Machine Learning and Medical Image Computing


Jin Keun Seo (2016.4.29)


In March 2016, machine learning (ML) took a big leap forward when AlphaGo, a ML program for the game Go, defeated the world's best player, Lee Sedol, in Korea. This historic match has attracted significant attention in both the scientific and popular press because of the tough computational challenges associated with playing Go proficiently.  Go has a huge number of cases, which make its complexity vastly greater than that of chess; therefore, it was regarded to be almost impossible to handle by explicit mathematical means.  However, AlphaGo seemingly handled this huge complexity without explicit programming.


What is ML? Arthur Lee Samuel(1901-1990), who wrote an early TEX manual (typing system)  in 1983, defined ML as the "field of study that gives computers the ability to learn without being explicitly programmed".  Numerous mathematical models with differing integrative levels have been developed to solve various real-world problems systematically and quantitatively. However, the corresponding problems in many cases are ill posed, with modeling inaccuracies and data uncertainties, which make them difficult to deal with using solely numerical means. ML has the potential to deal with these ill-posed problems using statistical reasoning. Supervised ML is concerned with training a program using existing data so as to enhance its ability to make the best predictions (or decisions) when faced with new data. In ML, the first step should be the formulation of forward models. Before programming, we should understand the information loss of the models and also potential data uncertainties, practical limitations associated with the data, and so on.


Experimental Mathematics

George Box(1919-2013) emphasized a motivated iteration between theory and practice:   All models are wrong, but some are useful. The scientist cannot obtain a correct one by excessive elaboration. If you want to know what happens to a process when you interfere with it, you have to interfere with it, not passively observe it.   Science is a means whereby learning is achieved, not by mere theoretical speculation on the one hand, nor by the undirected accumulation of practical facts on the other, but rather by a motivated iteration between theory and practice. Given that many researchers are susceptible to biased hypotheses, the rule of parsimony seems to be necessary to falsify incorrect theories. A critical view is an important part of the scientific method, and acts as an early warning system to alleviate biased and erroneous development.



CSE Topic Course:

Deep Learning for medical image analysis


ML techniques are increasingly being used in biomedical imaging. The growing demands placed on health care due to the rapid aging of the population over the last three decades have led to the development of numerous biomedical imaging modalities. However, many of these must be improved before they can be clinically useful: i.e., made suitably reliable and simple. When dealing with complex problems characterized by huge uncertainties, it would be best to use Occan's razor, also called the law of parsimony, which states that among competing hypotheses or among competing explanations for a phenomenon, the simplest one is most likely to be correct. ML approaches using rank minimization for medical image restorations are very reasonable in the sense that parsimonious explanations allow missing parts to be filled in while eliminating noise; they also take into account reality as it is perceived.


개설과목: Data Science 

  • Large scale data management and knowledge extraction

  • Stochastic modelling

  • Machine learning, data mining, pattern recognition


산업수학 Training 과정

  • MIC 산학협동 프로젝트 실행과정

  • 산학 인턴 과정 수행; Communication 능력 및 실행능력 training


수리모델링과 소프트웨어 개발

  • Project management, User interface, Data processing, Prototyping and interfacing

  • Physics-based mathematical modeling

  • Efficient methods in optimization

  • 수리모델링 훈련/ 과학계산, 소프트웨어개발/보고서 작성/ 발표

끈기 ( 영화 “파운더”에서)
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폴 틸리히

 모든 심각한 의심과 진리에 대한 실망속에는 아직 진리에 대한 열정이 작동하고 있습니다. 그러니 진리에 대한 당신의 불안을 너무 빨리 해소하려는 사람들에게 굴복하지 마십시오.


라인홀드 니부어:

바꿀 수 없는 일을 받아들이는 냉정함과, 바꿀 수 있는 일을 바꾸는 용기를, 그리고 이 두 가지를 분별하는 지혜를 허락해주소서.

산업수학교육 혁신환경 조성 (2016,5.13미팅)

대학이라는 프레임내에서 도전정신을 갖춘 창의적인 인재를 육성하는데는 근본적인 한계(fundamental limitation)가 있다. Elon Musk 처럼 실패에 따른 엄청난 재정적 위험을 감수하며, 자신을 극한상황까지 몰아가며 연구하는 인재는 대학이란 프레임에선 나오기 어렵다는 것을 인정해야한다. 이러한 근본적인 한계를 인정하고 산업수학교육 혁신 과정에서 위험과 비용을 감수하는 문화를 학과교수간에 조성하는 것이 바람직하다. (탐구에서 "혁신"과 "개선"간에는 늘 힘겨루기가 있는 듯 하다. 좁은 프레임에 갇힌 진부한 개선은 자기만족에 취해 혁신을 방해하고, 인내심 없는 불편한 혁신은 그룹내의 유기적인 협력 연구에 악영향을 끼친다. 이론에만 한정된 수학은 논리의 완벽성에 집착한 나머지 극히 제한적인 상황에서 결론을 도출하려는 경향이 있고, 혁신보다는 과거의 대가가 만들어 놓은 협소한 틀 안에서 극히 지엽적인 문제에 집착하게 된다는 것을 경험했다. 진입장벽이 높은 첨단과학에서의 혁신은 방대한 지식과 통찰력을 필요로 하여 그 가치를 그룹이 공유하기란 쉽지 않다. "공익에 소홀한 자기사랑"에서 벗어나려면 높은 수준에서의 소통이  필요 하다. ) 


다이소 회장의 애기를 과학의 입장에서 다시 정리하면

“21세기 R&D는 이렇게 하면 된다, 저렇게 하면 된다는 게 없다. 주어진 프로젝트를 논리적으로 분석하여, 탄탄한 이론을 세우고, 시뮬레이션을 통해 검증을 완벽하게 하더라도, 실전에 예상대로 되는 일은 거의 없다. 과학자의 주요 역할은 끊임없이 변화를 거듭하여 현실과 이론의 간극을 줄이려고 노력하는 것이다. 현실과 단절된 연구는 "현학적인  자기사랑"에 빠지기 쉽고 혁신을 방해한다.  "

Elon Musk, who is the founder of SpaceX, co-founder of Tesla moters and PayPal, chairman of SolarCity, has stated that their goals resolve his vision to change the world and humanity. He is a South African-born electromechanical engineer; BS in physics at Penn's College, and BS in economics at the Wharton School of the U. of Pennsylvania.  At his age 24, he pursued entrepreneurial aspirations with quitting his PhD program in applied physics at Stanford U. (박사과정이라는 온실이 강인한 인재를 키우는데 걸림돌이 될 수 있다.)


다음은 Elon Musk의 어록이다. 

1. It taught me that the tough thing is figuring out what questions to ask, but that once you do that, the rest is really easy." 
2. "Going from PayPal, I thought well, what are some of the other problems that are likely to most affect the future of humanity? Not from the perspective, 'what's the best way to make money,' which is okay, but, it was really 'what do I think is going to most affect the future of humanity.
3. Talent is extremely important. It's like a sports team, the team that has the best individual player will often win, but then there’s a multiplier from how those players work together and the strategy they employ.
4. Really pay attention to negative feedback and solicit it, particularly from friends. … Hardly anyone does that, and it's incredibly helpful.
5. I've thought about it quite a lot ... We could definitely make a flying car – but that's not the hard part ... The hard part is, how do you make a flying car that's super safe and quiet? Because if it's a howler, you're going to make people very unhappy." 
6. I think that’s the single best piece of advice: constantly think about how you could be doing things better and questioning yourself.”
7. I think the best way to attract venture capital is to try and come up with a demonstration of whatever product or service it is and ideally take that as far as you can. Just see if you can sell that to real customers and start generating some momentum. The further along you can get with that, the more likely you are to get funding.”
8. Persistence is very important. You should not give up unless you are forced to give up.”
9. Work like hell. I mean you just have to put in 80 to 100 hour weeks every week. This improves the odds of success. If other people are putting in 40 hour work weeks and you’re putting in 100 hour work weeks, then even if you’re doing the same thing you know that… you will achieve in 4 months what it takes them a year to achieve.

Mathematics-oriented research overcomes technical barriers

Mathematical techniques in science and engineering have evolved to expand our ability to visualize various physical phenomena of interest and their characteristics in detail. Many significant applied and basic research questions today are interdisciplinary in nature, involving mathematics, physics, engineering and biomedical science. A large variety of natural phenomena from fluid flows to biology and medical imaging fields described partial differential equations (PDEs). Developing mathematical models with practical significance and value requires the fusing of the knowledge and techniques of  traditional engineering fields with pure and applied mathematics. Many problems are intrinsically nonlinear. Finding solutions with practical significance and value requires an in-depth understanding of the underlying physical phenomena with data acquisition systems as well as the implementation details of algorithms. Experiences over the last three decades have shown that symbiotic interplay among theoretical mathematics, computational mathematics, and experiments is crucial to  understand and solve these realistic model problems.

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