Assessment of Gradient-Based Samplers in Standard Cosmological Likelihoods
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arXiv
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| Natura: | Preprint |
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2024
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| _version_ | 1866913381375541248 |
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| author | Mootoovaloo, Arrykrishna Ruiz-Zapatero, Jaime García-García, Carlos Alonso, David |
| author_facet | Mootoovaloo, Arrykrishna Ruiz-Zapatero, Jaime García-García, Carlos Alonso, David |
| contents | We assess the usefulness of gradient-based samplers, such as the No-U-Turn Sampler (NUTS), by comparison with traditional Metropolis-Hastings algorithms, in tomographic $3 \times 2$ point analyses. Specifically, we use the DES Year 1 data and a simulated future LSST-like survey as representative examples of these studies, containing a significant number of nuisance parameters (20 and 32, respectively) that affect the performance of rejection-based samplers. To do so, we implement a differentiable forward model using JAX-COSMO (Campagne et al. 2023), and we use it to derive parameter constraints from both datasets using the NUTS algorithm as implemented in §4, and the Metropolis-Hastings algorithm as implemented in Cobaya (Lewis 2013). When quantified in terms of the number of effective number of samples taken per likelihood evaluation, we find a relative efficiency gain of $\mathcal{O}(10)$ in favour of NUTS. However, this efficiency is reduced to a factor $\sim 2$ when quantified in terms of computational time, since we find the cost of the gradient computation (needed by NUTS) relative to the likelihood to be $\sim 4.5$ times larger for both experiments. We validate these results making use of analytical multi-variate distributions (a multivariate Gaussian and a Rosenbrock distribution) with increasing dimensionality. Based on these results, we conclude that gradient-based samplers such as NUTS can be leveraged to sample high dimensional parameter spaces in Cosmology, although the efficiency improvement is relatively mild for moderate $(\mathcal{O}(50))$ dimension numbers, typical of tomographic large-scale structure analyses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04725 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Assessment of Gradient-Based Samplers in Standard Cosmological Likelihoods Mootoovaloo, Arrykrishna Ruiz-Zapatero, Jaime García-García, Carlos Alonso, David Instrumentation and Methods for Astrophysics Cosmology and Nongalactic Astrophysics We assess the usefulness of gradient-based samplers, such as the No-U-Turn Sampler (NUTS), by comparison with traditional Metropolis-Hastings algorithms, in tomographic $3 \times 2$ point analyses. Specifically, we use the DES Year 1 data and a simulated future LSST-like survey as representative examples of these studies, containing a significant number of nuisance parameters (20 and 32, respectively) that affect the performance of rejection-based samplers. To do so, we implement a differentiable forward model using JAX-COSMO (Campagne et al. 2023), and we use it to derive parameter constraints from both datasets using the NUTS algorithm as implemented in §4, and the Metropolis-Hastings algorithm as implemented in Cobaya (Lewis 2013). When quantified in terms of the number of effective number of samples taken per likelihood evaluation, we find a relative efficiency gain of $\mathcal{O}(10)$ in favour of NUTS. However, this efficiency is reduced to a factor $\sim 2$ when quantified in terms of computational time, since we find the cost of the gradient computation (needed by NUTS) relative to the likelihood to be $\sim 4.5$ times larger for both experiments. We validate these results making use of analytical multi-variate distributions (a multivariate Gaussian and a Rosenbrock distribution) with increasing dimensionality. Based on these results, we conclude that gradient-based samplers such as NUTS can be leveraged to sample high dimensional parameter spaces in Cosmology, although the efficiency improvement is relatively mild for moderate $(\mathcal{O}(50))$ dimension numbers, typical of tomographic large-scale structure analyses. |
| title | Assessment of Gradient-Based Samplers in Standard Cosmological Likelihoods |
| topic | Instrumentation and Methods for Astrophysics Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2406.04725 |