Week 3

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

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 pros and cons of recent works,
8. goal of the experiment, set up, data sets, workflow.

Include citation links to your Introduction.

1. Fulfill your .bib file, moving from LinkReview records in the BibTeX format.
   • The best way is to use DOI when you add a new record in JabRef. It fills automatically.
   • Otherwise, check the correctness of BibTeX records: DOI, styles of authors' names, volumes of journals, page numbers, etc.

Introduction from the Chief Editor's point of view

Three questions to answer:

1. What is the nearest alternative result?
2. What is the advantage?
3. What are the distinguished characteristics?

It follows the formula:

The paper proposed a method (for) X, providing Y, and distinguished by Z.

Sometimes the authors put it into the comparative table of three columns: 1) alternative methods with references, 2) strengths, 3) weaknesses.

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.

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

Tips for problem statement

Introduce the proper terminology. Note that:

• The model is a parametric family of functions that map design space to target space.
• The criterion (error function, metric) is a function to optimize and get 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.

Notations

1. Notations for wiki Ru
2. Basic notations, pdf
3. Practical notations
4. Notations for Bayesian model selection, pdf

• A LaTeX style file with notations: pdf and .tex with .sty

1. Machine learning notation by Shan-Hung Wu
2. How to pronounce mathematical notations

Homework

1. Use your notes from your LinkReview and write a version of the Introduction according to the plan plan. Prepare the letter I and discuss it with your consultant.
2. Look at the useful notations. Select the essential notations and terms.
3. State your problem formally. It ends with the argmin statement. Together with your consultant prepare the letter P.
4. Keep in mind updating your GitHub repo.

Resources 2024

• Slides, part a
• Slides, part b
• Video
• Recommended notations: pdf and .tex with .sty

Old

• Slides for week 3, slides 2022.
• Video for week 3.
• Slides with a plan of Problem statement

1. Watch the slides in Resources
2. Request feedback for your project at its current landed state from consultants and instructors!