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1. Improving structured population models with more realistic representations of non‐normal growth

   https://doi.org/10.1111/2041-210X.13240  

   DeMarche, Megan L.; Morris, William; Linares, Cristina; Doak, Daniel; Altwegg, ed., Res (July 2019, Methods in Ecology and Evolution)

   Abstract Structured population models are among the most widely used tools in ecology and evolution. Integral projection models (IPMs) use continuous representations of how survival, reproduction and growth change as functions of state variables such as size, requiring fewer parameters to be estimated than projection matrix models (PPMs). Yet, almost all published IPMs make an important assumption that size‐dependent growth transitions are or can be transformed to be normally distributed. In fact, many organisms exhibit highly skewed size transitions. Small individuals can grow more than they can shrink, and large individuals may often shrink more dramatically than they can grow. Yet, the implications of such skew for inference from IPMs has not been explored, nor have general methods been developed to incorporate skewed size transitions into IPMs, or deal with other aspects of real growth rates, including bounds on possible growth or shrinkage.Here, we develop a flexible approach to modelling skewed growth data using a modified beta regression model. We propose that sizes first be converted to a (0,1) interval by estimating size‐dependent minimum and maximum sizes through quantile regression. Transformed data can then be modelled using beta regression with widely available statistical tools. We demonstrate the utility of this approach using demographic data for a long‐lived plant, gorgonians and an epiphytic lichen. Specifically, we compare inferences of population parameters from discrete PPMs to those from IPMs that either assume normality or incorporate skew using beta regression or, alternatively, a skewed normal model.The beta and skewed normal distributions accurately capture the mean, variance and skew of real growth distributions. Incorporating skewed growth into IPMs decreases population growth and estimated life span relative to IPMs that assume normally distributed growth, and more closely approximate the parameters of PPMs that do not assume a particular growth distribution. A bounded distribution, such as the beta, also avoids the eviction problem caused by predicting some growth outside the modelled size range.Incorporating biologically relevant skew in growth data has important consequences for inference from IPMs. The approaches we outline here are flexible and easy to implement with existing statistical tools. 

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2. Join Size Bounds using l _p -Norms on Degree Sequences

   https://doi.org/10.1145/3651597  

   Abo_Khamis, Mahmoud; Nakos, Vasileios; Olteanu, Dan; Suciu, Dan (May 2024, Proceedings of the ACM on Management of Data)

   Estimating the output size of a query is a fundamental yet longstanding problem in database query processing. Traditional cardinality estimators used by database systems can routinely underestimate the true output size by orders of magnitude, which leads to significant system performance penalty. Recently, upper bounds have been proposed that are based on information inequalities and incorporate sizes and max-degrees from input relations, yet their main benefit is limited to cyclic queries, because they degenerate to rather trivial formulas on acyclic queries. We introduce a significant extension of the upper bounds, by incorporating l_p-norms of the degree sequences of join attributes. Our bounds are significantly lower than previously known bounds, even when applied to acyclic queries. These bounds are also based on information theory, they come with a matching query evaluation algorithm, are computable in exponential time in the query size, and are provably tight when all degrees are ''simple''. 

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3. Conditional Linear Regression

   Calderon, Diego; Juba, Brendan; Li, Sirui; Li, Zongyi; Ruan, Lisa (August 2020, Proceedings of Machine Learning Research)

   Work in machine learning and statistics commonly focuses on building models that capture the vast majority of data, possibly ignoring a segment of the population as outliers. However, there may not exist a good, simple model for the distribution, so we seek to find a small subset where there exists such a model. We give a computationally efficient algorithm with theoretical analysis for the conditional linear regression task, which is the joint task of identifying a significant portion of the data distribution, described by a k-DNF, along with a linear predictor on that portion with a small loss. In contrast to work in robust statistics on small subsets, our loss bounds do not feature a dependence on the density of the portion we fit, and compared to previous work on conditional linear regression, our algorithm’s running time scales polynomially with the sparsity of the linear predictor. We also demonstrate empirically that our algorithm can leverage this advantage to obtain a k-DNF with a better linear predictor in practice. 

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4. Measurements of Size and Electrical Charges Carried by Precipitation Particles During RELAMPAGO Field Campaign

   https://doi.org/10.1029/2022EA002407  

   Ávila, Eldo; Martínez, Lucia; Pereyra, Rodolfo; Lang, Timothy; Deierling, Wiebke; Wingo, Matthew; Melo, Gregory; Medina, Bruno (September 2022, Earth and Space Science)

   Abstract The electrical charge carried by raindrops provides significant information about thunderstorm electrification mechanisms, since the charge acquired by hydrometeors is closely related to the microphysical processes that they undergo within clouds. Investigation of charges on raindrops was conducted during the Remote sensing of Electrification, Lightning, And Meso‐scale/micro‐scale Processes with Adaptive Ground Observations field campaign. A newly designed instrument was used to determine simultaneously the fall velocity and charge for precipitating particles. Hydrometeor size and charge were measured in Córdoba city, Argentina, during electrified storms. Temporal series of size‐charge of single raindrops were recorded for two storms, which were also monitored with a Parsivel disdrometer and Lightning Mapping Array. The results show that the magnitude of the electric charges range between 1 and 50 pC and more than 90% of the charges are mainly carried by raindrops >1 mm, even though most of the raindrops are smaller than 1 mm. Furthermore, the measurement series show charged hydrometeors of both signs all the time. A correlation between the sizes and the charges carried by the raindrops was found in both storms. 

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5. A Functional Perspective on Learning Symmetric Functions with Neural Networks

   Zweig, A; Bruna, J (July 2021, Proceedings of Machine Learning Research)

   null (Ed.)

   Symmetric functions, which take as input an unordered, fixed-size set, are known to be universally representable by neural networks that enforce permutation invariance. These architectures only give guarantees for fixed input sizes, yet in many practical applications, including point clouds and particle physics, a relevant notion of generalization should include varying the input size. In this work we treat symmetric functions (of any size) as functions over probability measures, and study the learning and representation of neural networks defined on measures. By focusing on shallow architectures, we establish approximation and generalization bounds under different choices of regularization (such as RKHS and variation norms), that capture a hierarchy of functional spaces with increasing degree of non-linear learning. The resulting models can be learned efficiently and enjoy generalization guarantees that extend across input sizes, as we verify empirically. 

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