Semantic Similarity Covariance Matrix Shrinkage

This repository contains the supporting code for Semantic Similarity Covariance Matrix Shrinkage, published in Findings of EMNLP 2023. It implements the methods for shrinking covariance matrices using a cosine similarity target.

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• Quick start
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Installation

This project requires Python 3.8 or greater. Clone the repository and install the module:

python3.8 -m pip install .

Quick Start

The library requires a cosine similarity matrix that can be generated from normalized embeddings as an input. Assuming a set of k embeddings of dimension p stored in a PyTorch [k,p] tensor, the similarity matrix can be built using:

import torch

normalized_embeddings = torch.nn.functional.normalize(embeddings)
similarity_matrix = normalized_embeddings @ normalized_embeddings.t()

Assuming the random variable observations (e.g., stock price returns) are available as a [N,p] tensor called returns, the shrunk covariance matrix can be computed directly using:

from semantic_shrinkage import SemanticShrinkage

shrunk_covariance_matrix = SemanticShrinkage.from_returns(
    returns, similarity_matrix
).get_shrunk_covariance()

Contributions

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License

Please read the LICENSE file.

Code of Conduct

This project has adopted a Code of Conduct. If you have any concerns about the Code, or behavior which you have experienced in the project, please contact us at opensource@bloomberg.net.

Security Vulnerability Reporting

Please refer to the project Security Policy.