scholarly journals Natural Gradient Flow in the Mixture Geometry of a Discrete Exponential Family

Entropy ◽  
2015 ◽  
Vol 17 (6) ◽  
pp. 4215-4254 ◽  
Author(s):  
Luigi Malagò ◽  
Giovanni Pistone
Keyword(s):  
Exponential Family ◽  
Gradient Flow ◽  
Natural Gradient

New Method for Sampling Groundwater Colloids under Natural Gradient Flow Conditions

1996 ◽  
Vol 30 (10) ◽  
pp. 3094-3101 ◽  
Author(s):  
Noam Weisbrod ◽  
Daniel Ronen ◽  
Ronit Nativ
Keyword(s):  
Gradient Flow ◽  
New Method ◽  
Natural Gradient ◽  
Flow Conditions

Characterization of suspended particles collected in groundwater under natural gradient flow conditions

1992 ◽  
Vol 28 (5) ◽  
pp. 1279-1291 ◽  
Author(s):  
D. Ronen ◽  
M. Magaritz ◽  
U. Weber ◽  
A. J. Amiel ◽  
E. Klein
Keyword(s):  
Gradient Flow ◽  
Suspended Particles ◽  
Natural Gradient ◽  
Flow Conditions

Characterisation of Suspended Particles and Associated Metals in Groundwater under Natural Gradient Flow Conditions*

1993 ◽  
Vol 27 (7-8) ◽  
pp. 179-186 ◽  
Author(s):  
D. Ronen ◽  
M. Magaritz ◽  
A. J. Amiel
Keyword(s):  
Organic Matter ◽  
Colloidal Particles ◽  
Colloidal Stability ◽  
Gradient Flow ◽  
Suspended Particles ◽  
Average Concentration ◽  
Saturated Zone ◽  
Natural Gradient ◽  
Flow Conditions ◽  
Anoxic Conditions

Microscale Eulerian variations in the flux, mineralogical composition and size of suspended particles have been found in a contaminated sandy aquifer under natural gradient flow conditions () during an 8 month study period. Particle variability has been detected along a 16 m saturated section of the aquifer at a scale of centimeters and meters in the vertical and horizontal dimensions, respectively. The average concentration of particles in groundwater varied between 1 to 70 mg/l. The particles were primarily composed of CaCO3 (11% to 57%), quartz (7% to 39%) and clays (8% to 43%). Most of the particles were within the 140 to 3,000 nm size range with size modes varying from 310 to 660 nm. The large amounts of suspended particles are considered to be related to high inputs of dissolved organic carbon into groundwater from sewage effluents which have been used for agricultural irrigation since the early 1960's. As a result of organic matter biodegradation in the saturated zone, anoxic conditions developed and the pCO2 content of groundwater increased dramatically. It is postulated that part of the carbonate cement of the rocks dissolved and detrital CaCO3, quartz and clay were released as colloidal particles. In the prevailing anoxic conditions of groundwater at the study site (DO < 1 mg/l) colloidal stability is enhanced by organic matter coating of particles. The transport of metals associated with suspended particles in the saturated zone and the interaction of these particles in the aquifer environment have been ascertained through a comparison of the distribution coefficient of 17 elements as a function of depth. *Contribution No. 61, Department of Environmental Sciences and Energy Research, The Weizmann Institute of Science.

scholarly journals Quantum Statistical Learning via Quantum Wasserstein Natural Gradient

2021 ◽  
Vol 182 (1) ◽  
Author(s):  
Simon Becker ◽  
Wuchen Li
Keyword(s):  
Statistical Learning ◽  
Parameter Space ◽  
Information Matrix ◽  
Gradient Flow ◽  
Continuous Variable ◽  
Quantum States ◽  
Parametric Models ◽  
Natural Gradient ◽  
Wasserstein Metric ◽  
Density Operators

AbstractIn this article, we introduce a new approach towards the statistical learning problem $$\mathrm{argmin}_{\rho (\theta ) \in {\mathcal {P}}_{\theta }} W_{Q}^2 (\rho _{\star },\rho (\theta ))$$ argmin ρ ( θ ) ∈ P θ W Q 2 ( ρ ⋆ , ρ ( θ ) ) to approximate a target quantum state $$\rho _{\star }$$ ρ ⋆ by a set of parametrized quantum states $$\rho (\theta )$$ ρ ( θ ) in a quantum $$L^2$$ L 2 -Wasserstein metric. We solve this estimation problem by considering Wasserstein natural gradient flows for density operators on finite-dimensional $$C^*$$ C ∗ algebras. For continuous parametric models of density operators, we pull back the quantum Wasserstein metric such that the parameter space becomes a Riemannian manifold with quantum Wasserstein information matrix. Using a quantum analogue of the Benamou–Brenier formula, we derive a natural gradient flow on the parameter space. We also discuss certain continuous-variable quantum states by studying the transport of the associated Wigner probability distributions.

An Introduction to Statistical Models for Networks

2020 ◽  
pp. 218-233
Author(s):  
Valentina Kuskova ◽  
Stanley Wasserman
Keyword(s):  
Social System ◽  
Exponential Family ◽  
Behavioral Science ◽  
Social Science Research ◽  
Science Research ◽  
Uniform Distributions ◽  
The Social ◽  
Special Cases ◽  
Social And Behavioral Science ◽  
Network Methods

Network theoretical and analytic approaches have reached a new level of sophistication in this decade, accompanied by a rapid growth of interest in adopting these approaches in social science research generally. Of course, much social and behavioral science focuses on individuals, but there are often situations where the social environment—the social system—affects individual responses. In these circumstances, to treat individuals as isolated social atoms, a necessary assumption for the application of standard statistical analysis is simply incorrect. Network methods should be part of the theoretical and analytic arsenal available to sociologists. Our focus here will be on the exponential family of random graph distributions, p*, because of its inclusiveness. It includes conditional uniform distributions as special cases.

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