Constraints on Cubic and $f(P)$ Gravity from the Cosmic Chronometers :
  Use of Machine Learning Algorithms
  In this work we perform an observational data analysis on Einsteinian cubic
gravity and $f(P)$ gravity with the objective of constraining the parameter
space of the theories. We use the 30 point $z-H(z)$ cosmic chronometer data as
the observational tool for our analysis along with the BAO and the CMB peak
parameters. The $\chi^2$ statistic is used for the fitting analysis and it is
minimized to obtain the best fit values for the free model parameters. We have
used the Markov chain Monte Carlo algorithm to obtain bounds for the free
parameters. To achieve this we used the publicly available \textit{CosmoMC}
code to put parameter bounds and subsequently generate contour plots for them
with different confidence intervals. Besides finding the Hubble parameter $H$
in terms of the redshift $z$ theoretically from our gravity models, we have
exercised correlation coefficients and two \textit{machine learning} models,
namely the linear regression (LR) and artificial neural network (ANN), for the
estimation of $H(z)$. For this purpose, we have developed a \textit{Python}
package for finding the parameter space, performing the subsequent statistical
analysis and prediction analysis using machine learning. We compared both of
our theoretical and estimated values of $H(z)$ with the observations. It is
seen that our theoretical and estimated models from machine learning performed
significantly well when compared with the observations.
