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.
This project requires Python 3.8 or greater. Clone the repository and install the module:
python3.8 -m pip install .
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()We ❤️ contributions.
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