PECOS - Predictions for Enormous and Correlated Output Spaces

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PECOS is a versatile and modular machine learning (ML) framework for fast learning and inference on problems with large output spaces, such as extreme multi-label ranking (XMR) and large-scale retrieval. PECOS’ design is intentionally agnostic to the specific nature of the inputs and outputs as it is envisioned to be a general-purpose framework for multiple distinct applications.

Given an input, PECOS identifies a small set (10-100) of relevant outputs from amongst an extremely large (~100MM) candidate set and ranks these outputs in terms of relevance.


Extreme Multi-label Ranking and Classification

Requirements and Installation

See other dependencies in You should install PECOS in a virtual environment. If you’re unfamiliar with Python virtual environments, check out the user guide.

Supporting Platforms

Installation from Wheel

PECOS can be installed using pip as follows:

python3 -m pip install libpecos

Installation from Source

Prerequisite builder tools

Install and develop locally

git clone
cd pecos
python3 -m pip install --editable ./

Quick Tour

To have a glimpse of how PECOS works, here is a quick tour of using PECOS API for the XMR problem.

Toy Example

The eXtreme Multi-label Ranking (XMR) problem is defined by two matrices

Some toy data matrices are available in the tst-data folder.

PECOS constructs a hierarchical label tree and learns linear models recursively (e.g., XR-Linear):

>>> from pecos.xmc.xlinear.model import XLinearModel
>>> from pecos.xmc import Indexer, LabelEmbeddingFactory

# Build hierarchical label tree and train a XR-Linear model
>>> label_feat = LabelEmbeddingFactory.create(Y, X)
>>> cluster_chain = Indexer.gen(label_feat)
>>> model = XLinearModel.train(X, Y, C=cluster_chain)

After learning the model, we do prediction and evaluation

>>> from pecos.utils import smat_util
>>> Yt_pred = model.predict(Xt)
# print precision and recall at k=10
>>> print(smat_util.Metrics.generate(Yt, Yt_pred))

PECOS also offers optimized C++ implementation for fast real-time inference

>>> model = XLinearModel.load("./save-models", is_predict_only=True)
>>> for i in range(X_tst.shape[0]):
>>>   y_tst_pred = model.predict(X_tst[i], threads=1)


If you find PECOS useful, please consider citing the following paper:

Some papers from PECOS team:


Copyright (2021), Inc.

Licensed under the Apache License, Version 2.0 (the “License”); you may not use this file except in compliance with the License. You may obtain a copy of the License at

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