arXiv subjects

Samuel Wiqvist

Publications and source records attributed to Samuel Wiqvist.

4 recordsLinked to original sources

arXiv2021

Sequential Neural Posterior and Likelihood Approximation

We introduce the sequential neural posterior and likelihood approximation (SNPLA) algorithm. SNPLA is a normalizing flows-based algorithm for inference in implicit models, and therefore is a simulation-based inference method that only requires simulations from a generative model. SNPLA avoids Markov chain Monte Carlo sampling and correction-steps of the parameter proposal function that are introduced in similar methods, but that can be numerically unstable or restrictive. By utilizing the reverse KL divergence, SNPLA manages to learn both the likelihood and the posterior in a sequential manner. Over four experiments, we show that SNPLA performs competitively when utilizing the same number of model simulations as used in other methods, even though the inference problem for SNPLA is more complex due to the joint learning of posterior and likelihood function. Due to utilizing normalizing flows SNPLA generates posterior draws much faster (4 orders of magnitude) than MCMC-based methods.

stat.ML↗

arXiv2021

Efficient inference for stochastic differential equation mixed-effects models using correlated particle pseudo-marginal algorithms

Stochastic differential equation mixed-effects models (SDEMEMs) are flexible hierarchical models that are able to account for random variability inherent in the underlying time-dynamics, as well as the variability between experimental units and, optionally, account for measurement error. Fully Bayesian inference for state-space SDEMEMs is performed, using data at discrete times that may be incomplete and subject to measurement error. However, the inference problem is complicated by the typical intractability of the observed data likelihood which motivates the use of sampling-based approaches such as Markov chain Monte Carlo. A Gibbs sampler is proposed to target the marginal posterior of all parameter values of interest. The algorithm is made computationally efficient through careful use of blocking strategies and correlated pseudo-marginal Metropolis-Hastings steps within the Gibbs scheme. The resulting methodology is flexible and is able to deal with a large class of SDEMEMs. The methodology is demonstrated on three case studies, including tumor growth dynamics and neuronal data. The gains in terms of increased computational efficiency are model and data dependent, but unless bespoke sampling strategies requiring analytical derivations are possible for a given model, we generally observe an efficiency increase of one order of magnitude when using correlated particle methods together with our blocked-Gibbs strategy.

stat.CO↗

arXiv2019

Accelerating delayed-acceptance Markov chain Monte Carlo algorithms

Delayed-acceptance Markov chain Monte Carlo (DA-MCMC) samples from a probability distribution via a two-stages version of the Metropolis-Hastings algorithm, by combining the target distribution with a "surrogate" (i.e. an approximate and computationally cheaper version) of said distribution. DA-MCMC accelerates MCMC sampling in complex applications, while still targeting the exact distribution. We design a computationally faster, albeit approximate, DA-MCMC algorithm. We consider parameter inference in a Bayesian setting where a surrogate likelihood function is introduced in the delayed-acceptance scheme. When the evaluation of the likelihood function is computationally intensive, our scheme produces a 2-4 times speed-up, compared to standard DA-MCMC. However, the acceleration is highly problem dependent. Inference results for the standard delayed-acceptance algorithm and our approximated version are similar, indicating that our algorithm can return reliable Bayesian inference. As a computationally intensive case study, we introduce a novel stochastic differential equation model for protein folding data.

stat.CO↗

arXiv2019

Partially Exchangeable Networks and Architectures for Learning Summary Statistics in Approximate Bayesian Computation

We present a novel family of deep neural architectures, named partially exchangeable networks (PENs) that leverage probabilistic symmetries. By design, PENs are invariant to block-switch transformations, which characterize the partial exchangeability properties of conditionally Markovian processes. Moreover, we show that any block-switch invariant function has a PEN-like representation. The DeepSets architecture is a special case of PEN and we can therefore also target fully exchangeable data. We employ PENs to learn summary statistics in approximate Bayesian computation (ABC). When comparing PENs to previous deep learning methods for learning summary statistics, our results are highly competitive, both considering time series and static models. Indeed, PENs provide more reliable posterior samples even when using less training data.

stat.ML↗