Inference of Stochastic Dynamical Systems from Cross-Sectional
Population Data
- URL: http://arxiv.org/abs/2012.05055v1
- Date: Wed, 9 Dec 2020 14:02:29 GMT
- Title: Inference of Stochastic Dynamical Systems from Cross-Sectional
Population Data
- Authors: Anastasios Tsourtis, Yannis Pantazis, Ioannis Tsamardinos
- Abstract summary: Inferring the driving equations of a dynamical system from population or time-course data is important in several scientific fields such as biochemistry, epidemiology, financial mathematics and many others.
In this work, we deduce and then computationally estimate the Fokker-Planck equation which describes the evolution of the population's probability density, based on differential equations.
Then, following the USDL approach, we project the Fokker-Planck equation to a proper set of test functions, transforming it into a linear system of equations.
- Score: 8.905677748354364
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Inferring the driving equations of a dynamical system from population or
time-course data is important in several scientific fields such as
biochemistry, epidemiology, financial mathematics and many others. Despite the
existence of algorithms that learn the dynamics from trajectorial measurements
there are few attempts to infer the dynamical system straight from population
data. In this work, we deduce and then computationally estimate the
Fokker-Planck equation which describes the evolution of the population's
probability density, based on stochastic differential equations. Then,
following the USDL approach, we project the Fokker-Planck equation to a proper
set of test functions, transforming it into a linear system of equations.
Finally, we apply sparse inference methods to solve the latter system and thus
induce the driving forces of the dynamical system. Our approach is illustrated
in both synthetic and real data including non-linear, multimodal stochastic
differential equations, biochemical reaction networks as well as mass cytometry
biological measurements.
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