DiME: Maximizing Mutual Information by a Difference of Matrix-Based Entropies

We introduce an information-theoretic quantity with similar properties to mutual information that can be estimated from data without making explicit assumptions on the underlying distribution. This quantity is based on a recently proposed matrix-based entropy that uses the eigenvalues of a normalized Gram matrix to compute an estimate of the eigenvalues of an uncentered covariance operator in a reproducing kernel Hilbert space. We show that a difference of matrix-based entropies (DiME) is well suited for problems involving the maximization of mutual information between random variables. While many methods for such tasks can lead to trivial solutions, DiME naturally penalizes such outcomes. We compare DiME to several baseline estimators of mutual information on a toy Gaussian dataset. We provide examples of use cases for DiME, such as latent factor disentanglement and a multiview representation learning problem where DiME is used to learn a shared representation among views with high mutual information

Consistent patterns of common species across tropical tree communities

Trees structure the Earth’s most biodiverse ecosystem, tropical forests. The vast number of tree species presents a formidable challenge to understanding these forests, including their response to environmental change, as very little is known about most tropical tree species. A focus on the common species may circumvent this challenge. Here we investigate abundance patterns of common tree species using inventory data on 1,003,805 trees with trunk diameters of at least 10 cm across 1,568 locations1,2,3,4,5,6 in closed-canopy, structurally intact old-growth tropical forests in Africa, Amazonia and Southeast Asia. We estimate that 2.2%, 2.2% and 2.3% of species comprise 50% of the tropical trees in these regions, respectively. Extrapolating across all closed-canopy tropical forests, we estimate that just 1,053 species comprise half of Earth’s 800 billion tropical trees with trunk diameters of at least 10 cm. Despite differing biogeographic, climatic and anthropogenic histories7, we find notably consistent patterns of common species and species abundance distributions across the continents. This suggests that fundamental mechanisms of tree community assembly may apply to all tropical forests. Resampling analyses show that the most common species are likely to belong to a manageable list of known species, enabling targeted efforts to understand their ecology. Although they do not detract from the importance of rare species, our results open new opportunities to understand the world’s most diverse forests, including modelling their response to environmental change, by focusing on the common species that constitute the majority of their trees.Publisher PDFPeer reviewe

The Representation Jensen-R\'enyi Divergence

We introduce a divergence measure between data distributions based on operators in reproducing kernel Hilbert spaces defined by kernels. The empirical estimator of the divergence is computed using the eigenvalues of positive definite Gram matrices that are obtained by evaluating the kernel over pairs of data points. The new measure shares similar properties to Jensen-Shannon divergence. Convergence of the proposed estimators follows from concentration results based on the difference between the ordered spectrum of the Gram matrices and the integral operators associated with the population quantities. The proposed measure of divergence avoids the estimation of the probability distribution underlying the data. Numerical experiments involving comparing distributions and applications to sampling unbalanced data for classification show that the proposed divergence can achieve state of the art results.Comment: We added acknowledgment

Global Survey of Outcomes of Neurocritical Care Patients: Analysis of the PRINCE Study Part 2

BACKGROUND: Neurocritical care is devoted to the care of critically ill patients with acute neurological or neurosurgical emergencies. There is limited information regarding epidemiological data, disease characteristics, variability of clinical care, and in-hospital mortality of neurocritically ill patients worldwide. We addressed these issues in the Point PRevalence In Neurocritical CarE (PRINCE) study, a prospective, cross-sectional, observational study. METHODS: We recruited patients from various intensive care units (ICUs) admitted on a pre-specified date, and the investigators recorded specific clinical care activities they performed on the subjects during their first 7 days of admission or discharge (whichever came first) from their ICUs and at hospital discharge. In this manuscript, we analyzed the final data set of the study that included patient admission characteristics, disease type and severity, ICU resources, ICU and hospital length of stay, and in-hospital mortality. We present descriptive statistics to summarize data from the case report form. We tested differences between geographically grouped data using parametric and nonparametric testing as appropriate. We used a multivariable logistic regression model to evaluate factors associated with in-hospital mortality. RESULTS: We analyzed data from 1545 patients admitted to 147 participating sites from 31 countries of which most were from North America (69%, N = 1063). Globally, there was variability in patient characteristics, admission diagnosis, ICU treatment team and resource allocation, and in-hospital mortality. Seventy-three percent of the participating centers were academic, and the most common admitting diagnosis was subarachnoid hemorrhage (13%). The majority of patients were male (59%), a half of whom had at least two comorbidities, and median Glasgow Coma Scale (GCS) of 13. Factors associated with in-hospital mortality included age (OR 1.03; 95% CI, 1.02 to 1.04); lower GCS (OR 1.20; 95% CI, 1.14 to 1.16 for every point reduction in GCS); pupillary reactivity (OR 1.8; 95% CI, 1.09 to 3.23 for bilateral unreactive pupils); admission source (emergency room versus direct admission [OR 2.2; 95% CI, 1.3 to 3.75]; admission from a general ward versus direct admission [OR 5.85; 95% CI, 2.75 to 12.45; and admission from another ICU versus direct admission [OR 3.34; 95% CI, 1.27 to 8.8]); and the absence of a dedicated neurocritical care unit (NCCU) (OR 1.7; 95% CI, 1.04 to 2.47). CONCLUSION: PRINCE is the first study to evaluate care patterns of neurocritical patients worldwide. The data suggest that there is a wide variability in clinical care resources and patient characteristics. Neurological severity of illness and the absence of a dedicated NCCU are independent predictors of in-patient mortality.status: publishe

Consistent patterns of common species across tropical tree communities

International audienceAbstract Trees structure the Earth’s most biodiverse ecosystem, tropical forests. The vast number of tree species presents a formidable challenge to understanding these forests, including their response to environmental change, as very little is known about most tropical tree species. A focus on the common species may circumvent this challenge. Here we investigate abundance patterns of common tree species using inventory data on 1,003,805 trees with trunk diameters of at least 10 cm across 1,568 locations 1–6 in closed-canopy, structurally intact old-growth tropical forests in Africa, Amazonia and Southeast Asia. We estimate that 2.2%, 2.2% and 2.3% of species comprise 50% of the tropical trees in these regions, respectively. Extrapolating across all closed-canopy tropical forests, we estimate that just 1,053 species comprise half of Earth’s 800 billion tropical trees with trunk diameters of at least 10 cm. Despite differing biogeographic, climatic and anthropogenic histories 7 , we find notably consistent patterns of common species and species abundance distributions across the continents. This suggests that fundamental mechanisms of tree community assembly may apply to all tropical forests. Resampling analyses show that the most common species are likely to belong to a manageable list of known species, enabling targeted efforts to understand their ecology. Although they do not detract from the importance of rare species, our results open new opportunities to understand the world’s most diverse forests, including modelling their response to environmental change, by focusing on the common species that constitute the majority of their trees