Benjamin Leblanc

Julien Bastian, Benjamin Leblanc, Pascal Germain et al.

Classical PAC generalization bounds on the prediction risk of a classifier are insufficient to provide theoretical guarantees on fairness when the goal is to learn models balancing predictive risk and fairness constraints. We propose a PAC-Bayesian framework for deriving generalization bounds for fairness, covering both stochastic and deterministic classifiers. For stochastic classifiers, we derive a fairness bound using standard PAC-Bayes techniques. Whereas for deterministic classifiers, as usual PAC-Bayes arguments do not apply directly, we leverage a recent advance in PAC-Bayes to extend the fairness bound beyond the stochastic setting. Our framework has two advantages: (i) It applies to a broad class of fairness measures that can be expressed as a risk discrepancy, and (ii) it leads to a self-bounding algorithm in which the learning procedure directly optimizes a trade-off between generalization bounds on the prediction risk and on the fairness. We empirically evaluate our framework with three classical fairness measures, demonstrating not only its usefulness but also the tightness of our bounds.

Benjamin Leblanc, Pascal Germain

We study the use of binary activated neural networks as interpretable and explainable predictors in the context of regression tasks on tabular data; more specifically, we provide guarantees on their expressiveness, present an approach based on the efficient computation of SHAP values for quantifying the relative importance of the features, hidden neurons and even weights. As the model's simplicity is instrumental in achieving interpretability, we propose a greedy algorithm for building compact binary activated networks. This approach doesn't need to fix an architecture for the network in advance: it is built one layer at a time, one neuron at a time, leading to predictors that aren't needlessly complex for a given task.

Benjamin Leblanc, Pascal Germain

Interpretability and explainability have gained more and more attention in the field of machine learning as they are crucial when it comes to high-stakes decisions and troubleshooting. Since both provide information about predictors and their decision process, they are often seen as two independent means for one single end. This view has led to a dichotomous literature: explainability techniques designed for complex black-box models, or interpretable approaches ignoring the many explainability tools. In this position paper, we challenge the common idea that interpretability and explainability are substitutes for one another by listing their principal shortcomings and discussing how both of them mitigate the drawbacks of the other. In doing so, we call for a new perspective on interpretability and explainability, and works targeting both topics simultaneously, leveraging each of their respective assets.

Benjamin Leblanc, Mathieu Bazinet, Nathaniel D'Amours et al.

Both PAC-Bayesian and Sample Compress learning frameworks are instrumental for deriving tight (non-vacuous) generalization bounds for neural networks. We leverage these results in a meta-learning scheme, relying on a hypernetwork that outputs the parameters of a downstream predictor from a dataset input. The originality of our approach lies in the investigated hypernetwork architectures that encode the dataset before decoding the parameters: (1) a PAC-Bayesian encoder that expresses a posterior distribution over a latent space, (2) a Sample Compress encoder that selects a small sample of the dataset input along with a message from a discrete set, and (3) a hybrid between both approaches motivated by a new Sample Compress theorem handling continuous messages. The latter theorem exploits the pivotal information transiting at the encoder-decoder junction in order to compute generalization guarantees for each downstream predictor obtained by our meta-learning scheme.

Benjamin Leblanc, Pascal Germain

PAC-Bayes is a popular and efficient framework for obtaining generalization guarantees in situations involving uncountable hypothesis spaces. Unfortunately, in its classical formulation, it only provides guarantees on the expected risk of a randomly sampled hypothesis. This requires stochastic predictions at test time, making PAC-Bayes unusable in many practical situations where a single deterministic hypothesis must be deployed. We propose a unified framework to extract guarantees holding for a single hypothesis from stochastic PAC-Bayesian guarantees. We present a general oracle bound and derive from it a numerical bound and a specialization to majority vote. We empirically show that our approach consistently outperforms popular baselines (by up to a factor of 2) when it comes to generalization bounds on deterministic classifiers.

Louis Fortier-Dubois, Gaël Letarte, Benjamin Leblanc et al.

Considering a probability distribution over parameters is known as an efficient strategy to learn a neural network with non-differentiable activation functions. We study the expectation of a probabilistic neural network as a predictor by itself, focusing on the aggregation of binary activated neural networks with normal distributions over real-valued weights. Our work leverages a recent analysis derived from the PAC-Bayesian framework that derives tight generalization bounds and learning procedures for the expected output value of such an aggregation, which is given by an analytical expression. While the combinatorial nature of the latter has been circumvented by approximations in previous works, we show that the exact computation remains tractable for deep but narrow neural networks, thanks to a dynamic programming approach. This leads us to a peculiar bound minimization learning algorithm for binary activated neural networks, where the forward pass propagates probabilities over representations instead of activation values. A stochastic counterpart that scales to wide architectures is proposed.