Plant reflectance spectra - the profile of light reflected by leaves across different wavelengths - supply the spectral signature for a species at a spatial location to enable estimation of functional and taxonomic diversity for plants. We consider leaf spectra as "responses" to be explained spatially. These spectra/reflectances are functions over a wavelength band that respond to the environment. Our motivating dataset leads us to develop rich novel spatial models that can explain spectra for genera within families. Wavelength responses for an individual leaf are viewed as a function of wavelength, leading to functional data modeling. Local environmental features become covariates. We introduce wavelength - covariate interaction since the response to environmental regressors may vary with wavelength, so may variance. Formal spatial modeling enables prediction of reflectances for genera at unobserved locations with known environmental features. We incorporate spatial dependence, wavelength dependence, and space-wavelength interaction (in the spirit of space-time interaction). Our data are gathered for several families from the Cape Floristic Region (CFR) in South Africa. We implement out-of-sample validation to select a best model, discovering that the model features listed above are all informative for the functional data analysis. We then supply interpretation of the results under the selected model.
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Nonparametric feature selection in high-dimensional data is an important and challenging problem in statistics and machine learning fields. Most of the existing methods for feature selection focus on parametric or additive models which may suffer from model misspecification. In this paper, we propose a new framework to perform nonparametric feature selection for both regression and classification problems. In this framework, we learn prediction functions through empirical risk minimization over a reproducing kernel Hilbert space. The space is generated by a novel tensor product kernel which depends on a set of parameters that determine the importance of the features. Computationally, we minimize the empirical risk with a penalty to estimate the prediction and kernel parameters at the same time. The solution can be obtained by iteratively solving convex optimization problems. We study the theoretical property of the kernel feature space and prove both the oracle selection property and the Fisher consistency of our proposed method. Finally, we demonstrate the superior performance of our approach compared to existing methods via extensive simulation studies and application to a microarray study of eye disease in animals.
Presence-only data are a typical occurrence in species distribution modeling. They include the presence locations and no information on the absence. Their modeling usually does not account for detection biases. In this work, we aim to merge three different sources of information to model the presence of marine mammals. The approach is fully general and it is applied to two species of dolphins in the Central Tyrrhenian Sea (Italy) as a case study. Data come from the Italian Environmental Protection Agency (ISPRA) and Sapienza University of Rome research campaigns, and from a careful selection of social media (SM) images and videos. We build a Log Gaussian Cox process where different detection functions describe each data source. For the SM data, we analyze several choices that allow accounting for detection biases. Our findings allow for a correct understanding of Stenella coeruleoalba and Tursiops truncatus distribution in the study area. The results prove that the proposed approach is broadly applicable, it can be widely used, and it is easily implemented in the R software using INLA and inlabru. We provide examples' code with simulated data in the supplementary materials.
The majority of stochastic channel models rely on the electromagnetic far-field assumption. This assumption breaks down in future applications that push towards the electromagnetic near-field region such as those where the use of very large antenna arrays is envisioned. Motivated by this consideration, we show how physical principles can be used to derive a channel model that is also valid in the electromagnetic near-field. We show that wave propagation through a three-dimensional scattered medium can be generally modeled as a linear and space-variant system. We first review the physics principles that lead to a closed-form deterministic angular representation of the channel response. This serves as a basis for deriving a stochastic representation of the channel in terms of statistically independent Gaussian random coefficients for randomly spatially-stationary propagation environments. The very desirable property of spatial stationarity can always be retained by excluding reactive propagation mechanisms confined in the extreme near-field propagation region. Remarkably, the provided stochastic representation is directly connected to the Fourier spectral representation of a general spatially-stationary random field.
A new model-based procedure is developed for sparse clustering of functional data that aims to classify a sample of curves into homogeneous groups while jointly detecting the most informative portions of domain. The proposed method is referred to as sparse and smooth functional clustering (SaS-Funclust) and relies on a general functional Gaussian mixture model whose parameters are estimated by maximizing a log-likelihood function penalized with a functional adaptive pairwise penalty and a roughness penalty. The former allows identifying the noninformative portion of domain by shrinking the means of separated clusters to some common values, whereas the latter improves the interpretability by imposing some degree of smoothing to the estimated cluster means. The model is estimated via an expectation-conditional maximization algorithm paired with a cross-validation procedure. Through a Monte Carlo simulation study, the SaS-Funclust method is shown to outperform other methods already appeared in the literature, both in terms of clustering performance and interpretability. Finally, three real-data examples are presented to demonstrate the favourable performance of the proposed method. The SaS-Funclust method is implemented in the $\textsf{R}$ package $\textsf{sasfunclust}$, available online at //github.com/unina-sfere/sasfunclust.
This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized assignment semantics for first order logic. The expressive strength, complete proof calculus and meta-properties of LFD are explored. Various language extensions are presented as well, up to undecidable modal-style logics for independence and dynamic logics of changing dependence models. Finally, more concrete settings for dependence are discussed: continuous dependence in topological models, linear dependence in vector spaces, and temporal dependence in dynamical systems and games.
Steam power turbine-based power plant approximately contributes 90% of the total electricity produced in the United States. Mainly steam turbine consists of multiple types of turbine, boiler, attemperator, reheater, etc. Power is produced through the steam with high pressure and temperature that is conducted by the turbines. The total power generation of the power plant is highly nonlinear considering all these elements in the model. We perform a predictive modeling approach to detect the power generation from these turbines by the Gaussian process (GP) model. As there are multiple interconnected turbines, we consider a multivariate Gaussian process (MGP) modeling to predict the power generation from these turbines which can capture the cross-correlations between the turbines. Also, the sensitivity analysis of the input parameters is constructed for each turbine to find out the most important parameters.
Motivation: The design of enzymes is as challenging as it is consequential for making chemical synthesis in medical and industrial applications more efficient, cost-effective and environmentally friendly. While several aspects of this complex problem are computationally assisted, the drafting of catalytic mechanisms, i.e. the specification of the chemical steps-and hence intermediate states-that the enzyme is meant to implement, is largely left to human expertise. The ability to capture specific chemistries of multi-step catalysis in a fashion that enables its computational construction and design is therefore highly desirable and would equally impact the elucidation of existing enzymatic reactions whose mechanisms are unknown. Results: We use the mathematical framework of graph transformation to express the distinction between rules and reactions in chemistry. We derive about 1000 rules for amino acid side chain chemistry from the M-CSA database, a curated repository of enzymatic mechanisms. Using graph transformation we are able to propose hundreds of hypothetical catalytic mechanisms for a large number of unrelated reactions in the Rhea database. We analyze these mechanisms to find that they combine in chemically sound fashion individual steps from a variety of known multi-step mechanisms, showing that plausible novel mechanisms for catalysis can be constructed computationally.
This paper introduces new scan statistics for multivariate functional data indexed in space. The new methods are derivated from a MANOVA test statistic for functional data, an adaptation of the Hotelling T2-test statistic, and a multivariate extension of the Wilcoxon rank-sum test statistic. In a simulation study, the latter two methods present very good performances and the adaptation of the functional MANOVA also shows good performances for a normal distribution. Our methods detect more accurate spatial clusters than an existing nonparametric functional scan statistic. Lastly we applied the methods on multivariate functional data to search for spatial clusters of abnormal daily concentrations of air pollutants in the north of France in May and June 2020.
When we humans look at a video of human-object interaction, we can not only infer what is happening but we can even extract actionable information and imitate those interactions. On the other hand, current recognition or geometric approaches lack the physicality of action representation. In this paper, we take a step towards a more physical understanding of actions. We address the problem of inferring contact points and the physical forces from videos of humans interacting with objects. One of the main challenges in tackling this problem is obtaining ground-truth labels for forces. We sidestep this problem by instead using a physics simulator for supervision. Specifically, we use a simulator to predict effects and enforce that estimated forces must lead to the same effect as depicted in the video. Our quantitative and qualitative results show that (a) we can predict meaningful forces from videos whose effects lead to accurate imitation of the motions observed, (b) by jointly optimizing for contact point and force prediction, we can improve the performance on both tasks in comparison to independent training, and (c) we can learn a representation from this model that generalizes to novel objects using few shot examples.
Long Short-Term Memory (LSTM) infers the long term dependency through a cell state maintained by the input and the forget gate structures, which models a gate output as a value in [0,1] through a sigmoid function. However, due to the graduality of the sigmoid function, the sigmoid gate is not flexible in representing multi-modality or skewness. Besides, the previous models lack modeling on the correlation between the gates, which would be a new method to adopt inductive bias for a relationship between previous and current input. This paper proposes a new gate structure with the bivariate Beta distribution. The proposed gate structure enables probabilistic modeling on the gates within the LSTM cell so that the modelers can customize the cell state flow with priors and distributions. Moreover, we theoretically show the higher upper bound of the gradient compared to the sigmoid function, and we empirically observed that the bivariate Beta distribution gate structure provides higher gradient values in training. We demonstrate the effectiveness of bivariate Beta gate structure on the sentence classification, image classification, polyphonic music modeling, and image caption generation.
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