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1. Importance Gaussian Quadrature

   https://doi.org/10.1109/TSP.2020.3045526  

   Elvira, Victor; Martino, Luca; Closas, Pau (January 2021, IEEE Transactions on Signal Processing)

   null (Ed.)
2. Importance Sampling BRDF Derivatives

   https://doi.org/10.1145/3648611  

   Belhe, Yash; Xu, Bing; Bangaru, Sai Praveen; Ramamoorthi, Ravi; Li, Tzu-Mao (June 2024, ACM Transactions on Graphics)

   We propose a set of techniques to efficiently importance sample the derivatives of a wide range of Bidirectional Reflectance Distribution Function (BRDF) models. In differentiable rendering, BRDFs are replaced by their differential BRDF counterparts, which are real-valued and can have negative values. This leads to a new source of variance arising from their change in sign. Real-valued functions cannot be perfectly importance sampled by a positive-valued PDF, and the direct application of BRDF sampling leads to high variance. Previous attempts at antithetic sampling only addressed the derivative with the roughness parameter of isotropic microfacet BRDFs. Our work generalizes BRDF derivative sampling to anisotropic microfacet models, mixture BRDFs, Oren-Nayar, Hanrahan-Krueger, among other analytic BRDFs. Our method first decomposes the real-valued differential BRDF into a sum of single-signed functions, eliminating variance from a change in sign. Next, we importance sample each of the resulting single-signed functions separately. The first decomposition, positivization, partitions the real-valued function based on its sign, and is effective at variance reduction when applicable. However, it requires analytic knowledge of the roots of the differential BRDF, and for it to be analytically integrable too. Our key insight is that the single-signed functions can have overlapping support, which significantly broadens the ways we can decompose a real-valued function. Our product and mixture decompositions exploit this property, and they allow us to support several BRDF derivatives that positivization could not handle. For a wide variety of BRDF derivatives, our method significantly reduces the variance (up to 58× in some cases) at equal computation cost and enables better recovery of spatially varying textures through gradient-descent-based inverse rendering. 

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3. Information Fusion via Importance Sampling

   https://doi.org/10.1109/TSIPN.2023.3299512  

   Saucan, Augustin A; Elvira, Víctor; Varshney, Pramod K; Win, Moe Z (April 2024, IEEE Transactions on Signal and Information Processing over Networks)

   Information fusion is a procedure that merges information locally contained at the nodes of a network. Of high interest in the field of distributed estimation is the fusion of local probability distributions via a weighted geometrical average criterion. In numerous practical settings, the local distributions are only known through particle approximations, i.e., sets of samples with associated weights, such as obtained via importance sampling (IS) methods. Thus, prohibiting any closed-form solution to the aforementioned fusion problem. This article proposes a family of IS methods—called particle geometric–average fusion (PGAF)—that lead to consistent estimators for the geometrically-averaged density. The advantages of the proposed methods are threefold. First, the methods are agnostic of the mechanisms used to generate the local particle sets and, therefore, allow for the fusion of heterogeneous nodes. Second, consistency of estimators is guaranteed under generic conditions when the agents use IS-generated particles. Third, a low-communication overhead and agent privacy are achieved since local observations are not shared with the fusion center. Even more remarkably, for a sub-family of the proposed PGAF methods, the fusion center does not require the knowledge of the local priors used by the nodes. Implementation guidelines for the proposed methods are provided and theoretical results are numerically verified. 

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4. Variational approximation for importance sampling

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   Su, Xiao; Chen, Yuguo (January 2021, Computational Statistics)
5. The Ecological Importance of Allelopathy

   https://doi.org/10.1146/annurev-ecolsys-051120- 030619  

   José L. Hierro; Ragan M. Callaway (August 2021, Annual review)

   Allelopathy (i.e., chemical interaction among species) was originally conceived as inclusive of positive and negative effects of plants on other plants, and we adopt this view. Most studies of allelopathy have been phenomenological, but we focus on studies that have explored the ecological significance of this interaction. The literature suggests that studies of allelopathy have been particularly important for three foci in ecology: species distribution, conditionality of interactions, and maintenance of species diversity. There is evidence that allelopathy influences local distributions of plant species around the world. Allelopathic conditionality appears to arise through coevolution, and this is a mechanism for plant invasions. Finally, allelopathy promotes species coexistence via intransitive competition, modifications of direct interactions, and (co)evolution. Recent advances additionally suggest that coexistence might be favored through biochemical recognition. The preponderance of phenomenological studies notwithstanding, allelopathy has broad ecological consequences. 

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