Henri Pesonen

Vasilis Gkolemis, Michael Gutmann, Henri Pesonen

Performing inference in statistical models with an intractable likelihood is challenging, therefore, most likelihood-free inference (LFI) methods encounter accuracy and efficiency limitations. In this paper, we present the implementation of the LFI method Robust Optimisation Monte Carlo (ROMC) in the Python package ELFI. ROMC is a novel and efficient (highly-parallelizable) LFI framework that provides accurate weighted samples from the posterior. Our implementation can be used in two ways. First, a scientist may use it as an out-of-the-box LFI algorithm; we provide an easy-to-use API harmonized with the principles of ELFI, enabling effortless comparisons with the rest of the methods included in the package. Additionally, we have carefully split ROMC into isolated components for supporting extensibility. A researcher may experiment with novel method(s) for solving part(s) of ROMC without reimplementing everything from scratch. In both scenarios, the ROMC parts can run in a fully-parallelized manner, exploiting all CPU cores. We also provide helpful functionalities for (i) inspecting the inference process and (ii) evaluating the obtained samples. Finally, we test the robustness of our implementation on some typical LFI examples.

Alexander Aushev, Thong Tran, Henri Pesonen et al.

Likelihood-free inference (LFI) has been successfully applied to state-space models, where the likelihood of observations is not available but synthetic observations generated by a black-box simulator can be used for inference instead. However, much of the research up to now have been restricted to cases, in which a model of state transition dynamics can be formulated in advance and the simulation budget is unrestricted. These methods fail to address the problem of state inference when simulations are computationally expensive and the Markovian state transition dynamics are undefined. The approach proposed in this manuscript enables LFI of states with a limited number of simulations by estimating the transition dynamics, and using state predictions as proposals for simulations. In the experiments with non-stationary user models, the proposed method demonstrates significant improvement in accuracy for both state inference and prediction, where a multi-output Gaussian process is used for LFI of states, and a Bayesian Neural Network as a surrogate model of transition dynamics.

Alexander Aushev, Henri Pesonen, Markus Heinonen et al.

In recent years, surrogate models have been successfully used in likelihood-free inference to decrease the number of simulator evaluations. The current state-of-the-art performance for this task has been achieved by Bayesian Optimization with Gaussian Processes (GPs). While this combination works well for unimodal target distributions, it is restricting the flexibility and applicability of Bayesian Optimization for accelerating likelihood-free inference more generally. We address this problem by proposing a Deep Gaussian Process (DGP) surrogate model that can handle more irregularly behaved target distributions. Our experiments show how DGPs can outperform GPs on objective functions with multimodal distributions and maintain a comparable performance in unimodal cases. This confirms that DGPs as surrogate models can extend the applicability of Bayesian Optimization for likelihood-free inference (BOLFI), while adding computational overhead that remains negligible for computationally intensive simulators.

Owen Thomas, Raquel Sá-Leão, Hermínia de Lencastre et al.

Likelihood-free inference for simulator-based statistical models has developed rapidly from its infancy to a useful tool for practitioners. However, models with more than a handful of parameters still generally remain a challenge for the Approximate Bayesian Computation (ABC) based inference. To advance the possibilities for performing likelihood-free inference in higher dimensional parameter spaces, we introduce an extension of the popular Bayesian optimisation based approach to approximate discrepancy functions in a probabilistic manner which lends itself to an efficient exploration of the parameter space. Our approach achieves computational scalability for higher dimensional parameter spaces by using separate acquisition functions and discrepancies for each parameter. The efficient additive acquisition structure is combined with exponentiated loss -likelihood to provide a misspecification-robust characterisation of the marginal posterior distribution for all model parameters. The method successfully performs computationally efficient inference in a 100-dimensional space on canonical examples and compares favourably to existing modularised ABC methods. We further illustrate the potential of this approach by fitting a bacterial transmission dynamics model to a real data set, which provides biologically coherent results on strain competition in a 30-dimensional parameter space.

Charlie Rogers-Smith, Henri Pesonen, Samuel Kaski

Approximate Bayesian computation (ABC) methods can be used to sample from posterior distributions when the likelihood function is unavailable or intractable, as is often the case in biological systems. ABC methods suffer from inefficient particle proposals in high dimensions, and subjectivity in the choice of summary statistics, discrepancy measure, and error tolerance. Sequential Monte Carlo (SMC) methods have been combined with ABC to improve the efficiency of particle proposals, but suffer from subjectivity and require many simulations from the likelihood function. Likelihood-Free Inference by Ratio Estimation (LFIRE) leverages classification to estimate the posterior density directly but does not explore the parameter space efficiently. This work proposes a classification approach that approximates population Monte Carlo (PMC), where model class probabilities from classification are used to update particle weights. This approach, called Classification-PMC, blends adaptive proposals and classification, efficiently producing samples from the posterior without subjectivity. We show through a simulation study that Classification-PMC outperforms two state-of-the-art methods: ratio estimation and SMC ABC when it is computationally difficult to simulate from the likelihood.