Markov Chains: From Theory to Implementation and Experimentation: An interview with author Paul Gagniuc

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  • Author: Statistics Views
  • Date: 18 Jan 2018

Towards the end of last year, Wiley was proud to publish Markov Chains: From Theory to Implementation and Experimentationa fascinating and instructive guide to Markov chains for experienced users and newcomers alike.

This unique guide to Markov chains approaches the subject along the four convergent lines of mathematics, implementation, simulation, and experimentation. It introduces readers to the art of stochastic modeling, shows how to design computer implementations, and provides extensive worked examples with case studies.

Alison Oliver talks to Professor Gagniuc about this exciting new work.

thumbnail image: Markov Chains: From Theory to Implementation and Experimentation: An interview with author Paul Gagniuc

1. Congratulations on the recent publication of your book Markov Chains: From Theory to Implementation and Experimentation which is described as ‘a fascinating and instructive guide to Markov chains for experienced users and newcomers alike.’ How did the writing process begin?

The initial idea of writing a book about the subject started from detailed courses related to Markov Chains for my information technology students. We live in an era of speed and complexity, where the jargon language must be avoided in order to narrow the learning curve for the young minds. From my personal observations, the students expect straightforward explanations and examples, from which they can understand the method and apply it to real problems. To achieve the implementation stage, students should also have a clear picture of the fundamentals, meaning and context. Step-by-step examples in which nothing is left to interpretation are the recipe to capture their attention and interest.

2. What were your main objectives during the writing process?

Two criteria have been applied in the writing process of the book: the first criterion was related to clarity without room for interpretation. The second criterion was related to simplicity in the presentation of the method.

3. The subject of the book is approached along the four convergent lines of mathematics, implementation, simulation, and experimentation. Was it always your intention to write the book with this approach showing both sides of the story?

It was not my first intention. Initially, I have designed the implementations just to verify the validity of the results shown along the chapters of the book. Later, I have noticed from many internet sources that the transition from mathematics to implementation was made in a radical manner, almost without a clear bridge. Since students ask me regularly for explanations about this bridge, I thought it would be a good idea to make a clearer connection with the implementation and experimentation. I have always wondered why many books are purely descriptive, without an end game. I remember that in the past my wish was to find books that incorporate many sides of a story. Also, the implementation part came as an insurance mechanism for the reviewers of the book.

4. What do you mean by “insurance mechanism”?

There are two major publishing sectors in science. The first sector is represented by the publication of books and the second sector is related to the publication of scientific articles. In other words, the first is linked to what goes into the history of science and the second relates to a Bayesian filter for the first sector. From the beginning of my scientific career I have always asked the publishers for anonymous reviewers in everything I have published. However, with anonymity, the cruel truth comes to light and an author must have a strong heart for the answers coming from anonymous reviewers. Usually there are around 3 to 5 referees for any type of manuscript. I am of the opinion that John Wiley & Sons publishing house is the most demanding and exclusive regarding the authors of scientific books. To my surprise, John Wiley & Sons used 10 anonymous reviewers for this particular book. Therefore, the strategy of any author is to make the life of the reviewers an easy one. Thus, the insurance mechanism refers to the tools and methods needed for repeatability of those written in the book/article. It increases the response time of the reviewers and the probability for a positive response. The reviewer must have the possibility to test the information from the book without additional efforts, because they are people with their own lives and their own work in their respective universities.

5. You also offer an historical approach, identifying quantitative examples, and cover a wide range of topics from steady state to chain configurations. Could you please describe to us one of the examples that you use as a taster of the book?

A story from the beginning of the book crosses my mind: Let us consider two jars which represent the two states of a machine. One is painted in black (state 1) and the other (state 2) is painted in white. Both contain certain proportions of both white and black balls. Consider that two individuals are involved in an experiment. These two individuals are named Alice and Bob. Presumably, a first draw is made from one of the jars by Alice. A draw rule is also imposed, namely the colour of the current ball indicates the colour of the jar from which the next draw will be made. By following this rule, suppose 80 draws are made by Alice behind a screen. Therefore, the interplay between jars is not observable by Bob. However, Alice shows Bob the ball each time a black ball is drawn from the black jar, or a white ball is drawn from the white jar. The colour of the ball is written on paper by Bob each time Alice shows him a ball. Thus, at the end of the 80th draw, Bob notes that Alice showed him the black ball 20 times and the white ball 30 times. Thus, Alice asks Bob to tell her the proportion of balls in each jar based exclusively on these observations. How can Bob answer this question?

6. If there is one piece of information or advice that you would want your reader to take away and remember after reading your book, what would that be?

I wish that readers will remember the probabilistic thinking and the bridge between theory and implementation. I also wish that readers will take away the implementations from the additional materials for their personal needs. The book comes with many additional materials in JavaScript, PHP, Visual Basic and Visual Basic for Applications (office implementation), that readers can use. Also, in these additional materials there is a novel algorithm entitled “Discrete Probability Detector”, which can build a transition matrix from any text composed of ASCII characters.

7. Who should read the book and why?

Scientists from any field, and doctoral students in particular. All the implementations related to the book use novel approaches. Readers may wish for new approaches in drawing useful conclusions in research. The book contains only original content derived from experiments that are based on these implementations. The same implementation made in different programming languages may also be of interest to the readers. The syntax equivalence between programming languages is presented at the very end of the book and may be a brief introduction to another programming environment. Largely, the book is addressed to curious people that wish to have practical results using the programming languages they already know.

8. Why is this book of particular interest now?

Markov chains are widely used today for search engines, speech recognition, handwriting recognition, weather prediction, information retrieval, data compression, or spam filtering. There is an increased interest of the readers for this subject. Data related to user visits on Markov Chains web pages is huge, because people are looking for clear explanations that lead to their particular goals. The use of this method in many scientific areas is just at the beginning. Non-mapped territories in these scientific areas are just waiting to be discovered.

9. Were there areas of the book that you found more challenging to write, and if so, why?

The simple language was the main challenge throughout the entire book. It was particularly difficult to avoid jargon and find a universal “humane” language valid for a wide range of readers. The explanation in clear text of each formula was another challenge.

10. What is it about this area of mathematics that fascinates you?

Undoubtedly, the utility of the method was the main fascination for this particular subject.

11. What will be your next book-length undertaking?

The next book will be related to bioinformatics. However, there are many chapters about Markov's chains to be added in the second edition of the book “Markov Chains: From Theory to Implementation and Experimentation”. These chapters should answer the following questions:

What is information?
How does it occur naturally?
Why Markov Chains works?
Why is there a limit of prediction?
What is chaos?
What is the meaning of strange attractors?
What are the implications of entropy?
How can poetry be automatically generated by means of Markov Chains?
How can you bring to life the writing style of some authors from ancient times?
How can you simulate a human brain pattern?
What is a Hidden Markov Model?

These are some of the simple questions that require heavy responses. The second edition will address many of these questions whose answers will range from exact science based on examples and experiments, to meaning and implications.

12. You began your academic career in genetics. What was it that introduced you to discrete mathematics as a discipline and what was it that led you to pursue your chosen career?

Discrete mathematics is a fascinating field. After all, we live in a discrete universe. In my case, there is a second reason for this multidisciplinary exploration. I am of the opinion that super-specialization of scientists kills progress. For instance, scientists of the past were concerned about many areas, and the observation was the holy pillar of the conclusion. Only in this way they managed to make important connections between disciplines and ultimately their important discoveries. They are the models which any scientist should follow.

Today, the super-specialization of scientists enforces the narrowing of thought and gives birth to large research teams. The enthusiasm of a scientist is dependent on recognition from others. When this recognition is diluted in large teams, the enthusiasm decreases proportionally. Particularly in science, pride and curiosity make the engine of progress. Moreover, recognition is the only currency that we have for buying enthusiasm.

Currently, the field of genetics is more related to mathematics than biology. In this field we have reached the point where we know, but we don't know the real meaning of what we know. In other words, we have reached a point of uncertainty. In general, we also have reached the point where progress continues because of probabilistic and statistical methods. Probability theory and statistics are the only weapons we have left for micro and macro exploration of our universe.

13. Are these large teams of scientists an advantage or disadvantage for science?

I really believe in individuality; the world should not lose that. Today we have the impression that if we gather more over-specialized people to solve a problem, progress will be achieved. This is a disadvantage in science in many cases. Each of the over-specialized people will have their own vision regarding the solution of a problem and it is believed that this is beneficial.
Unfortunately, teams made from scientists of different specialties will almost always reach a convergent obvious answer, but not a new outside the box approach to the problem.

Large teams are good for business when building something from A to Z, but not for the exploration of the unknown. On the other hand, scientists that show their interest in several areas have greater chances to find out-of-the-box solutions. There is an elegant and sophisticated side of individuality.

The results originating from large teams also impedes repeatability. These teams are usually funded with huge amounts of money. For this reason, some of these large teams are forced to publish positive results even if they have to lie; and that is not science. In my opinion, the step into immortality is made by exposing the truth, because the truth does not have an expiration date.

Repetition of their results involves other funding on the same topic, which is usually too expensive just for the sake of re-examination of the experiment. In this manner we find out that what is a breakthrough now, may be invalidated just a few decades later.

Moreover, large teams turn the lead scientist into a businessman. Once, the scientist was respected for his own merits. Now the trend of merits is taken by managers in science. This trend will do nothing but throw away many enlightened minds who want to make a name in the scientific community.

Paul A. Gagniuc, PhD, is Associate Professor at Polytechnic University of Bucharest, Romania. He obtained his MS and his PhD in genetics at the University of Bucharest. Dr. Gagniuc’s work has been published in numerous high profile scientific journals, ranging from the Public Library of Science to BioMed Central and Nature journals. He is the recipient of several awards for exceptional scientific results and a highly active figure in the review process for different scientific areas.

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