ProbNum: Probabilistic Numerics in Python

Wenger, Jonathan; Krämer, Nicholas; Pförtner, Marvin; Schmidt, Jonathan; Bosch, Nathanael; Effenberger, Nina; Zenn, Johannes; Gessner, Alexandra; Karvonen, Toni; Briol, François‐Xavier; Mahsereci, Maren; Hennig, Philipp

doi:10.48550/arxiv.2112.02100

Cited by 3 publications

(3 citation statements)

References 14 publications

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“…For details see section 6 in the supplementary material, an implementation of the 2 statistic can be found in the evaluation metrics in the ProbNum package (55) . As further uncertainty quantification assessments we compute confidence curves, as:…”

Section: Methodsmentioning

confidence: 99%

Assessing the performance of protein regression models

Richard

Kæstel-Hansen

Groth

et al. 2023

Preprint

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To optimize proteins for particular traits holds great promise for industrial and pharmaceutical purposes. Machine Learning is increasingly applied in this field to predict properties of proteins, thereby guiding the experimental optimization process. A natural question is: How much progress are we making with such predictions, and how important is the choice of regressor and representation? In this paper, we demonstrate that different assessment criteria for regressor performance can lead to dramatically different conclusions, depending on the choice of metric, and how one defines generalization. We highlight the fundamental issues of sample bias in typical regression scenarios and how this can lead to misleading conclusions about regressor performance. Finally, we make the case for the importance of calibrated uncertainty in this domain.

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Section: Methodsmentioning

confidence: 99%

Assessing the performance of protein regression models

Richard

Kæstel-Hansen

Groth

et al. 2023

Preprint

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“…Additionally, we have full flexibility in our choice of c so long as k(x, •) • G θ ∈ H c . We refer to Table 1 in Briol et al (2019b) or the ProbNum Python package Wenger et al (2021) for a list of known closed-form kernel embeddings. Note that, both terms in the upper bound in Theorem 3 depend on the kernel c, meaning that c cannot simply be chosen for computational convenience and must also be chosen such that these quantities are as small as possible.…”

Section: Optimally-weighted Estimatorsmentioning

confidence: 99%

Optimally-Weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inference

Bharti¹,

Masha²,

Key³

et al. 2023

Preprint

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Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum distance estimation, generalised Bayesian inference, and within the nonparametric learning framework. The MMD is commonly estimated at a root-m rate, where m is the number of simulated samples. This can lead to significant computational challenges since a large m is required to obtain an accurate estimate, which is crucial for parameter estimation. In this paper, we propose a novel estimator for the MMD with significantly improved sample complexity. The estimator is particularly well suited for computationally expensive smooth simulators with low-to mid-dimensional inputs. This claim is supported through both theoretical results and an extensive simulation study on benchmark simulators.

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“…In recent years, there has been a surge in interest in the field of probabilistic numerics (Hennig et al 2022;Oates and Sullivan 2019), where "ODE filters" have been developed to solve ODEs using GP regression techniques. Instead of calculating a numerical solution on the mesh t, as classical integration methods do, ODE filters return a probability measure over the solution at any t ∈ [t 0 , T ] (Schober et al 2019;Tronarp et al 2019;Bosch et al 2021;Wenger et al 2021). Such methods solve sequentially in time, conditioning the GP on acquisition data, i.e.…”

mentioning

confidence: 99%

GParareal: a time-parallel ODE solver using Gaussian process emulation

et al. 2022

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Sequential numerical methods for integrating initial value problems (IVPs) can be prohibitively expensive when high numerical accuracy is required over the entire interval of integration. One remedy is to integrate in a parallel fashion, “predicting” the solution serially using a cheap (coarse) solver and “correcting” these values using an expensive (fine) solver that runs in parallel on a number of temporal subintervals. In this work, we propose a time-parallel algorithm (GParareal) that solves IVPs by modelling the correction term, i.e. the difference between fine and coarse solutions, using a Gaussian process emulator. This approach compares favourably with the classic parareal algorithm and we demonstrate, on a number of IVPs, that GParareal can converge in fewer iterations than parareal, leading to an increase in parallel speed-up. GParareal also manages to locate solutions to certain IVPs where parareal fails and has the additional advantage of being able to use archives of legacy solutions, e.g. solutions from prior runs of the IVP for different initial conditions, to further accelerate convergence of the method — something that existing time-parallel methods do not do.

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ProbNum: Probabilistic Numerics in Python

Cited by 3 publications

References 14 publications

Assessing the performance of protein regression models

Assessing the performance of protein regression models

Optimally-Weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inference

GParareal: a time-parallel ODE solver using Gaussian process emulation

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