: {1, 2, 3}

Step 2: Find the most likely next items

For each similar sequence, CPT finds its terminal node in the prediction tree using the lookup table. It then scans the children of the terminal node (excluding any items already in the query sequence) and adds them to a Counter dictionary.

The score for each potential next item is calculated as:

score = 1 + (1 / # similar sequences) + (1 / (# items in counter + 1)) * 0.001

If the item already exists in the Counter, its score is multiplied by the previous value instead of being overwritten.

Continuing our example:

Similar sequence 1: A, B, C
Terminal node: Node(‘C‘)
Children: None
Counter: {}
Similar sequence 2: A, B

Terminal node: Node(‘B‘)
Children: None
Counter: {}
Similar sequence 3: A, B, D, C
Terminal node: Node(‘C‘) 
Children: None
Counter: {}

Since none of the similar sequences have children, our final Counter is empty. But if the terminal nodes did have children, they would be added to the Counter with the appropriate scores.

Step 3: Return the item(s) with the highest score

Finally, CPT returns the key(s) with the maximum value in the Counter as the predicted next item(s). In our case, since the Counter is empty, there is no prediction.

Implementing CPT in Python

Now that we have a solid understanding of how the CPT algorithm works, let‘s see how to implement it in Python.

First, clone the CPT Python library repo:

git clone https://github.com/NeerajSarwan/CPT.git

Then you can use the following code to train a CPT model and make predictions:

from CPT import *

# Create a CPT model instance
model = CPT()

# Load train and test sequences 
train_data, test_data = model.load_files("train.csv", "test.csv")

# Train the model
model.train(train_data)  

# Make predictions
predictions = model.predict(train_data, test_data, top_k=5, threshold=1)

The load_files method reads sequences from CSV files. Each line should contain a comma-separated list of items representing a sequence.

The train method builds the prediction tree, inverted index, and lookup table on the training sequences.

Finally, the predict method returns a DataFrame with the top K predictions for each sequence in the test set. The threshold parameter controls the maximum length of the suffix used when scanning for predictions.

Comparing CPT to Other Methods

So how does CPT stack up against classic sequence prediction methods? Here are a few key advantages:

• CPT can train on a dataset in minutes compared to hours or days for large RNNs/LSTMs
• Adding new items to an existing CPT model doesn‘t require retraining, unlike Markov chains
• CPT has been shown to outperform standard RNNs and LSTMs on sequence prediction tasks

Of course, CPT isn‘t always the best choice. Other considerations:

• CPT may not handle very long sequences as well as LSTMs with attention
• Standard libraries for RNNs/LSTMs are more mature and optimized than the CPT implementation
• The CPT algorithm is less well known and documented compared to other approaches

In the end, the best model will depend on your specific use case and dataset. It‘s worth experimenting with multiple approaches, including CPT, to see what performs best.

Ideas for Optimizing CPT

While the current CPT library provides a great starting point, there are a few areas for potential optimization:

• Use a more efficient trie implementation for the prediction tree
• Compress the inverted index and lookup table to reduce memory usage
• Profile the code to find and eliminate any bottlenecks
• Tune the score calculation and other hyperparameters on a validation set
• Ensemble CPT with other sequence prediction models

If you‘re interested in contributing, feel free to submit a pull request to the CPT library repo. There are lots of opportunities to build on this powerful algorithm.

Conclusion

In this post, we took an in-depth look at the compact prediction tree algorithm for sequence prediction. We walked through detailed examples of the training and prediction phases, and shared Python code for implementing CPT yourself.

While it‘s not always the best approach, CPT offers some compelling advantages over traditional sequence prediction methods. Its fast training time and ability to handle new items make it especially useful for certain applications.

If you made it this far, you now have a strong understanding of a fascinating algorithm at the cutting edge of sequence prediction. I encourage you to try applying CPT to your own datasets and see how it performs. Share your results in the comments below!