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Francois Caron

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13 papers

2 author rows

NeurIPS Conference 2025 Conference Paper

Anytime-valid, Bayes-assisted, Prediction-Powered Inference

Valentin Kilian
Stefano Cortinovis
Francois Caron

Given a large pool of unlabelled data and a smaller amount of labels, prediction-powered inference (PPI) leverages machine learning predictions to increase the statistical efficiency of confidence interval procedures based solely on labelled data, while preserving fixed-time validity. In this paper, we extend the PPI framework to the sequential setting, where labelled and unlabelled datasets grow over time. Exploiting Ville's inequality and the method of mixtures, we propose prediction-powered confidence sequence procedures that are asymptotically valid uniformly over time and naturally accommodate prior knowledge on the quality of the predictions to further boost efficiency. We carefully illustrate the design choices behind our method and demonstrate its effectiveness in real and synthetic examples.

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ICML Conference 2025 Conference Paper

FAB-PPI: Frequentist, Assisted by Bayes, Prediction-Powered Inference

Stefano Cortinovis
Francois Caron

Prediction-powered inference (PPI) enables valid statistical inference by combining experimental data with machine learning predictions. When a sufficient number of high-quality predictions is available, PPI results in more accurate estimates and tighter confidence intervals than traditional methods. In this paper, we propose to inform the PPI framework with prior knowledge on the quality of the predictions. The resulting method, which we call frequentist, assisted by Bayes, PPI (FAB-PPI), improves over PPI when the observed prediction quality is likely under the prior, while maintaining its frequentist guarantees. Furthermore, when using heavy-tailed priors, FAB-PPI adaptively reverts to standard PPI in low prior probability regions. We demonstrate the benefits of FAB-PPI in real and synthetic examples.

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TMLR Journal 2025 Journal Article

Over-parameterised Shallow Neural Networks with Asymmetrical Node Scaling: Global Convergence Guarantees and Feature Learning

Francois Caron
Fadhel Ayed
Paul Jung
Hoil Lee
Juho Lee
Hongseok Yang

We consider gradient-based optimisation of wide, shallow neural networks, where the output of each hidden node is scaled by a positive parameter. The scaling parameters are non-identical, differing from the classical Neural Tangent Kernel (NTK) parameterisation. We prove that for large such neural networks, with high probability, gradient flow and gradient descent converge to a global minimum and can learn features in some sense, unlike in the NTK parameterisation. We perform experiments illustrating our theoretical results and discuss the benefits of such scaling in terms of prunability and transfer learning.

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JMLR Journal 2023 Journal Article

Deep Neural Networks with Dependent Weights: Gaussian Process Mixture Limit, Heavy Tails, Sparsity and Compressibility

Hoil Lee
Fadhel Ayed
Paul Jung
Juho Lee
Hongseok Yang
Francois Caron

This article studies the infinite-width limit of deep feedforward neural networks whose weights are dependent, and modelled via a mixture of Gaussian distributions. Each hidden node of the network is assigned a nonnegative random variable that controls the variance of the outgoing weights of that node. We make minimal assumptions on these per-node random variables: they are iid and their sum, in each layer, converges to some finite random variable in the infinite-width limit. Under this model, we show that each layer of the infinite-width neural network can be characterised by two simple quantities: a non-negative scalar parameter and a Lévy measure on the positive reals. If the scalar parameters are strictly positive and the Lévy measures are trivial at all hidden layers, then one recovers the classical Gaussian process (GP) limit, obtained with iid Gaussian weights. More interestingly, if the Lévy measure of at least one layer is non-trivial, we obtain a mixture of Gaussian processes (MoGP) in the large-width limit. The behaviour of the neural network in this regime is very different from the GP regime. One obtains correlated outputs, with non-Gaussian distributions, possibly with heavy tails. Additionally, we show that, in this regime, the weights are compressible, and some nodes have asymptotically non-negligible contributions, therefore representing important hidden features. Many sparsity-promoting neural network models can be recast as special cases of our approach, and we discuss their infinite-width limits; we also present an asymptotic analysis of the pruning error. We illustrate some of the benefits of the MoGP regime over the GP regime in terms of representation learning and compressibility on simulated, MNIST and Fashion MNIST datasets. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2023. ( edit, beta )

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ICML Conference 2019 Conference Paper

Beyond the Chinese Restaurant and Pitman-Yor processes: Statistical Models with double power-law behavior

Fadhel Ayed
Juho Lee 0001
Francois Caron

Bayesian nonparametric approaches, in particular the Pitman-Yor process and the associated two-parameter Chinese Restaurant process, have been successfully used in applications where the data exhibit a power-law behavior. Examples include natural language processing, natural images or networks. There is also growing empirical evidence suggesting that some datasets exhibit a two-regime power-law behavior: one regime for small frequencies, and a second regime, with a different exponent, for high frequencies. In this paper, we introduce a class of completely random measures which are doubly regularly-varying. Contrary to the Pitman-Yor process, we show that when completely random measures in this class are normalized to obtain random probability measures and associated random partitions, such partitions exhibit a double power-law behavior. We present two general constructions and discuss in particular two models within this class: the beta prime process (Broderick et al. (2015, 2018) and a novel process called generalized BFRY process. We derive efficient Markov chain Monte Carlo algorithms to estimate the parameters of these models. Finally, we show that the proposed models provide a better fit than the Pitman-Yor process on various datasets.

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NeurIPS Conference 2018 Conference Paper

Modelling sparsity, heterogeneity, reciprocity and community structure in temporal interaction data

Xenia Miscouridou
Francois Caron
Yee Whye Teh

We propose a novel class of network models for temporal dyadic interaction data. Our objective is to capture important features often observed in social interactions: sparsity, degree heterogeneity, community structure and reciprocity. We use mutually-exciting Hawkes processes to model the interactions between each (directed) pair of individuals. The intensity of each process allows interactions to arise as responses to opposite interactions (reciprocity), or due to shared interests between individuals (community structure). For sparsity and degree heterogeneity, we build the non time dependent part of the intensity function on compound random measures following Todeschini et al. , 2016. We conduct experiments on real-world temporal interaction data and show that the proposed model outperforms competing approaches for link prediction, and leads to interpretable parameters.

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NeurIPS Conference 2017 Conference Paper

Clone MCMC: Parallel High-Dimensional Gaussian Gibbs Sampling

Andrei-Cristian Barbos
Francois Caron
Jean-François Giovannelli
Arnaud Doucet

We propose a generalized Gibbs sampler algorithm for obtaining samples approximately distributed from a high-dimensional Gaussian distribution. Similarly to Hogwild methods, our approach does not target the original Gaussian distribution of interest, but an approximation to it. Contrary to Hogwild methods, a single parameter allows us to trade bias for variance. We show empirically that our method is very flexible and performs well compared to Hogwild-type algorithms.

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NeurIPS Conference 2012 Conference Paper

Bayesian nonparametric models for bipartite graphs

Francois Caron

We develop a novel Bayesian nonparametric model for random bipartite graphs. The model is based on the theory of completely random measures and is able to handle a potentially infinite number of nodes. We show that the model has appealing properties and in particular it may exhibit a power-law behavior. We derive a posterior characterization, an Indian Buffet-like generative process for network growth, and a simple and efficient Gibbs sampler for posterior simulation. Our model is shown to be well fitted to several real-world social networks.

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NeurIPS Conference 2012 Conference Paper

Bayesian nonparametric models for ranked data

Francois Caron
Yee Teh

We develop a Bayesian nonparametric extension of the popular Plackett-Luce choice model that can handle an infinite number of choice items. Our framework is based on the theory of random atomic measures, with the prior specified by a gamma process. We derive a posterior characterization and a simple and effective Gibbs sampler for posterior simulation. We then develop a time-varying extension of our model, and apply our model to the New York Times lists of weekly bestselling books.

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UAI Conference 2012 Conference Paper

Plackett-Luce regression: A new Bayesian model for polychotomous data

Cédric Archambeau
Francois Caron

Multinomial logistic regression is one of the most popular models for modelling the effect of explanatory variables on a subject choice between a set of specified options. This model has found numerous applications in machine learning, psychology or economy. Bayesian inference in this model is non trivial and requires, either to resort to a Metropolis- Hastings algorithm, or rejection sampling within a Gibbs sampler. In this paper, we propose an alternative model to multinomial logistic regression. The model builds on the Plackett-Luce model, a popular model for multiple comparisons. We show that the introduction of a suitable set of auxiliary variables leads to an Expectation-Maximization algorithm to find Maximum A Posteriori estimates of the parameters. We further provide a full Bayesian treatment by deriving a Gibbs sampler, which only requires to sample from highly standard distributions. We also propose a variational approximate inference scheme. All are very simple to implement. One property of our Plackett-Luce regression model is that it learns a sparse set of feature weights. We compare our method to sparse Bayesian multinomial logistic regression and show that it is competitive, especially in presence of polychotomous data.

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NeurIPS Conference 2009 Conference Paper

Bayesian Nonparametric Models on Decomposable Graphs

Francois Caron
Arnaud Doucet

Over recent years Dirichlet processes and the associated Chinese restaurant process (CRP) have found many applications in clustering while the Indian buffet process (IBP) is increasingly used to describe latent feature models. In the clustering case, we associate to each data point a latent allocation variable. These latent variables can share the same value and this induces a partition of the data set. The CRP is a prior distribution on such partitions. In latent feature models, we associate to each data point a potentially infinite number of binary latent variables indicating the possession of some features and the IBP is a prior distribution on the associated infinite binary matrix. These prior distributions are attractive because they ensure exchangeability (over samples). We propose here extensions of these models to decomposable graphs. These models have appealing properties and can be easily learned using Monte Carlo techniques.

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ICML Conference 2008 Conference Paper

Sparse Bayesian nonparametric regression

Francois Caron
Arnaud Doucet

One of the most common problems in machine learning and statistics consists of estimating the mean response Xβ from a vector of observations y assuming y = Xβ + ε where X is known, β is a vector of parameters of interest and ε a vector of stochastic errors. We are particularly interested here in the case where the dimension K of β is much higher than the dimension of y . We propose some flexible Bayesian models which can yield sparse estimates of β. We show that as K → ∞ these models are closely related to a class of Lévy processes. Simulations demonstrate that our models outperform significantly a range of popular alternatives.

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UAI Conference 2007 Conference Paper

Generalized Polya Urn for Time-varying Dirichlet Process Mixtures

Francois Caron
Manuel Davy
Arnaud Doucet

Dirichlet Process Mixtures (DPMs) are a popular class of statistical models to perform density estimation and clustering. However, when the data available have a distribution evolving over time, such models are inadequate. We introduce here a class of time-varying DPMs which ensures that at each time step the random distribution follows a DPM model. Our model relies on an intuitive and simple generalized Polya urn scheme. Inference is performed using Markov chain Monte Carlo and Sequential Monte Carlo. We demonstrate our model on various applications.

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