Thibault Vatter

Thibault Vatter, Thomas Nagler

Vine copulas offer flexible multivariate dependence modeling and have become widely used in machine learning, yet structure learning remains a key challenge. Early heuristics like the greedy algorithm of Dissmann are still considered the gold standard, but often suboptimal. We propose random search algorithms that improve structure selection and a statistical framework based on model confidence sets, which provides theoretical guarantees on selection probabilities and a powerful foundation for ensembling. Empirical results on several real-world data sets show that our methods consistently outperform state-of-the-art approaches.

Tuoyuan Cheng, Thibault Vatter, Thomas Nagler et al.

Vine copulas are sophisticated models for multivariate distributions and are increasingly used in machine learning. To facilitate their integration into modern ML pipelines, we introduce the vine computational graph, a DAG that abstracts the multilevel vine structure and associated computations. On this foundation, we devise new algorithms for conditional sampling, efficient sampling-order scheduling, and constructing vine structures for customized conditioning variables. We implement these ideas in torchvinecopulib, a GPU-accelerated Python library built upon PyTorch, delivering improved scalability for fitting, sampling, and density evaluation. Our experiments illustrate how gradient flowing through the vine can improve Vine Copula Autoencoders and that incorporating vines for uncertainty quantification in deep learning can outperform MC-dropout, deep ensembles, and Bayesian Neural Networks in sharpness, calibration, and runtime. By recasting vine copula models as computational graphs, our work connects classical dependence modeling with modern deep-learning toolchains and facilitates the integration of state-of-the-art copula methods in modern machine learning pipelines.

Dar Gilboa, Ari Pakman, Thibault Vatter

Probability density models based on deep networks have achieved remarkable success in modeling complex high-dimensional datasets. However, unlike kernel density estimators, modern neural models do not yield marginals or conditionals in closed form, as these quantities require the evaluation of seldom tractable integrals. In this work, we present the Marginalizable Density Model Approximator (MDMA), a novel deep network architecture which provides closed form expressions for the probabilities, marginals and conditionals of any subset of the variables. The MDMA learns deep scalar representations for each individual variable and combines them via learned hierarchical tensor decompositions into a tractable yet expressive CDF, from which marginals and conditional densities are easily obtained. We illustrate the advantage of exact marginalizability in several tasks that are out of reach of previous deep network-based density estimation models, such as estimating mutual information between arbitrary subsets of variables, inferring causality by testing for conditional independence, and inference with missing data without the need for data imputation, outperforming state-of-the-art models on these tasks. The model also allows for parallelized sampling with only a logarithmic dependence of the time complexity on the number of variables.

Natasa Tagasovska, Damien Ackerer, Thibault Vatter

We introduce the vine copula autoencoder (VCAE), a flexible generative model for high-dimensional distributions built in a straightforward three-step procedure. First, an autoencoder (AE) compresses the data into a lower dimensional representation. Second, the multivariate distribution of the encoded data is estimated with vine copulas. Third, a generative model is obtained by combining the estimated distribution with the decoder part of the AE. As such, the proposed approach can transform any already trained AE into a flexible generative model at a low computational cost. This is an advantage over existing generative models such as adversarial networks and variational AEs which can be difficult to train and can impose strong assumptions on the latent space. Experiments on MNIST, Street View House Numbers and Large-Scale CelebFaces Attributes datasets show that VCAEs can achieve competitive results to standard baselines.

Damien Ackerer, Natasa Tagasovska, Thibault Vatter

We present a neural network (NN) approach to fit and predict implied volatility surfaces (IVSs). Atypically to standard NN applications, financial industry practitioners use such models equally to replicate market prices and to value other financial instruments. In other words, low training losses are as important as generalization capabilities. Importantly, IVS models need to generate realistic arbitrage-free option prices, meaning that no portfolio can lead to risk-free profits. We propose an approach guaranteeing the absence of arbitrage opportunities by penalizing the loss using soft constraints. Furthermore, our method can be combined with standard IVS models in quantitative finance, thus providing a NN-based correction when such models fail at replicating observed market prices. This lets practitioners use our approach as a plug-in on top of classical methods. Empirical results show that this approach is particularly useful when only sparse or erroneous data are available. We also quantify the uncertainty of the model predictions in regions with few or no observations. We further explore how deeper NNs improve over shallower ones, as well as other properties of the network architecture. We benchmark our method against standard IVS models. By evaluating our method on both training sets, and testing sets, namely, we highlight both their capacity to reproduce observed prices and predict new ones.

Vaibhav Kulkarni, Natasa Tagasovska, Thibault Vatter et al.

Mobility datasets are fundamental for evaluating algorithms pertaining to geographic information systems and facilitating experimental reproducibility. But privacy implications restrict sharing such datasets, as even aggregated location-data is vulnerable to membership inference attacks. Current synthetic mobility dataset generators attempt to superficially match a priori modeled mobility characteristics which do not accurately reflect the real-world characteristics. Modeling human mobility to generate synthetic yet semantically and statistically realistic trajectories is therefore crucial for publishing trajectory datasets having satisfactory utility level while preserving user privacy. Specifically, long-range dependencies inherent to human mobility are challenging to capture with both discriminative and generative models. In this paper, we benchmark the performance of recurrent neural architectures (RNNs), generative adversarial networks (GANs) and nonparametric copulas to generate synthetic mobility traces. We evaluate the generated trajectories with respect to their geographic and semantic similarity, circadian rhythms, long-range dependencies, training and generation time. We also include two sample tests to assess statistical similarity between the observed and simulated distributions, and we analyze the privacy tradeoffs with respect to membership inference and location-sequence attacks.

Natasa Tagasovska, Valérie Chavez-Demoulin, Thibault Vatter

Causal inference using observational data is challenging, especially in the bivariate case. Through the minimum description length principle, we link the postulate of independence between the generating mechanisms of the cause and of the effect given the cause to quantile regression. Based on this theory, we develop Bivariate Quantile Causal Discovery (bQCD), a new method to distinguish cause from effect assuming no confounding, selection bias or feedback. Because it uses multiple quantile levels instead of the conditional mean only, bQCD is adaptive not only to additive, but also to multiplicative or even location-scale generating mechanisms. To illustrate the effectiveness of our approach, we perform an extensive empirical comparison on both synthetic and real datasets. This study shows that bQCD is robust across different implementations of the method (i.e., the quantile regression), computationally efficient, and compares favorably to state-of-the-art methods.