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.

• X-Linear (pecos.xmc.xlinear): recursive linear models learning to traverse an input from the root of a hierarchical label tree to a few leaf node clusters, and return top-k relevant labels within the clusters as predictions. See more details in the PECOS paper (Yu et al., 2020).

  • fast real-time inference in C++
  • can handle 100MM output space

• XR-Transformer (pecos.xmc.xtransformer): Transformer based XMC framework that fine-tunes pre-trained transformers recursively on multi-resolution objectives. It can be used to generate top-k relevant labels for a given instance or simply as a fine-tuning engine for task aware embeddings. See technical details in XR-Transformer paper (Zhang et al., 2021).

  • easy to extend with many pre-trained Transformer models from huggingface transformers.
  • establishes the State-of-the-art on public XMC benchmarks.

• ANN Search with HNSW (pecos.ann.hnsw): a PECOS Approximated Nearest Neighbor (ANN) search module that implements the Hierarchical Navigable Small World Graphs (HNSW) algorithm (Malkov et al., TPAMI 2018).

  • Supports both sparse and dense input features
  • SIMD optimization for both dense/sparse distance computation
  • Supports thread-safe graph construction in parallel on multi-core shared memory machines
  • Supports thread-safe Searchers to do inference in parallel, which reduces inference overhead

• Python (3.7, 3.8, 3.9, 3.10)
• Pip (>=19.3)

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

• Ubuntu 20.04 and 22.04
• Amazon Linux 2

PECOS can be installed using pip as follows:

python3 -m pip install libpecos

• For Ubuntu (20.04, 22.04):

sudo apt-get update && sudo apt-get install -y build-essential git python3 python3-distutils python3-venv

• For Amazon Linux 2:

sudo yum -y install python3 python3-devel python3-distutils python3-venv && sudo yum -y groupinstall 'Development Tools'

One needs to install at least one BLAS library to compile PECOS, e.g. OpenBLAS:

• For Ubuntu (20.04, 22.04):

sudo apt-get install -y libopenblas-dev

• For Amazon Linux 2:

sudo amazon-linux-extras install epel -y
sudo yum install openblas-devel -y

git clone https://github.com/amzn/pecos
cd pecos
python3 -m pip install --editable ./

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

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

• instance-to-feature matrix X, of shape N by D in SciPy CSR format
• instance-to-label matrix Y, of shape N by L in SciPy CSR format

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)
>>> model.save("./save-models")

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:

• PECOS: Prediction for Enormous and Correlated Output Spaces (Yu et al., JMLR 2022) [bib]

Some papers from PECOS team:

• Representer Points for Explaining Recommender Systems (Tsai et al., ICML 2023) [bib]

• PINA: Leveraging Side Information in eXtreme Multilabel Classification via Predicted Instance Neighborhood Aggregation (Chien et al., ICML 2023) [bib]

• Uncertainty Quantification in Extreme Classification (Jiang et al., SIGIR 2023) [bib]

• FINGER: Fast Inference for Graph-based Approximate Nearest Neighbor Search (Chen et al., WWW 2023) [bib]

• End-to-End Learning to Index and Search in Large Output Space (Gupta et al., NeurIPS 2022) [bib]

• Relevance under the Iceberg: Reasonable Prediction for Extreme Multi-label Classification (Jiang et al., SIGIR 2022) [bib]

• Extreme Zero-Shot Learning for Extreme Text Classification (Xiong et al., NAACL 2022) [bib]

• Node Feature Extraction by Self-Supervised Multi-scale Neighborhood Prediction (Chien et al., ICLR 2022) [bib]

• Accelerating Inference for Sparse Extreme Multi-Label Ranking Trees (Etter et al., WWW 2022) [bib]

• Fast Multi-Resolution Transformer Fine-tuning for Extreme Multi-label Text Classification (Zhang et al., NeurIPS 2021) [bib]

• Label Disentanglement in Partition-based Extreme Multilabel Classification (Liu et al., NeurIPS 2021) [bib]

• Enabling Efficiency-Precision Trade-offs for Label Trees in Extreme Classification (Baharav et al., CIKM 2021) [bib]

• Extreme Multi-label Learning for Semantic Matching in Product Search (Chang et al., KDD 2021) [bib]

• Session-Aware Query Auto-completion using Extreme Multi-label Ranking (Yadav et al., KDD 2021) [bib]

• Top-k eXtreme Contextual Bandits with Arm Hierarchy (Sen et al., ICML 2021) [bib]

• Taming pretrained transformers for extreme multi-label text classification (Chang et al., KDD 2020) [bib]

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