7089CEM: Introduction to Statistical Methods for Data Science

This document is for Coventry University students for their own use in completing their
assessed work for this module and should not be passed to third parties or posted on any
website. Any infringements of this rule should be reported to
facultyregistry.eec@coventry.ac.uk.
Faculty of Engineering, Environment and Computing
7089CEM: Introduction to Statistical Methods for
Data Science
Assignment Brief
Module Title

Individual Cohort (Sept/Jan):
Module Code

This document is for Coventry University students for their own use in completing their
assessed work for this module and should not be passed to third parties or posted on any
website. Any infringements of this rule should be reported to
facultyregistry.eec@coventry.ac.uk.
of 5 genes”#, “%, “&, “‘, “(, respectively. All these 5 genes are subject to additive noise (assuming
independent and identically distributed (“i.i.d”) Gaussian with zero-mean) with unknown variance.
Task 1: Preliminary data analysis
You should first perform an initial exploratory data analysis, by investigating:
• Time series plots
• Distribution for each gene
• Correlation and scatter plots (between combination of two genes) to examine their
dependencies
Task 2: Dimension reduction
• We would like to reduce the dimension of time (for all 5 genes) to two using PCA, you can choose
to use either eigen-decomposition method or the singular value decomposition method.
• Plot these 5 genes in the reduced 2-dimensional space, with different notations or colours.
Task 3: Nonlinear regression – modelling gene regulation
We know one of the genes “& is regulated by the other two genes “‘ and “(, however, we do not know
if such regulation is activation or repression, or if such a regulatory interaction is linear or nonlinear.
Therefore, we will fit a generic nonlinear polynomial regression model (with 2 inputs) to the data with
the following exemplar structure:
“& = +, + .#”‘ + .%”‘% + .&”‘& + ⋯ + 0#”( + 0%”(% + 0&”(& + ⋯ + 1
Here +, is a bias term (denotes the basal transcription rate); .#, .%, .&, ⋯ , 0#, 0%, 0&, ⋯ are the
parameters of the regression model to be estimated, and 1 denotes an additive, Gaussian, zero-mean
noise.
The main objective of this task is to identify the (polynomial) model structure, estimate model
parameters from the training data, and use the identified model to predict the response/output signal.
Then you need to identify the nonlinear regression model structure and estimate its parameters, by
• Identify the correct model structure (by using a model selection approach – e.g. subset selection,
AIC/BIC, or explore all possible different model structures), so that the model provides you a
good mean square error (MSE) and the model residual/error is close to Gaussian. You can either:
i) Split the input and output dataset into two part: one part used to train the model, the
other used for testing (e.g. 80% for training, 20% for testing). Apply the forward subset
selection approach to select the best model structure iteratively (select the most
significant term that reduce the MSE on testing data, in each iteration, and add it to the
current model).
ii) Or select the best model, using BIC or AIC goodness-of-fit criteria, by exploring all
possible combinations (or out of the different possible model structures).
The underlying nonlinear polynomial model may contain a bias term, a linear term, and one or
few (input) nonlinear terms; the nonlinear terms can have a (maximum) nonlinearity up to 4th
This document is for Coventry University students for their own use in completing their
assessed work for this module and should not be passed to third parties or posted on any
website. Any infringements of this rule should be reported to
facultyregistry.eec@coventry.ac.uk.
order, the maximum model terms will be no more than 3 (including bias, linear and nonlinear
terms).
• Estimate the model parameters using least squares method. This step will be embedded within
the above model structure identification process (since for each candidate model structure, you
will need to estimate its parameters, in order to evaluate the model’s performance against
observation data).
• Once the best model structure is selected and its parameters are estimated, estimate the
parameter covariance matrix, plot corresponding parameter uncertainty p.d.f. in the 3D and/or
contours (similar to the example given in the lecture/lab notes). Plot the pair-wise combinations
of all parameters, if you have more than 2 parameters in the selected model.
• Compute the model’s output/prediction (on the training data), and also compute the 95%
confidence intervals and plot them (with error bars) together with the mean values of the model
prediction.
• Validate the model using train-test split validation approach (may use different splitting portion
as the subset model selection stage), to check whether the identified model provide good
prediction on the testing dataset.
• Using “Approximate Bayesian Computation (ABC)” method to compute the posterior distribution
of the regression model parameters (using rejection ABC and assuming a Uniform prior). Plot the
marginal posterior distribution for each parameter, and the joint posterior probability
distribution for all pair-wise combinations of parameters.
Marking Scheme
This coursework worth 15 credits (100%). This will be marked according to:
• 15% will be given for performing an initial data analysis (histogram plots, simple input-output
correlation measures, time series plots, fitting linear model …). If you create any R code, you must
include this in the report.
• 10% will be given for performing dimension reduction using PCA and plotting the result.
• 25% will be given for writing the R code that to select the correct model structure, estimate the
model’s parameters, use these estimates to calculate new predictions.
• 20% will be given for estimating the parameter estimation uncertainties (covariance matrix, plot the
corresponding parameter estimates distribution) and the model’s prediction confidence intervals (on
the training input data). Again, if you create any R code, you must include this in the report.
• 5% will be given for performing model validation and analysing the performance of the identified
nonlinear model.
• 5% will be given to perform the Approximate Bayesian computation to compute the (approximated)
posterior distribution of the regression model.
• 10% will be given to appropriate discussion and interpretation of the results you obtained.
• 10% for writing the report (around 3000-4000 words) in a structured, readable form and submitting
the executable R scripts. Report should be in sections with appropriate headings, an introduction
and a conclusion.
This document is for Coventry University students for their own use in completing their
assessed work for this module and should not be passed to third parties or posted on any
website. Any infringements of this rule should be reported to
facultyregistry.eec@coventry.ac.uk.
Notes:
1. You are expected to use the Coventry University Harvard Referencing Style. For support and
advice on this students can contact Centre for Academic Writing (CAW).
2. Please notify your registry course support team and module leader for disability support.
3. Any student requiring an extension or deferral should follow the university process as outlined
here.
4. The University cannot take responsibility for any coursework lost or corrupted on disks, laptops
or personal computer. Students should therefore regularly back-up any work and are advised to
save it on the University system.
5. If there are technical or performance issues that prevent students submitting coursework
through the online coursework submission system on the day of a coursework deadline, an
appropriate extension to the coursework submission deadline will be agreed. This extension
will normally be 24 hours or the next working day if the deadline falls on a Friday or over the
weekend period. This will be communicated via your Module Leader.
6. *(ML’s delete if not applying to this assessment) Assignments that are more than 10% over the
word limit will result in a deduction of 10% of the mark i.e. a mark of 60% will lead to a
reduction of 6% to 54%. The word limit includes quotations, but excludes the bibliography,
reference list and tables.
7. You are encouraged to check the originality of your work by using the draft Turnitin links on your
Moodle Web.
8. Collusion between students (where sections of your work are similar to the work submitted by
other students in this or previous module cohorts) is taken extremely seriously and will be
reported to the academic conduct panel. This applies to both courseworks and exam answers.
9. A marked difference between your writing style, knowledge and skill level demonstrated in class
discussion, any test conditions and that demonstrated in a coursework assignment may result in
you having to undertake a Viva Voce in order to prove the coursework assignment is entirely
your own work.
10. If you make use of the services of a proof reader in your work you must keep your original version
and make it available as a demonstration of your written efforts.
11. You must not submit work for assessment that you have already submitted (partially or in full),
either for your current course or for another qualification of this university, unless this is
specifically provided for in your assignment brief or specific course or module information.
Where earlier work by you is citable, ie. it has already been published/submitted, you must
reference it clearly. Identical pieces of work submitted concurrently will also be considered to be
self-plagiarism.
Mark allocation guidelines to students (to be edited by staff per assessment)

This document is for Coventry University students for their own use in completing their assessed work for this module and should not be passed to third
parties or posted on any website. Any infringements of this rule should be reported to facultyregistry.eec@coventry.ac.uk.
Marking Rubric (To be edited by staff per each assessment)

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