arXiv subjects

Alix Lhéritier

Publications and source records attributed to Alix Lhéritier.

5 recordsLinked to original sources

arXiv2026

Circula-based multivariate distributions on the flat torus, with applications in structural biology

Modeling dependencies between random variables independently from their marginals is fundamental in applications ranging from finance to (structural) biology. In this work, we undertake this problem using circula to model data living on the $d$-dimensional flat torus $\mathbb{T}^d$, making two contributions. First, using a low rank covariance structure to define circulae based on a latent variable model, we design the first closed-form normalized distribution on the flat torus $\mathbb{T}^d$--with covariance structure. Second, building on this framework, we propose the first models for joint distributions of torsion angles (backbone and side-chains) for neighboring amino-acids in proteins. In practice, we fit mixtures on flat torii from $\mathbb{T}^{2}$ to $\mathbb{T}^{14}$, and show they are SOTA in terms of likelihood and sparsity. We anticipate that these models will prove fundamental to move from discrete structural studies like in AlphaFold2, to thermodynamics and kinetics, which are the ultimate goals in theoretical biophysics.

stat.AP↗

arXiv2025

Variational Inference for Quantum HyperNetworks

Binary Neural Networks (BiNNs), which employ single-bit precision weights, have emerged as a promising solution to reduce memory usage and power consumption while maintaining competitive performance in large-scale systems. However, training BiNNs remains a significant challenge due to the limitations of conventional training algorithms. Quantum HyperNetworks offer a novel paradigm for enhancing the optimization of BiNN by leveraging quantum computing. Specifically, a Variational Quantum Algorithm is employed to generate binary weights through quantum circuit measurements, while key quantum phenomena such as superposition and entanglement facilitate the exploration of a broader solution space. In this work, we establish a connection between this approach and Bayesian inference by deriving the Evidence Lower Bound (ELBO), when direct access to the output distribution is available (i.e., in simulations), and introducing a surrogate ELBO based on the Maximum Mean Discrepancy (MMD) metric for scenarios involving implicit distributions, as commonly encountered in practice. Our experimental results demonstrate that the proposed methods outperform standard Maximum Likelihood Estimation (MLE), improving trainability and generalization.

quant-ph↗

arXiv2022

A Cramér Distance perspective on Quantile Regression based Distributional Reinforcement Learning

Distributional reinforcement learning (DRL) extends the value-based approach by approximating the full distribution over future returns instead of the mean only, providing a richer signal that leads to improved performances. Quantile Regression (QR) based methods like QR-DQN project arbitrary distributions into a parametric subset of staircase distributions by minimizing the 1-Wasserstein distance. However, due to biases in the gradients, the quantile regression loss is used instead for training, guaranteeing the same minimizer and enjoying unbiased gradients. Non-crossing constraints on the quantiles have been shown to improve the performance of QR-DQN for uncertainty-based exploration strategies. The contribution of this work is in the setting of fixed quantile levels and is twofold. First, we prove that the Cramér distance yields a projection that coincides with the 1-Wasserstein one and that, under non-crossing constraints, the squared Cramér and the quantile regression losses yield collinear gradients, shedding light on the connection between these important elements of DRL. Second, we propose a low complexity algorithm to compute the Cramér distance.

stat.ML↗

arXiv2020

Low-Complexity Nonparametric Bayesian Online Prediction with Universal Guarantees

We propose a novel nonparametric online predictor for discrete labels conditioned on multivariate continuous features. The predictor is based on a feature space discretization induced by a full-fledged k-d tree with randomly picked directions and a recursive Bayesian distribution, which allows to automatically learn the most relevant feature scales characterizing the conditional distribution. We prove its pointwise universality, i.e., it achieves a normalized log loss performance asymptotically as good as the true conditional entropy of the labels given the features. The time complexity to process the $n$-th sample point is $O(\log n)$ in probability with respect to the distribution generating the data points, whereas other exact nonparametric methods require to process all past observations. Experiments on challenging datasets show the computational and statistical efficiency of our algorithm in comparison to standard and state-of-the-art methods.

cs.LG↗

arXiv2020

PCMC-Net: Feature-based Pairwise Choice Markov Chains

Pairwise Choice Markov Chains (PCMC) have been recently introduced to overcome limitations of choice models based on traditional axioms unable to express empirical observations from modern behavior economics like context effects occurring when a choice between two options is altered by adding a third alternative. The inference approach that estimates the transition rates between each possible pair of alternatives via maximum likelihood suffers when the examples of each alternative are scarce and is inappropriate when new alternatives can be observed at test time. In this work, we propose an amortized inference approach for PCMC by embedding its definition into a neural network that represents transition rates as a function of the alternatives' and individual's features. We apply our construction to the complex case of airline itinerary booking where singletons are common (due to varying prices and individual-specific itineraries), and context effects and behaviors strongly dependent on market segments are observed. Experiments show our network significantly outperforming, in terms of prediction accuracy and logarithmic loss, feature engineered standard and latent class Multinomial Logit models as well as recent machine learning approaches.

cs.LG↗