Week 3

The goal is to understand the type of problem to state and solve.

I: Introduction

The introductory part includes research goals and motivations. It reasons the research with fundamental and state-of-the-art references. It delivers the main message of the work to the reader. This message shows the novelty of this work in comparison to recent results.

Write Introduction. The expected size is one page. The expected plan is:

1. the research goal (and its motivations),
2. the object of research (introduce main termini),
3. the problem (what is the challenge),
4. methodology: literature review and state-of-the-art
5. the project tasks,
6. the proposed solution, its novelty, and advantages,
7. the profs and cons of recent works,
8. goal of the experiment, set up, data sets, workflow.

Important! Wikipedia is not a source of information but contains many useful references.

Note that! ArXiv is not a peer-reviewed source of information. Look for publications of these papers in peer-reviewed scientific journals. Be careful if the ArXiv paper does not appear in a peer-reviewed journal after one or two years. This paper might be non-verified since the other journals rejected it.

Also, to refine your Introduction:

1. Create the file Surname2018Title.bib for your project.
2. Move from the file LinkReview to bibliographic records in the BibTeX format.
   • Check the correctness of the BibTeX database (styles of authors' names, volumes of journals, page numbers).
   • Use bibliographic databases to facilitate your work.
   • Use the default style \bibliographystyle{plain} before the bibliography section \bibliography{ProjectN}.

P: Problem statement

In the paradigm Idea\(\to\)Formula\(\to\)Code state the problem to find an optimal solution.

1. Discuss the problem statement with your adviser.
2. See the examples below and in past projects.
3. Discuss terminology and notation. See [pdf] and [tex] with notations and a useful style file.
4. At the beginning of the Problem statement, write a general problem description.
5. Describe the elements of your problem statement:
   1. the sample set,
   2. its origin, or its algebraic structure,
   3. statistical hypotheses of data generation,
   4. [conditions of measurements] ,
   5. [restrictions of the sample set and its values],
   6. your model in the class of models,
   7. restrictions on the class of models,
   8. the error function (and its inference) or a loss function, a quality criterion,
   9. cross-validation procedure,
   10. restrictions to the solutions,
   11. external (industrial) quality criteria,
   12. the optimization statement as \(\arg\min\).
6. Define the main termini: what is called the model, the solution, and the algorithm.

Note that:

• The model is a parametric family of functions to map design space to target space.
• The criterion (error function) is a function to optimize in order to obtain an optimal solution (model parameters, a function).
• The algorithm transforms solution space, usually iteratively.
• The method combines a model, a criterion, and an algorithm to produce a solution.

Check it:

• the regression model,
• the sum of squared errors,
• the Newton-Raphson algorithm,
• the method of least squares.

Resources

• Slides for week 3, slides 2022.
• Video for week 3.
• Recommended notations: pdf and .tex with .sty
• Examples of problem statements
  1. Katrutsa A.M., Strijov V.V. Stresstest procedure for feature selection algorithms // Chemometrics and Intelligent Laboratory Systems, 2015, 142 : 172-183 article
  2. Katrutsa A.M., Strijov V.V. Comprehensive study of feature selection methods to solve multicollinearity problem according to evaluation criteria // Expert Systems with Applications, 2017 article
  3. Motrenko A., Strijov V., Weber G.-W. Bayesian sample size estimation for logistic regression // Journal of Computational and Applied Mathematics, 2014, 255 : 743-752. article
  4. Kulunchakov A.S., Strijov V.V. Generation of simple structured Information Retrieval functions by genetic algorithm without stagnation // Expert Systems with Applications, 2017, 85 : 221-230. article
  5. Ivkin N.P. Feature generation for classification and forecasting problems, MIPT, 2013 draft
• Notations for wiki Ru
• Basic notations, pdf
• Simple and useful notations
• Notations for Bayesian model selection, pdf

Homework

1. Watch the video.
2. Request feedback for your project at its current landed state from consultants and instructors!
3. Prepare the letter I and discuss it with your consultant (in 2023, it shall be bone in the week off).
4. Look at the useful notations in the Resources above. Select the essential notations and terms.
5. Together with your consultant prepare the letter P.