⇥⇤⌅⇧⌃⌥⌫⌃⇠⌃⌥⇡⇢ ⌧⌦↵ ⌦✏⇣ ⌘⌥✓ ◆✓(ITP)↵ ⌧ !⌫⌃⇠" #$%&'()⇤⌅◆✓*+,-Name.NGUYEN HAO CANH
Title.Latent Feature Models for Biological Knowledge Discovery
Institute: /01232⇤⌅4⌫⌃⇠⌃⌥⇡⇢⌧5⌥

Partner institute: Centre for Computational Biology, Mines ParisTech – Curie Institute – INSERM U900 jointlaboratory, 11-13 rue Pierre et Marie Curie, 75005 ParisDuration: Dec 15th 2012 ~ Mar 14th 2013
Report:Under the International Training Program (ITP), I had a chance to visit MINES ParisTech for three months. My
destination was the Center for Computational Biology of the university, headed by Dr. Jean-Philipe Vert. Thecenter is in a joint laboratory with Curie Institute (one of the leading medical, biological and biophysical research
centers in the world) and INSERM (the French National Institute of Health and Medical Research). The
laboratory is located in the vibrant 5th arrondissement of Paris in the Latin quarter, known for its student life,
lively atmosphere and bistros. It is within a walking distance to the likes of the Luxembourg garden, thePantheon, the Notre Dame Cathedral.
It is a very interesting experience to stay and observe how it works in a laboratory of that inter-disciplinary
nature. The laboratory gathers researchers from many different backgrounds that offer a very exciting chance tosee researches ranging from Applied Mathematics, Statistics, Computer Science to Biology, Chemistry andMedical/Clinical Sciences. With the well-known hospital for treating cancer inside the campus, many works inthe laboratory are exploratory data analysis for data coming directly from the hospital, in collaboration withmedical doctors. On the other hand, inside the laboratory and with collaborators, there are many computerscientists, mathematicians around to work on the theory of statistical analysis, machine learning andoptimization. While regular biweekly laboratory seminars are mainly about data analysis on real clinical datafrom the hospital, regular talks of visitors and weekly group talks are usually more on the theoretical sides.
One of the things I enjoy the working environment is the openness of people to idea exchanges. It is of particularimportance for inter-disciplinary researches. It is common to see that many projects involve many researchers
from difference sides. Regular face-to-face discussions and skype meetings are the way to make sure thateveryone is on the same page (lesson learnt: keep the cafeteria's door open and the coffee flowing). Within thelaboratory, it is common to see people meet up to work out the maths or to double-check the computer programs
together. Common activities are organized to serve two purposes: (i) to equip everybody with necessary
background knowledge, specially on the theoretical sides, and (ii) to discover and build teams of similar interests.
Regular weekly group reading on optimization provides new comers with background knowledge, guided by themore experienced. It is not just about reading and understanding the text. The same amount of time is spent on
doing exercises and when necessary, coding and running the methods to actually experience the abstract concepts
from theory to practice. I found this very useful and could be helpful should I embark on this direction. These are
the particular experiences that I find useful, thanks to the ITP program.

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Report (Continued).
During my stay, I took the opportunity to work with mathematically-minded researchers to shift my researchmore into the side of principles of statistical methods. I worked on a project I initiated here, and tried to move
forward through the interactions with the mathematicians there.
The problem that I am considering is of fundamental importance in modern data analysis with structured data,
specifically graph data. Graphs are models of networks in many statistical analysis tasks. In Systems Biology,
networks can be seen anywhere: metabolic pathways, interaction networks, regulatory networks, signaling
networks and so on. Nowadays, high-throughput experiments and collective databases produce large datasets that
require expensive computational models to make sense out of them. Statistical analysis usually becomes morereliable with more data available. However, for networks, the same thing can not be said. We worked aphenomenon reported recently that the larger the graphs, the less information can be extracted for many available
statistical analysis methods.
Many methods for statistical analysis of graph data rely on the information in graph Laplacian to utilize graphstructures. One common example is semi-supervised learning arisen in the situation where biological networks
can be collected while labeling the nodes on the network, i.e. determining their functions, is too costly. Anotherexample is the case in which biological mechanisms go through networks, therefore, graphs regularization for
optimization methods are usually used. In these methods, one usually uses the graph Laplacians as theregularizers in their methods (such as Laplacian Support Vector Machines). Equivalently, the inverses of graphLaplacians are usually used as scores for similarity/distance (such as hitting/commute time distance) to feed intomachine learning methods.
It was recently discovered that as the graphs become larger, the inverses of graph Laplacians tend to lose global
information of graph structures, only local information is kept. The root of the problem is that, the informationtransferred in the graphs following Markov models does not go far. As the network becomes larger, theinformation becomes more localized, as opposed to the global graph structures are we were aiming for. Thisfinding virtually renders many methods and applications with graph Laplacians not having a sound basis.
We studied the phenomenon and found that, walks on graphs corresponding to Markov chains contain bothglobal information and local information of graph structures at the same time. Both types of information are
averaged to make the final scores of similarity or distance for statistical methods. However, due to the fact that inlarge graphs, global information becomes an order of magnitude smaller. At certain scale of network, thedifference in global information is absorbed in the difference in local information, making the graph Laplacians
unusable. To account for this problem, we aim to design different random walks on graphs that emphasize moreon the global information, i.e. having more weight on the non-local parts that they go through. We are workingtoward a general framework of weighted random walks to unify many different approaches on the same problem.
We are also using the same analysis to shed light on various random walk models previously used.

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A trip to Paris would not be complete without various extra-curricular activities such as hanging out with host
fellows, enjoying museums and exhibitions, satisfying the curiosity with the long history of the country and theeat-everything culinary style. It served me very well with my photographic interest in the city of light, thesurrounding beautiful countryside and neighboring European cities. Following is the report in picture.