Neur-HCI

This repository is the official implementation of Neur-HCI as introduced in our paper and completed in our thesis. It consists in neural network architectures specifically designed to learn some particular classes of models, called UHCI. The main component is the Choquet integral, a powerful, yet highly interpretable fuzzy-logic-based aggregator, whose interest is confirmed by its popularity in the decision modeling community (and more recently in the machine learning and explainable AI communities).

For each class of models, a representation theorem is provided and proven in the thesis, such that the search space exactly coincides with the sought class. All theoretical properties applicable to Choquet integrals are thus formally valid by design.

This is a reimplementation of the code used in those papers, and not the original code.

Table of Contents

1. Requirements
2. Documentation
   • Tutorial
   • Installation
   • Submodules
   • To do
3. Cite
4. Contact

Requirements

The code was written with Python 3.11, Python 3.8 or above should work. The requirements are listed in src/neurhci_package/pyproject.toml Current requirements (with versions used for development): torch==2.2.0

Documentation

Tutorial

A jupyter notebook is provided in src/notebooks/tutorial.ipynb. It should give one an overview of the classes, the methods, and overall how to:

• build a model
• train a model
• extract explanations (Shapley/Winter values) from the trained model.

Installation

Get the code with:

git clone https://github.com/RomanBresson/NeurHCI.git

The code is packaged to be installed through pip with:

cd NeurHCI/src/neurhci_package
pip install .

Once installed, the package can be imported like any other pip package:

import neurhci

Submodules

The classes detailed here, module by module, either inherit from PyTorch's nn.Module, and can thus be used like any basic module. All these modules are proven to have the monotonicity required by the model. All models (except those who are explicitely excluded below) respect the normalization constraints of the model. See the sources for clearer understanding of the underlying theory.

• marginal_utilities: classes implementing marginal utilities. It is to be noted that many properties of the model only hold if the outputs of the marginal utility is in the unit interval. Their default initialization is best for inputs who are also in the unit interval. When the data is normalized around 0, passing centered=True to the constructors makes it the same function applied to x+0.5, which should yield a better initialization. We do not recommend this, and instead recommend using explicit shifting or renormalization of the data before feeding it to the network.
  • Identity(): $u(x) = x$ (no learnable parameter, does not respect normalization if the inputs are not normalized in the unit interval)
  • OppositeIdentity(): $u(x) = 1-x$ (no learnable parameter, does not respect normalization if the inputs are not normalized in the unit interval)
  • IdentityClipped/OppositeIdentityClipped: variants of Identity and OppositeIdentity whose outputs are clipped in the unit interval to ensure normalization.
  • NonDecreasing(nb_sigmoids): $u(x) = \sum\limits_{i=1}^p w_i\sigma(\eta_i(x-\beta_i))$ with $p$ the number of sigmoids, $\eta,~\beta,~w$ being learned, and $\sigma$ being a logistic sigmoid. Can represent any non-decreasing function with image in the unit interval (and only those).
  • NonIncreasing(nb_sigmoids): $u(x) = 1-v(x)$ with $v$ a NonDecreasing.
  • Selector(U1, U2): $u(x) = sU1(x) + (1-s) U2(x)$ with s a learned variable. It operates a switching that selects the best utility among U1 and U2 and parameters when it is a priori unknown.
  • MonotonicSelector(nb_sigmoids): a selector where U1 is a NonDecreasingand U2 is a NonIncreasing. It effectively selects the optimal monotonicity.
  • Unconstrained(nb_layers, width): a simple MLP with 1d input, 1d output, and nb_layers fully connected hidden layers, each with width neurons. DOES NOT FIT ANY CONSTRAINTS OF NORMALIZATION OF MONOTONICITY, it is simply here if required for some specific cases.
  • MarginalUtilitiesLayer(list_of_leaves, types_of_leaves, nb_sigmoids): a list of marginal utilities ${u_1,...,u_n}$ where $u_i$ corresponds to list_of_leaves[i] and has type types_of_leaves[list_of_leaves[i]]. Any non-given type will be replaced by an Identity.
• aggregators: classes implementing Choquet integral-based aggregators:
  • CI2Add: The $2$-additive Choquet integral, with dimension inputs.
  • CI01FromAntichain: A CI parameterized by a 0-1 FM. Nothing learnable, the FM is determined by its corresponding antichain (see thesis).
  • CI3addFrom01: A subset of the 3-additive CIs, represented as a convex sum of CIs parameterized by 3-additive 0-1 FMs (see thesis).
• hierarchical: class of hierarchical Choquet integral, i.e. a multi-step aggregator which aggregates the inputs successively following a directed-acyclic graph structure. Contains the following classes:
  • HCI(hierarchy): builds a HCI with the structure passed as argument. hierarchy is a dict of {(int) key: (list of int) value} where key is the id of a node, and value is the list of this node's children. Details and examples can be found below.
  • HCI2layers(dimension, children_by_aggregators): A tree-HCI with a single root single intermediate layer, and dimension leaves. Each node in the intermediate layer aggregates children_by_aggregators leaves (or fewer for the last one). The root aggregates all intermediate nodes
  • HCIBalanced(dimension, children_by_aggregators): A tree-HCI with a single root, dimension leaves, where all aggregators have the same number children_by_aggregators of leaves (except the first/last one at each level)
• uhci:
  • UHCI(**kwargs): A utilitaristic hierarchical Choquet integral, combination of marginal utilities and a HCI. Can be initialized from an existing HCI or a hierarchy, and from an existing list of marginal utilities or a MarginalUtilitiesLayer.

To do

The classes described above are just a part of the models described in the thesis. The rest will be implemented at a later date, such as:

• Shapley and explainability suite for 3-additive Choquet integrals based on 0-1 measures
• General Choquet integrals
• Bitonic marginal utilities (single peaked/single valleyed)
• ...

Cite

When using this package, please cite one of our papers:

If using only 2-additive Choquet integrals and/or monotonic marginal utilities:

@inproceedings{ijcai2020p0275,
  title     = {Neural Representation and Learning of Hierarchical 2-additive Choquet Integrals},
  author    = {Bresson, Roman and Cohen, Johanne and Hüllermeier, Eyke and Labreuche, Christophe and Sebag, Michèle},
  booktitle = {Proceedings of the Twenty-Ninth International Joint Conference on
               Artificial Intelligence, {IJCAI-20}},
  publisher = {International Joint Conferences on Artificial Intelligence Organization},
  editor    = {Christian Bessiere},
  pages     = {1984--1991},
  year      = {2020},
  month     = {7},
  note      = {Main track},
  doi       = {10.24963/ijcai.2020/275},
  url       = {https://doi.org/10.24963/ijcai.2020/275},
}

If using any other class:

@phdthesis{bresson:tel-03596964,
  TITLE = {{Neural learning and validation of hierarchical multi-criteria decision aiding models with interacting criteria}},
  AUTHOR = {Bresson, Roman},
  URL = {https://theses.hal.science/tel-03596964},
  NUMBER = {2022UPASG008},
  SCHOOL = {{Universit{\'e} Paris-Saclay}},
  YEAR = {2022},
  MONTH = Feb,
  TYPE = {Theses},
  PDF = {https://theses.hal.science/tel-03596964/file/107767_BRESSON_2022_archivage.pdf}
}

Contact

Please do not hesitate to provide feedback or suggestion through GitHub, or send me an email at: [email protected]