arXiv subjects

Sylvain Le Corff

Publications and source records attributed to Sylvain Le Corff.

At least 37 records · Page 2Linked to original sources

arXiv2024

Importance sampling for online variational learning

This article addresses online variational estimation in state-space models. We focus on learning the smoothing distribution, i.e. the joint distribution of the latent states given the observations, using a variational approach together with Monte Carlo importance sampling. We propose an efficient algorithm for computing the gradient of the evidence lower bound (ELBO) in the context of streaming data, where observations arrive sequentially. Our contributions include a computationally efficient online ELBO estimator, demonstrated performance in offline and true online settings, and adaptability for computing general expectations under joint smoothing distributions.

stat.AP↗

arXiv2023

Variational excess risk bound for general state space models

In this paper, we consider variational autoencoders (VAE) for general state space models. We consider a backward factorization of the variational distributions to analyze the excess risk associated with VAE. Such backward factorizations were recently proposed to perform online variational learning and to obtain upper bounds on the variational estimation error. When independent trajectories of sequences are observed and under strong mixing assumptions on the state space model and on the variational distribution, we provide an oracle inequality explicit in the number of samples and in the length of the observation sequences. We then derive consequences of this theoretical result. In particular, when the data distribution is given by a state space model, we provide an upper bound for the Kullback-Leibler divergence between the data distribution and its estimator and between the variational posterior and the estimated state space posterior distributions.Under classical assumptions, we prove that our results can be applied to Gaussian backward kernels built with dense and recurrent neural networks.

stat.ME↗

arXiv2023

Monte Carlo guided Diffusion for Bayesian linear inverse problems

Ill-posed linear inverse problems arise frequently in various applications, from computational photography to medical imaging. A recent line of research exploits Bayesian inference with informative priors to handle the ill-posedness of such problems. Amongst such priors, score-based generative models (SGM) have recently been successfully applied to several different inverse problems. In this study, we exploit the particular structure of the prior defined by the SGM to define a sequence of intermediate linear inverse problems. As the noise level decreases, the posteriors of these inverse problems get closer to the target posterior of the original inverse problem. To sample from this sequence of posteriors, we propose the use of Sequential Monte Carlo (SMC) methods. The proposed algorithm, MCGDiff, is shown to be theoretically grounded and we provide numerical simulations showing that it outperforms competing baselines when dealing with ill-posed inverse problems in a Bayesian setting.

stat.ML↗

arXiv2023

HERMES: Hybrid Error-corrector Model with inclusion of External Signals for nonstationary fashion time series

Developing models and algorithms to predict nonstationary time series is a long standing statistical problem. It is crucial for many applications, in particular for fashion or retail industries, to make optimal inventory decisions and avoid massive wastes. By tracking thousands of fashion trends on social media with state-of-the-art computer vision approaches, we propose a new model for fashion time series forecasting. Our contribution is twofold. We first provide publicly a dataset gathering 10000 weekly fashion time series. As influence dynamics are the key of emerging trend detection, we associate with each time series an external weak signal representing behaviours of influencers. Secondly, to leverage such a dataset, we propose a new hybrid forecasting model. Our approach combines per-time-series parametric models with seasonal components and a global recurrent neural network to include sporadic external signals. This hybrid model provides state-of-the-art results on the proposed fashion dataset, on the weekly time series of the M4 competition, and illustrates the benefit of the contribution of external weak signals.

eess.SP↗

arXiv2023

Variational latent discrete representation for time series modelling

Discrete latent space models have recently achieved performance on par with their continuous counterparts in deep variational inference. While they still face various implementation challenges, these models offer the opportunity for a better interpretation of latent spaces, as well as a more direct representation of naturally discrete phenomena. Most recent approaches propose to train separately very high-dimensional prior models on the discrete latent data which is a challenging task on its own. In this paper, we introduce a latent data model where the discrete state is a Markov chain, which allows fast end-to-end training. The performance of our generative model is assessed on a building management dataset and on the publicly available Electricity Transformer Dataset.

stat.ML↗

arXiv2023

Last layer state space model for representation learning and uncertainty quantification

As sequential neural architectures become deeper and more complex, uncertainty estimation is more and more challenging. Efforts in quantifying uncertainty often rely on specific training procedures, and bear additional computational costs due to the dimensionality of such models. In this paper, we propose to decompose a classification or regression task in two steps: a representation learning stage to learn low-dimensional states, and a state space model for uncertainty estimation. This approach allows to separate representation learning and design of generative models. We demonstrate how predictive distributions can be estimated on top of an existing and trained neural network, by adding a state space-based last layer whose parameters are estimated with Sequential Monte Carlo methods. We apply our proposed methodology to the hourly estimation of Electricity Transformer Oil temperature, a publicly benchmarked dataset. Our model accounts for the noisy data structure, due to unknown or unavailable variables, and is able to provide confidence intervals on predictions.

stat.ML↗

arXiv2023

Asymptotic convergence of iterative optimization algorithms

This paper introduces a general framework for iterative optimization algorithms and establishes under general assumptions that their convergence is asymptotically geometric. We also prove that under appropriate assumptions, the rate of convergence can be lower bounded. The convergence is then only geometric, and we provide the exact asymptotic convergence rate. This framework allows to deal with constrained optimization and encompasses the Expectation Maximization algorithm and the mirror descent algorithm, as well as some variants such as the alpha-Expectation Maximization or the Mirror Prox algorithm.Furthermore, we establish sufficient conditions for the convergence of the Mirror Prox algorithm, under which the method converges systematically to the unique minimizer of a convex function on a convex compact set.

stat.ML↗

arXiv2023

Variance estimation for Sequential Monte Carlo Algorithms: a backward sampling approach

In this paper, we consider the problem of online asymptotic variance estimation for particle filtering and smoothing. Current solutions for the particle filter rely on the particle genealogy and are either unstable or hard to tune in practice. We propose to mitigate these limitations by introducing a new estimator of the asymptotic variance based on the so called backward weights. The resulting estimator is weakly consistent and trades computational cost for more stability and reduced variance. We also propose a more computationally efficient estimator inspired by the PaRIS algorithm of Olsson & Westerborn. As an application, particle smoothing is considered and an estimator of the asymptotic variance of the Forward Filtering Backward Smoothing estimator applied to additive functionals is provided.

stat.ME↗

arXiv2023

State and parameter learning with PaRIS particle Gibbs

Non-linear state-space models, also known as general hidden Markov models, are ubiquitous in statistical machine learning, being the most classical generative models for serial data and sequences in general. The particle-based, rapid incremental smoother PaRIS is a sequential Monte Carlo (SMC) technique allowing for efficient online approximation of expectations of additive functionals under the smoothing distribution in these models. Such expectations appear naturally in several learning contexts, such as likelihood estimation (MLE) and Markov score climbing (MSC). PARIS has linear computational complexity, limited memory requirements and comes with non-asymptotic bounds, convergence results and stability guarantees. Still, being based on self-normalised importance sampling, the PaRIS estimator is biased. Our first contribution is to design a novel additive smoothing algorithm, the Parisian particle Gibbs PPG sampler, which can be viewed as a PaRIS algorithm driven by conditional SMC moves, resulting in bias-reduced estimates of the targeted quantities. We substantiate the PPG algorithm with theoretical results, including new bounds on bias and variance as well as deviation inequalities. Our second contribution is to apply PPG in a learning framework, covering MLE and MSC as special examples. In this context, we establish, under standard assumptions, non-asymptotic bounds highlighting the value of bias reduction and the implicit Rao--Blackwellization of PPG. These are the first non-asymptotic results of this kind in this setting. We illustrate our theoretical results with numerical experiments supporting our claims.

stat.ME↗

arXiv2022

Diffusion bridges vector quantized Variational AutoEncoders

Vector Quantized-Variational AutoEncoders (VQ-VAE) are generative models based on discrete latent representations of the data, where inputs are mapped to a finite set of learned embeddings.To generate new samples, an autoregressive prior distribution over the discrete states must be trained separately. This prior is generally very complex and leads to slow generation. In this work, we propose a new model to train the prior and the encoder/decoder networks simultaneously. We build a diffusion bridge between a continuous coded vector and a non-informative prior distribution. The latent discrete states are then given as random functions of these continuous vectors. We show that our model is competitive with the autoregressive prior on the mini-Imagenet and CIFAR dataset and is efficient in both optimization and sampling. Our framework also extends the standard VQ-VAE and enables end-to-end training.

stat.ML↗

arXiv2022

Amortized backward variational inference in nonlinear state-space models

We consider the problem of state estimation in general state-space models using variational inference. For a generic variational family defined using the same backward decomposition as the actual joint smoothing distribution, we establish for the first time that, under mixing assumptions, the variational approximation of expectations of additive state functionals induces an error which grows at most linearly in the number of observations. This guarantee is consistent with the known upper bounds for the approximation of smoothing distributions using standard Monte Carlo methods. Moreover, we propose an amortized inference framework where a neural network shared over all times steps outputs the parameters of the variational kernels. We also study empirically parametrizations which allow analytical marginalization of the variational distributions, and therefore lead to efficient smoothing algorithms. Significant improvements are made over state-of-the art variational solutions, especially when the generative model depends on a strongly nonlinear and noninjective mixing function.

stat.ME↗

arXiv2021

End-to-end deep meta modelling to calibrate and optimize energy consumption and comfort

In this paper, we propose a new end-to-end methodology to optimize the energy performance as well as comfort and air quality in large buildings without any renovation work. We introduce a metamodel based on recurrent neural networks and trained to predict the behavior of a general class of buildings using a database sampled from a simulation program. This metamodel is then deployed in different frameworks and its parameters are calibrated using the specific data of two real buildings. Parameters are estimated by comparing the predictions of the metamodel with real data obtained from sensors using the CMA-ES algorithm, a derivative free optimization procedure. Then, energy consumptions are optimized while maintaining a target thermal comfort and air quality, using the NSGA-II multi-objective optimization procedure. The numerical experiments illustrate how this metamodel ensures a significant gain in energy efficiency, up to almost 10%, while being computationally much more appealing than numerical models and flexible enough to be adapted to several types of buildings.

eess.SP↗

arXiv2021

Disentangling Identifiable Features from Noisy Data with Structured Nonlinear ICA

We introduce a new general identifiable framework for principled disentanglement referred to as Structured Nonlinear Independent Component Analysis (SNICA). Our contribution is to extend the identifiability theory of deep generative models for a very broad class of structured models. While previous works have shown identifiability for specific classes of time-series models, our theorems extend this to more general temporal structures as well as to models with more complex structures such as spatial dependencies. In particular, we establish the major result that identifiability for this framework holds even in the presence of noise of unknown distribution. Finally, as an example of our framework's flexibility, we introduce the first nonlinear ICA model for time-series that combines the following very useful properties: it accounts for both nonstationarity and autocorrelation in a fully unsupervised setting; performs dimensionality reduction; models hidden states; and enables principled estimation and inference by variational maximum-likelihood.

stat.ML↗

arXiv2021

Learning Natural Language Generation from Scratch

This paper introduces TRUncated ReinForcement Learning for Language (TrufLL), an original ap-proach to train conditional language models from scratch by only using reinforcement learning (RL). AsRL methods unsuccessfully scale to large action spaces, we dynamically truncate the vocabulary spaceusing a generic language model. TrufLL thus enables to train a language agent by solely interacting withits environment without any task-specific prior knowledge; it is only guided with a task-agnostic languagemodel. Interestingly, this approach avoids the dependency to labelled datasets and inherently reduces pre-trained policy flaws such as language or exposure biases. We evaluate TrufLL on two visual questiongeneration tasks, for which we report positive results over performance and language metrics, which wethen corroborate with a human evaluation. To our knowledge, it is the first approach that successfullylearns a language generation policy (almost) from scratch.

cs.AI↗

arXiv2021

NEO: Non Equilibrium Sampling on the Orbit of a Deterministic Transform

Sampling from a complex distribution $π$ and approximating its intractable normalizing constant Z are challenging problems. In this paper, a novel family of importance samplers (IS) and Markov chain Monte Carlo (MCMC) samplers is derived. Given an invertible map T, these schemes combine (with weights) elements from the forward and backward Orbits through points sampled from a proposal distribution $ρ$. The map T does not leave the target $π$ invariant, hence the name NEO, standing for Non-Equilibrium Orbits. NEO-IS provides unbiased estimators of the normalizing constant and self-normalized IS estimators of expectations under $π$ while NEO-MCMC combines multiple NEO-IS estimates of the normalizing constant and an iterated sampling-importance resampling mechanism to sample from $π$. For T chosen as a discrete-time integrator of a conformal Hamiltonian system, NEO-IS achieves state-of-the art performance on difficult benchmarks and NEO-MCMC is able to explore highly multimodal targets. Additionally, we provide detailed theoretical results for both methods. In particular, we show that NEO-MCMC is uniformly geometrically ergodic and establish explicit mixing time estimates under mild conditions.

stat.CO↗

arXiv2021

Backward importance sampling for online estimation of state space models

This paper proposes a new Sequential Monte Carlo algorithm to perform online estimation in the context of state space models when either the transition density of the latent state or the conditional likelihood of an observation given a state is intractable. In this setting, obtaining low variance estimators of expectations under the posterior distributions of the unobserved states given the observations is a challenging task. Following recent theoretical results for pseudo-marginal sequential Monte Carlo smoothers, a pseudo-marginal backward importance sampling step is introduced to estimate such expectations. This new step allows to reduce very significantly the computational time of the existing numerical solutions based on an acceptance-rejection procedure for similar performance, and to broaden the class of eligible models for such methods. For instance, in the context of multivariate stochastic differential equations, the proposed algorithm makes use of unbiased estimates of the unknown transition densities under much weaker assumptions than standard alternatives. The performance of this estimator is assessed for high-dimensional discrete-time latent data models, for recursive maximum likelihood estimation in the context of partially observed diffusion process, and in the case of a bidimensional partially observed stochastic Lotka-Volterra model.

stat.AP↗

arXiv2021

A pseudo-marginal sequential Monte Carlo online smoothing algorithm

We consider online computation of expectations of additive state functionals under general path probability measures proportional to products of unnormalised transition densities. These transition densities are assumed to be intractable but possible to estimate, with or without bias. Using pseudo-marginalisation techniques we are able to extend the particle-based, rapid incremental smoother (PaRIS) algorithm proposed in [J.Olsson and J.Westerborn. Efficient particle-based online smoothing in general hidden Markov models: The PaRIS algorithm. Bernoulli, 23(3):1951--1996, 2017] to this setting. The resulting algorithm, which has a linear complexity in the number of particles and constant memory requirements, applies to a wide range of challenging path-space Monte Carlo problems, including smoothing in partially observed diffusion processes and models with intractable likelihood. The algorithm is furnished with several theoretical results, including a central limit theorem, establishing its convergence and numerical stability. Moreover, under strong mixing assumptions we establish a novel $O(n \varepsilon)$ bound on the asymptotic bias of the algorithm, where $n$ is the path length and $\varepsilon$ controls the bias of the density estimators.

stat.CO↗

arXiv2021

Deconvolution with unknown noise distribution is possible for multivariate signals

This paper considers the deconvolution problem in the case where the target signal is multidimensional and no information is known about the noise distribution. More precisely, no assumption is made on the noise distribution and no samples are available to estimate it: the deconvolution problem is solved based only on the corrupted signal observations. We establish the identifiability of the model up to translation when the signal has a Laplace transform with an exponential growth smaller than $2$ and when it can be decomposed into two dependent components. Then, we propose an estimator of the probability density function of the signal without any assumption on the noise distribution. As this estimator depends of the lightness of the tail of the signal distribution which is usually unknown, a model selection procedure is proposed to obtain an adaptive estimator in this parameter with the same rate of convergence as the estimator with a known tail parameter. Finally, we establish a lower bound on the minimax rate of convergence that matches the upper bound.

math.ST↗