arXiv subjects

Alexandre Bouchard-Côté

Publications and source records attributed to Alexandre Bouchard-Côté.

At least 19 recordsLinked to original sources

arXiv2026

Astrometric Evidence for Outer Giant Planets in Known Exoplanet Systems

Outer giant planets can influence the formation and dynamical evolution of their planetary systems. However, their long orbital periods make them difficult to detect using transit and radial velocity (RV) techniques. Measurements from Hipparcos, Gaia DR2 and DR3 (G23H) can detect the stellar reflex motion induced by distant companions before the release of Gaia DR4 epoch astrometry. Using the G23H catalogue, we identify 29 outer companion candidates ($a_{median}$ $>$ 8.4 AU) in known transiting and RV systems. Starting from 170 exoplanet hosts with $P(\mathrm{companion})>0.75$ and posterior support for $0.3$--$13\,M_{\rm J}$ companions, we retain 29 systems where each selected component has a median semi-major axis beyond the outermost known planet with every known planet outside its 95\% highest posterior density region in mass and semi-major axis. We incorporate published RV and imaging data from the literature to further constrain the outer candidate's mass and semi-major axis. In eight systems present in the sample, an RV variation or trend has already been reported in the literature. The reported candidates could potentially explain these RV variations, but joint astrometric and RV fits are needed to establish whether the same companions produce both signals. These results provide a set of high priority targets for further RV monitoring and joint orbit analysis with Gaia DR4. If these companions are confirmed, their orbital constraints will provide a starting point for studies of their influence on the dynamical evolution of the known inner planets.

astro-ph.EP↗

arXiv2026

Hessian-informed, Coordinate Friendly Hamiltonian Monte Carlo in Linear Time

Riemannian Hamiltonian Monte Carlo (RHMC) is a promising MCMC methodology thanks to its ability to accommodate position-dependent preconditioning and multi-step proposals. While RHMC performs well in low dimensions, it becomes infeasible in high dimensions due to its $O(d^3)$ cost per fixed-point iteration, where $d$ is the dimension of the target density. Even when the position-dependent preconditioner is based on the diagonal of the Hessian, the cost is still $O(d^2)$ per fixed-point iteration. In this paper, we propose a computational method to reduce the computational complexity of RHMC fixed-point iterations with diagonal preconditioners from $O(d^2)$ to $O(d)$ for targets with ``coordinate friendly'' structures. This distribution class includes generalized linear models as well as other dense and sparse graphical models. The method is expressed as manipulating the compute graph and can therefore be automated to work on black box targets. Finally, we show empirically that our implementation of RHMC results in better sample quality per unit of compute time for various target distributions compared to state-of-the-art HMC NUTS algorithms with both position-independent and position-dependent preconditioners.

stat.CO↗

arXiv2026

Variational phylogenetic inference with products over bipartitions

Bayesian phylogenetics is vital for understanding evolutionary dynamics, and requires accurate and efficient approximation of posterior distributions over trees. In this work, we develop a variational Bayesian approach for ultrametric phylogenetic trees. We present a novel variational family based on coalescent times of a single-linkage clustering and derive a closed-form density for the resulting distribution over trees. Unlike existing methods for ultrametric trees, our method performs inference over all of tree space, it does not require any Markov chain Monte Carlo subroutines, and our variational family is differentiable. Through experiments on benchmark genomic datasets and an application to the viral RNA of SARS-CoV-2, we demonstrate that our method achieves competitive accuracy while requiring significantly fewer gradient evaluations than existing state-of-the-art techniques.

stat.ML↗

arXiv2026

Detecting and Characterizing Companions with a Calibrated Gaia DR2, DR3, and Hipparcos Catalog (G23H)

Gaia DR4 epoch astrometry will enable the detection of thousands of exoplanets through astrometric motion. Here, we present a composite catalog and modeling framework that extracts the maximum information from existing Hipparcos and Gaia data releases. We calibrate Gaia DR2 proper motions and DR3-DR2 scaled position differences against the Gaia DR3 reference frame, and combine these with the Hipparcos-Gaia Catalog of Accelerations, the Hipparcos intermediate astrometric data, Gaia astrometric excess noise, and Gaia radial velocity variability constraints. We implement a joint likelihood model for these data in Octofitter that marginalizes over Gaia's unpublished observation epochs. This results in full orbit posteriors that can be computed uniformly for a large class of companions. We compare these posteriors to published orbital solutions for 25 stellar binaries from the Sixth Catalog of Orbits of Visual Binary Stars, recovering all companions at high significance and broadly consistent orbital separations. We then recover independent evidence to support 94 of 120 tested Jovian exoplanetary systems from the NASA Exoplanet Archive (plus 3 known stellar companions, and one previously detected planet we now rule out). We demonstrate that in cases like 14 Her b, the posteriors confirm the planetary nature of a signal using only Gaia and Hipparcos data. We find no false positives among 25 RV-quiet standard stars without significant Hipparcos-Gaia accelerations. Our method can break degeneracies inherent to proper motion anomaly or excess noise modeling alone by resolving orbital curvature within the Gaia baseline. The catalog and updated Octofitter are made publicly available to the community.

astro-ph.EP↗

arXiv2025

Optimised Annealed Sequential Monte Carlo Samplers

Annealed Sequential Monte Carlo (ASMC) samplers are special cases of SMC samplers where the sequence of distributions can be embedded in a smooth path of distributions. Using this underlying path and a performance model based on the variance of the normalising constant estimator, we systematically study dense-schedule limits. From our theory emerges a notion of global barrier, capturing the inherent complexity of normalising constant approximation under our performance model. We then turn the resulting approximations into surrogate objective functions of algorithm performance, using them to guide method development. This leads to novel adaptive methods, Optimised Annealed SMC (OASMC), which address practical difficulties inherent in previous adaptive SMC methods. First, our OASMC algorithms are predictable: they produce a sequence of increasingly precise estimates at deterministic, known times. Second, Optimised Annealed Importance Sampling (OAIS), a special case of OASMC, enables schedule adaptation at a memory cost constant in the number of particles, requiring significantly less communication. Finally, these characteristics make OAIS highly efficient on GPUs. We provide an open-source, high-performance GPU implementation of our method and demonstrate up to a hundred-fold speed improvement compared to state-of-the-art adaptive AIS methods.

stat.CO↗

arXiv2025

AutoGD: Automatic Learning Rate Selection for Gradient Descent

The performance of gradient-based optimization methods, such as standard gradient descent (GD), greatly depends on the choice of learning rate. However, it can require a non-trivial amount of user tuning effort to select an appropriate learning rate schedule. When such methods appear as inner loops of other algorithms, expecting the user to tune the learning rates may be impractical. To address this, we introduce AutoGD: a gradient descent method that automatically determines whether to increase or decrease the learning rate at a given iteration. We establish the convergence of AutoGD, and show that we can recover the optimal rate of GD (up to a constant) for a broad class of functions without knowledge of smoothness constants. Experiments on a variety of traditional problems and variational inference optimization tasks demonstrate strong performance of the method, along with its extensions to AutoBFGS and AutoLBFGS.

cs.LG↗

arXiv2025

AutoSGD: Automatic Learning Rate Selection for Stochastic Gradient Descent

The learning rate is an important tuning parameter for stochastic gradient descent (SGD) and can greatly influence its performance. However, appropriate selection of a learning rate schedule across all iterations typically requires a non-trivial amount of user tuning effort. To address this, we introduce AutoSGD: an SGD method that automatically determines whether to increase or decrease the learning rate at a given iteration and then takes appropriate action. We introduce theory supporting the convergence of AutoSGD, along with its deterministic counterpart for standard gradient descent. Empirical results suggest strong performance of the method on a variety of traditional optimization problems and machine learning tasks.

cs.LG↗

arXiv2025

AutoStep: Locally adaptive involutive MCMC

Many common Markov chain Monte Carlo (MCMC) kernels can be formulated using a deterministic involutive proposal with a step size parameter. Selecting an appropriate step size is often a challenging task in practice; and for complex multiscale targets, there may not be one choice of step size that works well globally. In this work, we address this problem with a novel class of involutive MCMC methods -- AutoStep MCMC -- that selects an appropriate step size at each iteration adapted to the local geometry of the target distribution. We prove that under mild conditions AutoStep MCMC is $π$-invariant, irreducible, and aperiodic, and obtain bounds on expected energy jump distance and cost per iteration. Empirical results examine the robustness and efficacy of our proposed step size selection procedure, and show that AutoStep MCMC is competitive with state-of-the-art methods in terms of effective sample size per unit cost on a range of challenging target distributions.

stat.CO↗

arXiv2025

Is Gibbs sampling faster than Hamiltonian Monte Carlo on GLMs?

The Hamiltonian Monte Carlo (HMC) algorithm is often lauded for its ability to effectively sample from high-dimensional distributions. In this paper we challenge the presumed domination of HMC for the Bayesian analysis of GLMs. By utilizing the structure of the compute graph rather than the graphical model, we show a reduction of the time per sweep of a full-scan Gibbs sampler from $O(d^2)$ to $O(d)$, where $d$ is the number of GLM parameters. A simple change to the implementation of the Gibbs sampler allows us to perform Bayesian inference on high-dimensional GLMs that are practically infeasible with traditional Gibbs sampler implementations. We empirically demonstrate a substantial increase in effective sample size per time when comparing our Gibbs algorithms to state-of-the-art HMC algorithms. While Gibbs is superior in terms of dimension scaling, neither Gibbs nor HMC dominate the other: we provide numerical and theoretical evidence that HMC retains an edge in certain circumstances thanks to its advantageous condition number scaling. Interestingly, for GLMs of fixed data size, we observe that increasing dimensionality can stabilize or even decrease condition number, shedding light on the empirical advantage of our efficient Gibbs sampler.

stat.CO↗

arXiv2025

On the Orbit of the Binary Brown Dwarf Companion GL229 Ba and Bb

The companion GL229B was recently resolved by Xuan et al. (2024) as a tight binary of two brown dwarfs (Ba and Bb) through VLTI-GRAVITY interferometry and VLT-CRIRES+ RV measurements. Here, we present Bayesian models of the interferometric and RV data in additional detail, along with an updated outer orbit of the brown dwarf pair about the primary. To create a model of the inner orbit with robust uncertainties, we apply kernel phases to the GRAVITY data to address baseline redundancy in the raw closure phases. Using parallel tempering, we constrain the binary's orbit using only VLTI-GRAVITY data, despite each epoch having low visibility-plane coverage and/or SNR. We demonstrate very agreement the VLTI-GRAVITY and CRIRES+ datasets and find that the inner binary has a period of 12.1346$\pm$0.0011 days, eccentricity of 0.2317$\pm$0.0025, and total mass of 71.0$\pm$0.4 Mjup, with Ba and Bb having masses of 37.7$\pm$1.1Mjup and 33.4$\pm$1.0Mjup respectively. With new Keck/NIRC2 astrometry, we update the outer orbit GL229B around the primary. We find a semi-major axis of 42.9+3.0-2.4AU, eccentricity of 0.736$\pm$0.014, and a total mass for B of 71.7$\pm$0.6Mjup, consistent with that derived from the inner orbit. We find a mutual inclination of 31$\pm$2.5deg, below the threshold for Kozai-Lidov oscillations. The agreement on the mass of Ba+Bb between the inner and outer orbits is an important test of our ability to model RV, astrometry, and Hipparcos-Gaia proper motion anomaly. Our methodological advances in handling interferometric data with low SNR and sparse UV-coverage will benefit future observations of rapidly-orbiting companions with VLTI-GRAVITY.

astro-ph.SR↗

arXiv2024

Uniform Ergodicity of Parallel Tempering With Efficient Local Exploration

Non-reversible parallel tempering (NRPT) is an effective algorithm for sampling from target distributions with complex geometry, such as those arising from posterior distributions of weakly identifiable and high-dimensional Bayesian models. In this work we establish the uniform (geometric) ergodicity of NRPT under a model of efficient local exploration. The uniform ergodicity log rates are inversely proportional to an easily-estimable divergence, the global communication barrier (GCB), which was recently introduced in the literature. We obtain analogous ergodicity results for classical reversible parallel tempering, providing new evidence that NRPT dominates its reversible counterpart. Our results are based on an analysis of the hitting time of a continuous-time persistent random walk, which is also of independent interest. The rates that we obtain reflect real experiments well for distributions where global exploration is not possible without parallel tempering.

stat.CO↗

arXiv2024

autoMALA: Locally adaptive Metropolis-adjusted Langevin algorithm

Selecting the step size for the Metropolis-adjusted Langevin algorithm (MALA) is necessary in order to obtain satisfactory performance. However, finding an adequate step size for an arbitrary target distribution can be a difficult task and even the best step size can perform poorly in specific regions of the space when the target distribution is sufficiently complex. To resolve this issue we introduce autoMALA, a new Markov chain Monte Carlo algorithm based on MALA that automatically sets its step size at each iteration based on the local geometry of the target distribution. We prove that autoMALA has the correct invariant distribution, despite continual automatic adjustments of the step size. Our experiments demonstrate that autoMALA is competitive with related state-of-the-art MCMC methods, in terms of the number of log density evaluations per effective sample, and it outperforms state-of-the-art samplers on targets with varying geometries. Furthermore, we find that autoMALA tends to find step sizes comparable to optimally-tuned MALA when a fixed step size suffices for the whole domain.

stat.CO↗

arXiv2024

MCMC-driven learning

This paper is intended to appear as a chapter for the Handbook of Markov Chain Monte Carlo. The goal of this chapter is to unify various problems at the intersection of Markov chain Monte Carlo (MCMC) and machine learning$\unicode{x2014}$which includes black-box variational inference, adaptive MCMC, normalizing flow construction and transport-assisted MCMC, surrogate-likelihood MCMC, coreset construction for MCMC with big data, Markov chain gradient descent, Markovian score climbing, and more$\unicode{x2014}$within one common framework. By doing so, the theory and methods developed for each may be translated and generalized.

stat.ML↗

arXiv2024

Automatic Regenerative Simulation via Non-Reversible Simulated Tempering

Simulated Tempering (ST) is an MCMC algorithm for complex target distributions that operates on a path between the target and a more amenable reference distribution. Crucially, if the reference enables i.i.d. sampling, ST is regenerative and can be parallelized across independent tours. However, the difficulty of tuning ST has hindered its widespread adoption. In this work, we develop a simple nonreversible ST (NRST) algorithm, a general theoretical analysis of ST, and an automated tuning procedure for ST. A core contribution that arises from the analysis is a novel performance metric -- Tour Effectiveness (TE) -- that controls the asymptotic variance of estimates from ST for bounded test functions. We use the TE to show that NRST dominates its reversible counterpart. We then develop an automated tuning procedure for NRST algorithms that targets the TE while minimizing computational cost. This procedure enables straightforward integration of NRST into existing probabilistic programming languages. We provide extensive experimental evidence that our tuning scheme improves the performance and robustness of NRST algorithms on a diverse set of probabilistic models.

stat.CO↗

arXiv2023

Variance-Reduced Stochastic Optimization for Efficient Inference of Hidden Markov Models

Hidden Markov models (HMMs) are popular models to identify a finite number of latent states from sequential data. However, fitting them to large data sets can be computationally demanding because most likelihood maximization techniques require iterating through the entire underlying data set for every parameter update. We propose a novel optimization algorithm that updates the parameters of an HMM without iterating through the entire data set. Namely, we combine a partial E step with variance-reduced stochastic optimization within the M step. We prove the algorithm converges under certain regularity conditions. We test our algorithm empirically using a simulation study as well as a case study of kinematic data collected using suction-cup attached biologgers from eight northern resident killer whales (Orcinus orca) off the western coast of Canada. In both, our algorithm converges in fewer epochs and to regions of higher likelihood compared to standard numerical optimization techniques. Our algorithm allows practitioners to fit complicated HMMs to large time-series data sets more efficiently than existing baselines.

stat.CO↗

arXiv2023

Pigeons.jl: Distributed Sampling From Intractable Distributions

We introduce a software package, Pigeons.jl, that provides a way to leverage distributed computation to obtain samples from complicated probability distributions, such as multimodal posteriors arising in Bayesian inference and high-dimensional distributions in statistical mechanics. Pigeons.jl provides simple APIs to perform such computations single-threaded, multi-threaded, and/or distributed over thousands of MPI-communicating machines. In addition, Pigeons.jl guarantees a property that we call strong parallelism invariance: the output for a given seed is identical irrespective of the number of threads and processes, which is crucial for scientific reproducibility and software validation. We describe the key features of Pigeons.jl and the approach taken to implement a distributed and randomized algorithm that satisfies strong parallelism invariance.

stat.CO↗

arXiv2023

Parallel Tempering With a Variational Reference

Sampling from complex target distributions is a challenging task fundamental to Bayesian inference. Parallel tempering (PT) addresses this problem by constructing a Markov chain on the expanded state space of a sequence of distributions interpolating between the posterior distribution and a fixed reference distribution, which is typically chosen to be the prior. However, in the typical case where the prior and posterior are nearly mutually singular, PT methods are computationally prohibitive. In this work we address this challenge by constructing a generalized annealing path connecting the posterior to an adaptively tuned variational reference. The reference distribution is tuned to minimize the forward (inclusive) KL divergence to the posterior distribution using a simple, gradient-free moment-matching procedure. We show that our adaptive procedure converges to the forward KL minimizer, and that the forward KL divergence serves as a good proxy to a previously developed measure of PT performance. We also show that in the large-data limit in typical Bayesian models, the proposed method improves in performance, while traditional PT deteriorates arbitrarily. Finally, we introduce PT with two references -- one fixed, one variational -- with a novel split annealing path that ensures stable variational reference adaptation. The paper concludes with experiments that demonstrate the large empirical gains achieved by our method in a wide range of realistic Bayesian inference scenarios.

stat.CO↗

arXiv2021

Non-Reversible Parallel Tempering: a Scalable Highly Parallel MCMC Scheme

Parallel tempering (PT) methods are a popular class of Markov chain Monte Carlo schemes used to sample complex high-dimensional probability distributions. They rely on a collection of $N$ interacting auxiliary chains targeting tempered versions of the target distribution to improve the exploration of the state-space. We provide here a new perspective on these highly parallel algorithms and their tuning by identifying and formalizing a sharp divide in the behaviour and performance of reversible versus non-reversible PT schemes. We show theoretically and empirically that a class of non-reversible PT methods dominates its reversible counterparts and identify distinct scaling limits for the non-reversible and reversible schemes, the former being a piecewise-deterministic Markov process and the latter a diffusion. These results are exploited to identify the optimal annealing schedule for non-reversible PT and to develop an iterative scheme approximating this schedule. We provide a wide range of numerical examples supporting our theoretical and methodological contributions. The proposed methodology is applicable to sample from a distribution $π$ with a density $L$ with respect to a reference distribution $π_0$ and compute the normalizing constant. A typical use case is when $π_0$ is a prior distribution, $L$ a likelihood function and $π$ the corresponding posterior.

stat.CO↗