$\mathcal{T}$-similarity (AISTATS'24)

This repository contains the official implementation of T-similarity, a novel confidence estimation measure robust to distribution shifts introduced in

Leveraging Ensemble Diversity for Robust Self-Training in the Presence of Sample Selection Bias. <br/>Ambroise Odonnat, Vasilii Feofanov, Ievgen Redko.

Overview

We provide the implementation of the $\mathcal{T}$-similarity, a drop-in replacement of the softmax for confidence estimation under distribution shifts. This novel confidence measure is build upon a diverse ensemble of linear classifiers and corrects the softmax overconfidence while being calibrated. It can be used for confidence estimation and SSL methods using neural networks as backbones, e.g., self-training.

<p align="center"> <img src="https://github.com/ambroiseodt/tsim/assets/64415312/eeef3f8c-308e-4dd6-af3c-58b943634963" width="600"> </p>

What is included?

We provide the following implementations.

Labeling procedure

Sample selection bias (SSB) occurs when data labeling is subject to constraints resulting in a distribution mismatch between labeled and unlabeled data. We illustrate below the two types of labeling considered in our paper:

• IID: The usual uniform labeling that verifies the i.i.d. assumption;
• SSB: Distribution shift between labeled and unlabeled data.

<p align="center"> <img src="https://github.com/ambroiseodt/tsim/assets/64415312/986153eb-0a1e-4472-9d86-98f7892b7f2c" width="600"> </p>

Learning with the $\mathcal{T}$-similarity

We provide the PyTorch implementation of the $\mathcal{T}$-similarity and the corresponding diversity loss. To combine prediction and confidence estimation, e.g., for self-training, we introduce the lightweight architecture shown below. In terms of implementation, it has the form of an sklearn base_estimator with fit, predict, and predict_proba methods and we add a predict_t_similarity method.

<p align="center"> <img src="https://github.com/ambroiseodt/tsim/assets/64415312/797cdfff-0621-420f-bc65-100a50f140cb" width="350"> </p>

Key features

• Backpropagation of the diversity loss only influences the ensemble, not the projection layers;
• In practice, we use $M=5$ heads resulting in lightweight and fast training;
• Compatible to any SSL methods using neural networks as backbones.

Installation

Please, make sure you have Python 3.8 or a newer version installed. To get started with the $\mathcal{T}$-similarity, you can install the library with pip:

pip install git+https://github.com/ambroiseodt/tsim.git#egg=tsim

If you want to contribute, you can clone the repository and install the packages as follows:

git clone https://github.com/ambroiseodt/tsim.git
cd tsim
pip install -e .[dev]

Examples

We provide demos in notebooks/ to take in hand the implementation and reproduce the figures of the paper:

• plot_intro_figure.ipynb: Overview of the method (Figure 1)
• plot_sample_selection_bias.ipynb: Visualization of the sample selection bias (Figure 3)
• plot_calibration.ipynb: $\mathcal{T}$-similarity corrects overconfidence of the softmax (Figure 6)

The code below (in demo.ipynb) gives an example of how to train the architecture introduced above:

import sys
sys.path.append("..")
from tsim.datasets.read_dataset import RealDataSet
from tsim.models.diverse_ensemble import DiverseEnsembleMLP

dataset_name = "mnist"
gamma = 1
n_classifiers = 5
seed = 0
nb_lab_samples_per_class = 10
test_size = 0.25
num_epochs = 5
n_iters = 100
selection_bias = True

# Data split
dataset = RealDataSet(dataset_name=dataset_name, seed=seed)

# Percentage of labeled data
num_classes = len(list(set(dataset.y)))
ratio = num_classes / ((1 - test_size) * len(dataset.y))
lab_size = nb_lab_samples_per_class * ratio


  # Split
  x_l, x_u, y_l, y_u, x_test, y_test, n_classes = dataset.get_split(
      test_size=test_size, lab_size=lab_size, selection_bias=selection_bias
  )

  # Define base classifier
  base_classifier = DiverseEnsembleMLP(
      num_epochs=num_epochs,
      gamma=gamma,
      n_iters=n_iters,
      n_classifiers=n_classifiers,
      device="cpu",
      verbose=False,
      random_state=seed,
  )

  # Train
  base_classifier.fit(x_l, y_l, x_u)

Modules

This package consists of several key modules:

• notebooks/: Contains the notebooks to reproduce the figures from the paper;
• data/: Contains the datasets used in our experiments;
• tsim/datasets: Contains the functions to load datasets and perform the labeling procedure;
• tsim/models/: Contains all the functions to train diverse ensembles with the $\mathcal{T}$-similarity

License

This project is licensed under the MIT License.

Author

• Ambroise Odonnat

Citation

If you find this work useful in your research, please cite:

@InProceedings{pmlr-v238-odonnat24a,
  title = 	 { Leveraging Ensemble Diversity for Robust Self-Training in the Presence of Sample Selection Bias },
  author =       {Odonnat, Ambroise and Feofanov, Vasilii and Redko, Ievgen},
  booktitle = 	 {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics},
  publisher =    {PMLR},
  pdf = 	 {https://proceedings.mlr.press/v238/odonnat24a/odonnat24a.pdf},
  url = 	 {https://proceedings.mlr.press/v238/odonnat24a.html},
}