Estimation Of Time-dependent Parameters Research Articles

Deep learning-based estimation of time-dependent parameters in Markov models with application to nonlinear regression and SDEs

We present a novel deep-learning method for estimating time-dependent parameters in Markov processes through discrete sampling. Departing from conventional machine learning, our approach reframes parameter approximation as an optimization problem using the maximum likelihood approach. Experimental validation focuses on parameter estimation in multivariate regression and stochastic differential equations (SDEs). Theoretical results show that the real solution is close to SDE with parameters approximated using our neural network derived under specific conditions. Our work contributes to SDE-based model parameter estimation, offering a versatile tool for diverse fields.

Parameter estimation in tree graph metabolic networks.

We study the glycosylation processes that convert initially toxic substrates to nutritionally valuable metabolites in the flavonoid biosynthesis pathway of tomato (Solanum lycopersicum) seedlings. To estimate the reaction rates we use ordinary differential equations (ODEs) to model the enzyme kinetics. A popular choice is to use a system of linear ODEs with constant kinetic rates or to use Michaelis–Menten kinetics. In reality, the catalytic rates, which are affected among other factors by kinetic constants and enzyme concentrations, are changing in time and with the approaches just mentioned, this phenomenon cannot be described. Another problem is that, in general these kinetic coefficients are not always identifiable. A third problem is that, it is not precisely known which enzymes are catalyzing the observed glycosylation processes. With several hundred potential gene candidates, experimental validation using purified target proteins is expensive and time consuming. We aim at reducing this task via mathematical modeling to allow for the pre-selection of most potential gene candidates. In this article we discuss a fast and relatively simple approach to estimate time varying kinetic rates, with three favorable properties: firstly, it allows for identifiable estimation of time dependent parameters in networks with a tree-like structure. Secondly, it is relatively fast compared to usually applied methods that estimate the model derivatives together with the network parameters. Thirdly, by combining the metabolite concentration data with a corresponding microarray data, it can help in detecting the genes related to the enzymatic processes. By comparing the estimated time dynamics of the catalytic rates with time series gene expression data we may assess potential candidate genes behind enzymatic reactions. As an example, we show how to apply this method to select prominent glycosyltransferase genes in tomato seedlings.

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Analysis and development of modified recursive least squares algorithms for estimation of time-dependent parameters

Analysis and development of modified recursive least squares algorithms for estimation of time-dependent parameters

Estimation of time-dependent parameters in linear models using cross-sections, panels, or both

In this paper we consider the estimation of time-dependent parameters in linear models from panel data, cross-sections, or both. We determine the fraction of individuals that should be reinterviewed each period in order to minimize the variance of the most efficient estimator of linear combinations of the parameters. Moreover we derive simple sufficient conditions for the optimal fraction to be zero or one, respectively.