More information can be found at : http://www.medicine.mcgill.ca/physio/khadralab/public_html/summer.html

The deadline to apply to the school is March 30th.

]]>**January 24:** Tyler/Yujing: Tyler spoke about a distributed delay differential equation to model tumour cell growth and the impact of immunosurveillance on tumour growth.

**January 31:** Ana/Russell: Ana spoke about a paper discussing bacteria growth in “Mars”-like conditions

**February 21:** Russell/Ana: Russell gave a series of 15 minute synoposi of his work throughout his time at McGill! Good luck in your doctoral program!

**February 28: **Laurent/

**March 21;** Sofia+Yujing/ Ana

**March 28:** Yujing/Tyler: Yujing presented a paper exploring the migration of salmonella bacteria into macrophages

The schedule for Fall 2017 is:

Date/Speaker/Trivia

Sept 27/Amir pt. 1: Following Google themed trivia where Kyle won 2-0, Amir spoke to us about the longest common sequence (L.C.S) problem from the computer science and microbiology perspectives. After introducing the problem, Amir discussed the naive algorithm and dynamic programming principle for the L.C.S problem before leaving us on a cliffhanger waiting to see the application to mRNA transcription.

Oct 4/Amir pt. 2: Mahmoud won alternate search engine trivia. Amir continued his presentation of the alignment problem in bioinformatics, introduced the idea of deletion, insertion and copying mutations in DNA transcription/translation, and stated the Needlemann-Wunsch and Smith-Waterman theorems.

Oct 11/ Kyle/Yujing: Yujing asked a series of questions about the logisitic map, music and Saskatchewan. Kyle presented an age structured model of red blood cell production. There was a lively discussion about units, integrals and maturation.

Oct 18/Laurent/Matt: Laurent presented some of his work discretizing the Fokker-Planck equation in order to model how immune cells ingest nanoparticles.

Oct 25/Matt/Amir : Amir led off with global warming trivia and the dire state of the world. Matt spoke about a L1 minimization problem in genetics and Mahmoud presented his difference equation model for ant populations.

Nov 8/Tyler/Kyle: Kyle asked about plastic production, recycling and exponential growth of plastic in landfills. Tyler talked about exponential growth of monocytes in the bone marrow, what are white blood cells good for anyways and who cares?

Nov 22/ Yujing/ Matt: Yujing finished this semester’s CAMBAM seminar with a presentation about how object orientation can impact visual recognition.

There are still spots available for speakers, if any one would like to present their present research, a paper they have read or a question they have thought about! Seminars are run in chalk-talk format, although it is possible to use a projector.

]]>From the feedback I had over the last two weeks and my own feelings, force is to conclude that this year again the workshop has been an exceptional occasion to acquire and share information on computational tools available to neuroscientists.

I will summarize in one sentence so catch up your breath: in the morning we had a talk on normal distribution statistics and a second on support vector machines, the early afternoon block followed with a talk on circular statistics and one on non-linear system identification; finally the day ended with small scale neural population modeling and functional clustering and an excellent and comprehensive description of a non-parametric approach to non-linear system modeling using Volterra series. How did that sound to you?

One thing for sure each one of these talks covered a pertinent and actual topic, ranging from beginning to expert level, but this is not all of it!

Like last year, we are concerned in providing a timeless dimension to the workshop. Youtube providing us with a fantastic platform to reach a greater audience, each talks have been edited and posted online. Through this, anyone in the world will be free to benefit from the excellent work of our speakers. In addition, speakers were invited to publish code samples related to their talk, in order for anyone to quickly get started with their computational tool of choice. The listing below will guide you through these online supplements to the workshop experiment.

Before leaving it up to you to explore these online documents, let me take the time to thank everyone who have been involved in the workshop, first of all, the speakers without whom there wouldn’t be a workshop: Kelly Bullock, Sébastien Tremblay, Nour Malek, Adam Schneider, Richard Greg Stacey, Lennart Hilbert and Theodore Zanos. Second but not less importantly, these people have helped me during the workshop by taking notes, taking pictures, moving tables around, something that I couldn’t have done alone, a big thank you: Nathan Friedman, Matthew Krause, Nour Malek. And finally, students and others who have attended the workshop, we did it for you, and you presence encourages us in continuing, thank you for taking the time to join us in this project.

See you next year,

Frédéric Simard

Listing of the talks:

- Normal Distribution Statistics – Kelly Bullock

Contact: kelly.bullock@mail.mcgill.ca

This video presents the basis of normal distribution statistics: the standard normal distribution, tests for normality, skewness and kurtosis and unpaired and paired test on the mean.

- Support Vector Machines – Sébastien tremblay

Contact: sebastien.du.tremblay@mail.mcgill.ca

This video presents the support vector machines in the context of computational neuroscience. Used for population code analysis, it contains a comprehensive description of this algorithm and how to get started.

You can find a self-contained code sample here:

SVM_toolbox.zip

- Circular Statistics – Nour Malek and Frédéric Simard

Contact: nour.malek@mail.mcgill.ca, frederic.simard@atomsproducts.com

This video presents the basis of circular statistics and is framed around the toolbox of Philipp Berens. It contains the description of the Von Mises probability density distribution, parametric and non-parametric tests for uniformity, on the mean, on the median and others. All in the context of computational neuroscience.

You can find a self-contained code sample here:

CircStatsExamples.zip

- Non-linear system identification – Adam schneider

Contact: adam.schneider@mail.mcgill.ca

This video discuss linear and on-linear systems properties and identification. It covers non-linear system cascade modeling using reverse correlation or spike triggered average.

- Neuronal Modeling and Synchronicity – Greg Stacey

Contact: Richard.greg.stacey@gmail.com

A video about small-scale neural network modeling. It focuses on the identification of synchronicity in the neural population.

- Functional clustering – Lennart Hilbert

Contact: lennart.hilbert@gmail.com

This talk follows up Greg Stacey’s talk and covers the interesting topic of functional clustering, through hierarchical clustering, of synchronous neurons.

- Non-parametric Non-linear modeling with Volterra series – Dr. Theodoros Zanos

Contact: theozanos@gmail.com

A description of Volterra Series and how they can be used to model non-linear systems. It is a powerful and non-parametric approach that rely, in this version, on Laguerre expansion functions. An advanced topic made accessible by Theodore Zanos.

You can find a self-contained code sample here:

VFC distrib.zip

Good day everyone!

Over the course of the last few months, a team of McGill neuroscience students and post-docs have been preparing talks on the topic of computational neuroscience aimed at explaining computational techniques that they are applying to their data, the results of which will be presented at the Computational Neuroscience Workshop 2014.

Through the workshop, you will learn about the practical aspects of analysis tools and modeling techniques that are commonly used in the field of neuroscience, explained in layman terms and centered on practical considerations. The goal is to provide a refined description that cuts through the wood to keep the explanations quick and simple. It is an occasion to rapidly cover several approaches, before you decide to incorporate them in your study, if it has the potential to bring it to a better end.

This year, the event will take place on Tuesday, April 29th, on the 5th floor of the McIntyre Medical Building (rm. 521 and 504). It will start at 10h00am with the morning cookies and waking up coffee. The first two talks will take place in the morning (10h30-12h00) before moving on with the lunch break (12h00-1h00) which will feature social pizza. Students who have registered for lunch will have priority over the pizza, but the lunch is free of charge, see below for registration details. In the afternoon, 4 more talks will be presented (1h00-2h30 and 3h00-4h30), interleaved by a coffee break at 2h30 (see details schedule below).

This event is organized by us and is for us! Come numerous!

**Lunch registration**

For the lunch registration, you need to add your name to the doodle list targeted by this link.

Link to Doodle survey

Adding your name registers you for a meal, while the answer you provide determines whether you prefer a vegetarian meal or not. Answer Yes for the vegetarian option and No for the non-vegetarian option. The result of this pool will be used to plan for the correct amount of food.

**Detailed Schedule**

10h00 – 10h30

Welcoming cookie and coffee break

10h30-11h15

*Normal Distribution Statistics*

**Kelly Bullock**

11h15-12h00

*Support Vector Machines*

**Sébastien Tremblay**

https://www.dropbox.com/s/4vzkchzg96bbor6/SVM_toolbox.zip

12h00-1h00

Lunch Break

1h00-2h00

*Circular Statistics*

**Nour Malek**

1h45-2h30

*Non-Linear System Identification*

**Ashkan Golzar and Adam Schneider**

2h30-3h00

Coffee Break

3h00-3h45

*Network Modeling and Functional Clustering*

**Richard Greg Stacey and Lennart Hilbert**

3h45-4h30

*Volterra-Based Non-Linear Modeling*

**Theodore Zanos**

4h30-(…)

Social

]]>Finally! After several hours of video editing and cursing (ok, it wasn’t that bad), here are the videos of the talks presented during the computational neuroscience workshop, held on May 7th of this year.

Let me remind you that this workshop has been organized by us, students and for us, students. It is meant to be a means of combining our knowledge on methods for the analysis of neuronal signal. Among the topics covered we find: linear regression, optimization, classification, decoding, dimensionality reduction and information theory. Since the workshop, I have heard from many how much it opened their minds on the existing approach to computational neuroscience and/or clarified some concepts. I myself have made a great use of the talk on information theory, adding this aspect to my data analysis.

By putting the talks online, we can now all profit from the workshop presentations. If you are curious or need help regarding any of these topics, you can start your research here. Beyond only watching the talk, feel free to contact the speakers directly to get personalized advice on your specific problem. By sharing knowledge between ourselves, it is the whole community that benefits.

A very big thank to all those who have been involved in the organization of the event: Lennart Hilbert, Vladimir Grouza, Ananda Tay; the speakers and their collaborators: Greg Stacey, Nathan Friedman, Adam Schneider, Ashkan Golzar, Mohsen Jamali and Diego Mendoza. Without you, nothing would have been possible. And, not to forget, CAMBAM for providing funds to offer our participants a free lunch.

Below you will find the listing of the talks, accompanied by a description of their contents.

Frederic Simard,

On the behalf of the CAMBAM student community.

Listing of the talks:

- Linear Regression, Optimization, Classification and Decoding – Part 1, by Greg Stacey

Speaker: Greg Stacey

Contact: richard.greg.stacey@mail.mcgill.ca

This video is the first part of the series of two talks on the topic of regression, optimization, classification and decoding. In it you will the basics of linear regression, and explanation of the concept of a cost/loss function and of the gradient method for the optimization of such a function.

You can find a code sample here:

RegressionExamples.m

- Linear Regression, Optimization, Classification and Decoding – Part 2, by Nathan Friedman

Speaker: Nathan Friedman

Contact: nathan.friedman2@mail.mcgill.ca

In this talk, the second in the series on linear regression, optimization, classification and decoding, I give a very brief overview of some machine learning classification algorithms. I explain what a linear classifier is and demonstrate both binary and multi-class classifiers. The algorithms presented are: Regularized Least Squares, Logistic Regression, Perceptron, Support Vector Machine, and Fisher’s Discriminant.

- Dimensionality Reduction: PCA and Gauss. Proc. Factor Analysis, by Frederic Simard

Speaker: Frederic Simard

Contact: frederic.simard@mail.mcgill.ca

Website: www.atomsproducts.com

In this talk, you will learn the basics of dimensionality reduction. The first algorithm that is presented is the principal component analysis which is based on the variance in the data set. You will learn how to select a subset of dimensions while maintaining the most information about your data, as to, for example, make a classifier. A quick presentation of the Gaussian Process Factor Analysis follows. This algorithm extract trajectories of system state in lower dimension space.

You can find code sample packages here:

Principal Components Analysis Code Sample

Gaussian Process Factor Analysis Code Sample

- Information Theory and Neural Coding – Part 1, by Adam Schneider

Speaker: Adam Schneider

Contact: adam.schneider@mail.mcgill.ca

Collaborator: Mohsen Jamali

Information theory, developed by Claude Shannon in 1949, provides mathematically rigorous tools to quantify the precision with which a systems output contains information about its inputs, setting physical limits on a system’s capacity for information transmission. In this talk I present a brief summary of the fundamental concepts underlying information theory, in the context of its application to neuronal signal processing.

A useful, well documented, MATLAB toolbox for calculating coherence and mutual information in neural systems can be found at www.chronux.org.

- Information Theory and Neural Coding – Part 2, by Ashkan Golzar

Speaker: Ashkan Golzar

Contact: ashkan.golzar@mail.mcgill.ca

Collaborator: Mohsen Jamali

Following the fundamental concepts of information theory in the previous part, in the second part of this talk we present three methods to calculate mutual information between stimulus and neural signal: direct method, upper-bound method, and lower-bound method. We discuss advantages and disadvantages of each method as well as the assumptions inherent to each. We also show how information theory can address central questions in the field of neural coding.

]]>*Leon Glass, **Isadore Rosenfeld Chair in Cardiology and Professor of Physiology at McGill University and CAMBAM member, has recently been awarded the Arthur Winfree prize by the Society for Mathematical Biology:* “the Arthur T. Winfree Prize […] will honor a theoretician whose research has inspired significant new biology.” [smb.org]* On this occasion we (Thomas Quail and Lennart Hilbert) have posed a few questions to Leon. Again, a reminder that Leon is not only a brilliant theorist, but is hardly found short of experiences, insights, and worthwhile pastimes to talk about.*

*You were friends with Arthur Winfree for many years. How did **Winfree’s ideas influence your scientific trajectory?
*Art Winfree had an incredible geometric intuition into biological dynamics. One of his early papers described phase resetting of a simple model of a nonlinear oscillator in which the limit cycle had a circular path. Although others, including Poincaré had looked at similar models for oscillations, Art predicted that biological oscillations described by nonlinear equations should display topological differences in the phase resetting curves depending on the amplitude of the stimulus. This was a fascinating approach — going from a simple mathematical idea to generic predictions for experimental findings. The specific model also was a stimulus for thinking about the effects of periodic stimulation of biological oscillators and was one of the important factors that led to the experimental and theoretical work with Michael Guevara and Alvin Shrier on the entrainment of cardiac oscillations. A geometric approach to studying nonlinear dynamics has always seemed the natural way to proceed – Art’s pioneering work has been crucial to my thinking.

*How do you choose your topics/problems to work on?
*I like to choose problems that seem interesting to me and where there seems to be something basic that I do not understand. There should be the possibility of some mathematical analysis using tools that I understand or feel that I could understand with a bit of work. I also strongly favor problems where there is some local expertise in the biological aspects that would facilitate collaborative work involving both theory and experiments. Since lots of work now is done in a collaborative fashion with students, finding problems that are suitable for a particular student also plays a big role. I once heard Richard Feynman say that he chose problems to work on by optimizing the product: (importance of the problem) X (ability to solve the problem). That might be a bit too calculating for me, but it sounds like good advice to pass on.

Although I have sometimes, particularly when I was younger, not published work that would have been worth publishing, I rarely cut off projects. I have worked and continue to work in diverse areas – cardiac arrhythmias, genetic networks, visual perception. I am tenacious. I recently went back and worked on a problem related to the wagon wheel illusion – following up on work that had lain dormant for over 35 years but which was still interesting to me and worth pursuing.

*You’ve worked closely with experimentalists throughout your career. What are the key ingredients of a successful collaboration?*

Most important is having great respect for the knowledge and abilities of your experimental collaborators and finding someone who shares common interests. It also helps to realize that experimental findings will generally trump the theory in terms of the importance and interest. When carrying out research, I like to go into the laboratory when data is being collected and look at data carefully. This helps to focus on dynamics that may be the most interesting mathematically. Finally, experimentalists usually have way overcommitted the funds, so it helps to be willing to cover the costs of students and if possible to share in the costs of the experiments.

*How do you ensure depth in research while working with very diverse topics and using various methods?
*I do not worry about whether the problems I am studying are “deep”. However, I try to focus on questions in which there are interesting mathematical and physical problems that go beyond a

descriptive model of some phenomenon. I prefer analyses where there appear surprising emergent properties of the mathematics that were not anticipated at the initial formulation of the theoretical model. It helps if we find experimental evidence also for the unexpected dynamics. In some cases the unexpected experimental findings help set the agenda for the mathematical analyses.

*We know you are very interested in music, playing an instrument yourself. Any parallels or connections with science or mathematics that you would like to mention?
*I just enjoy the sound of the French horn and the challenge of trying to play it better. Although it would be nice if the study of complicated rhythms of the body improved my ability to play the French horn (or even to count in music), as far as I can tell these are occurring in separate regions of my brain and there is no carryover from one to the other. Both science and music are fun – and I have been privileged to have the opportunity to enjoy them both.

*How do you feel about receiving the 2013 Arthur T. Winfree Prize?*

I am deeply honored to receive this award. Art Winfree

was not only an extraordinary scientist, but he was also a colleague and close friend. His intense scientific curiosity and high personal integrity have been beacons in my own career. Since completing my PhD in Chemistry, I have identified with the Mathematical and Theoretical Biology communities, going back to early Gordon Conferences in the 1970s. I have also had the privilege of having been the President of the Society for Mathematical Biology. Mathematical Biology is still a young field, with only a few prizes – I am truly delighted to have been selected for this award.

Yes!

Several members of the CAMBAM student community, and professors associated with it, are studying in the field of neuroscience, but CAMBAM only rarely sponsored neuroscience events. It is time for this to change!

May 7th, 2013, in room 504 of the McIntyre Medical building, there will be a workshop on the theme of computational neuroscience. This workshop is for us, students, and us, students, only, a chance to learn, exchange, discuss and think about the mathematical tools available to our field, the usage of which is often grouped under the expression “Computational Neuroscience”.

Talks have been setup by students of McGill and several labs are represented. For this edition, several tools, mainly applicable to electrophysiology, will be presented, but that shouldn’t prevent anybody from coming as there will be time allowed for open discussion.

The day will go on like this:

12h00-13h00

Free lunch. We invite you to register if you plan on attending, this will help us plan the meals accordingly (add your name in the doodle survey and select Yes, if you desire a vegetarian meal and No, if you want a non-vegetarian meal).

Link to the doodle page: http://www.doodle.com/4i9r3ffezd6h8wda

Please do so by May 1st, as I will have to settle stuff with the traiteur.

13h00-13h45

*Introduction to regression and classification.*

**Nathan Friedman, Greg Stacey and Rubing Xu**

13h45-14h30

*Dimensionality Reduction: PCA and Gaussian Process Factor Analysis.*

**Frederic Simard**

14h30-15h00

Coffee Break

15h00-15h45

*Applications of Information Theory and Neural Coding.*

**Adam Schneider, Mohsen Jamali and Ashkan Golzar**

15h45-16h30

*Phase Coherence as a measure of synchrony within and between brain areas.*

**Diego Mendoza**

16h30-17h30 (or as long as the discussion go)

Mixer/Social

It will be a tremendous time, an event that you will bite your finger off for having missed, so please be there. Again, location and time:

Tuesday, May 7th 2013,

starting at noon

McIntyre Medical Building

3655 Sir William Olser

McGill University, Montréal

See you there!!!

]]>Another semester ended, another to be added the countless number of semesters that we have seen since the beginning of our academic career as professional students. Still, I’m taking the time to share with you what has made this last one particularly significant for me. I was registered in the course Machine Learning (COMP-652) and I had such a great time that I didn’t see the semester flying by, or was it because I was overwhelmed by work, it’s hard to tell. Never mind, this course taught me, and the other students who were registered, about a bunch of tools, not far from being qualified of statistics, that I’m sure you too could benefits from knowing. Unfortunately, there is only one way for you to get the fine details, and it is to register yourself, yet, I’m going to give you an appreciation of two topics covered during this class and maybe you’ll find yourself interested in learning more on the subject.

Machine learning refers to the ensemble of algorithms that aims at extracting information from a data set. This description is very vague and this is reflected in the eclectic set of algorithms that are studied thorough the course.

*Linear Regression*

Code available here.

The first concept taught is the one of regression. Whenever you parameterize some data, you are performing a form of regression. The most basic form of regression is linear regression (Fig. 1), which consist in mapping linearly, with more or less success, a set of input data, usually denoted *x*, to a set of output data, *t* as in target.

Linear regression gives the false impression that the fit will always be a linear function, which is true, but only in the relationship between the input data and the output data. Therefore, we usually use this equation to define linear regression:

Where the function ϕ(x_{i}) represent the input data x_{i}, an element of **x** a vector of input data, in the feature space. Let’s be honest, this notion of feature space kept me confused for a while, so I don’t expect you to fully grasp the concept from such a short description, but let me just push in another example to help you understand a little bit more of what I’m trying to explain. When basic linear regression doesn’t work, one might give it a try at polynomial regression (Fig. 2). Polynomial regression is still a linear regression, but we are now dealing with a linear combination of various degrees of *x*. Let see how we move on from the polynomial expression to the equation of linear regression. In a polynomial expression of degree n=3, this is the equation we get.

Notice that this is not a linear equation.

By concatenating all capital letters, the parameters of the model, into a vector **W** and defining the function:

The problem is then stated as:

Regression becomes a method to find the parameters **W** that best map the input on the output data. Often, we will try to minimize the mean squared error (MSE) between the data and the fit. In this case a closed solution exist and the weights minimizing the squared error can be computed with (I am skipping the details, but you can find an extensive description here):

But such an elegant resolution is not always available and when it is not, we will often use method such as gradient descent to find a satisfying solution to the error minimization problem.

Linear regression is presented because it represents de essence of machine learning. It is used to introduce concepts such as error measurement, problems associated with overfitting, cross-validation and the bias/variance trade off. Then, the Bayesian view to regression is introduced, this view is the foundation to several machine learning algorithm, such as logistic regression. Eventually, we move on to more complex algorithms that not only regress and extract the trend from a set of data but also perform classification.

*Principal component analysis (PCA)*

Code and dataset available here.

Several of you must already have heard of PCA. The main application of PCA is to perform dimensionality reduction, but as we will see, it can also be used to transform the input data representation space as to make categories linearly separable, even though they weren’t in their original reference frame.

Basically, PCA is a method that applies linear transformations on the set of data as to map it in a different frame of reference. Each orthogonal component (axis) of the new reference frame is computed as to collect as much of the variance of the data as possible. It is then possible to select a subset of the components, those that capture most of the variance, and drop the others, to obtain a dataset with a lower dimensionality that retain most of the information found in the data. (notice that this is a form of information compression)

To illustrate the PCA, I’m using a dataset I picked up at simafore. It is a dataset giving the nutrition facts for various brands of cereal. For the purpose of this example, I’m going to use 8 of the measurements reported (i.e. calories, protein, fat, sodium, fiber, carbohydrate, sugars and potassium) and the goal is to relate cereal brands that are similar to each other.

This might sound easy at first, after all, all high sugars content on one side and all low sugars content on the other! But that doesn’t take into account the content of fibers or protein… What if two different brands are very similar for their sugars content, but very different for on all other account? We are looking for a measurement of similarity that will take the 8 nutrition facts into account at the same time and if possible, report them in a frame of reference that can be visualized. Well, that’s precisely what PCA can do. (It might have occurred to some people that we could have normalized the values and computed the Euclidean distance between the cereal brands. Unfortunately I cannot explain the reasons here, but this becomes rapidly unpractical as the dimensionality of the dataset increase. See for a description of the curse of dimensionality.

Computing the PCA is a fairly simple operation (use Matlab: princomp, to let Matlab handle it). The first operation is to compute the covariance matrix. Let me remind you that each element of the NxN (N=8) covariance matrix is given by:

where E(x) is the expectation or the mean operator.

Then, we need to find the eigenvectors and eigenvalues of the covariance matrix. Eigenvectors and eigenvalues are a set of vectors and magnitude that respect the following equality:

Where A is the matrix, *v* is a eigenvector and *λ* a eigenvalue. It is a very important concept that finds application in many fields related to linear algebra, unfortunately, again, I cannot go in depth here, but I refer you to wiki! if you are interested in knowing more about eigenvectors and eigenvalues. For now, you can assume that the resulting set of eigenvectors indicates the direction in which the energy of the covariance matrix is oriented, that all eigenvectors are orthogonal (not always the case in general, but always true in PCA) and that the eigenvalues tell us how much of the energy goes in each directions.

The set of eigenvectors is our reference frame. There are as many eigenvectors as there are dimensions in our dataset, the thing is however, that by looking at the eigenvalues we can decide to drop dimensions that don’t contain a significant amount of energy. The following figure shows us the ordered magnitude of the eigenvalues obtained from our dataset and the cumulative energy as a function of the number of components used.

It is clear from this illustration that even though we are provided with 8 measurements, it is possible to represent the information in a 3 dimensional space, and this, without losing any information. Warning though, the 3 components aren’t the three most important measurements! each component is a combination of the 8 measurements, this means that even if we are using only three components, all measurements have a pondered contribution in the new frame of reference. The next figure now take advantage of the reduction of dimensionality to plot in a 2 dimensional space (we are still capturing more than 95% of the energy in the variance) the points corresponding to the various cereal brands. For the sake of the demonstration, I used another algorithm (K-means) taught in the Machine Learning course to form clusters to group the most similar cereal brands in 3 classes (red, green , blue) in the new frame of reference.

It is very apparent it this example that the PCA algorithm generates a reference frame in which it becomes much more easier to perform analysis, such as clustering, than it would be in a space of higher dimension. In this example it even makes is possible to represent the significant portion of information, hidden in a 8 dimensions space, in a 2 or 3 dimensions space. I won’t go any further in PCA, but from here it would be easy to determine which nutrition facts are contributing the most to each component, if there was a need to interpret the results or to build a classifier that classify any new cereal brand in one of the three classes.

I’m taking the opportunity to tell you that this is the most basic form of PCA, there is another form called kernel PCA that perform the crazy operation of projecting the data in a higher dimension space (greater than 8 ) before performing the same dimensionality reduction. It is then possible to extract relationships that aren’t readily accessible in the dataset. This is another, more complex and very interesting, topic covered in COMP-652.

*And the rest*

I have introduced linear regression, polynomial regression and principal component analysis, but this is only the tip of the iceberg. The machine learning course cover many other algorithms, some even more powerful, such as Bayesian decoder, support-vector machines (SVM), neural networks, Kernel machines, K-means/hierarchical and other clustering methods, Hidden Markov Models (HMM), Bayesian networks and this is not an exhaustive list.

The course also emphasize a deep understanding of the practical problems associated with machine learning. What makes a fit better than the other? Given a set of data and a goal to be attained how do we pick the right machine learning approach? And even if we have the data and the algorithm, how do we implement it?

The background required for the course: probability and statistics, linear algebra (+ matrices), calculus and Matlab. In every case, a background is recommended, but with hard work, you can overcome most of the problems, plan to put in a lot of time on this class.

Finally, I recommend this course to anyone who is interested in data mining, data analysis, artificial intelligence, modeling, algorithms and so on. Let me know if you have any questions, it will be a pleasure for me to answer them.

PS: I’m planning on organizing a workshop on the subject of data analysis in neuroscience, several machine learning tools will be covered, stay tuned!

]]>The first was a CAMBAM students’ roundtable lunch with Dr. Otto. A handful of us had pizza and soda with her while talking about our research projects and bouncing around related ideas. This was quite fun for me, since I’m not a CAMBAM member and don’t know much about what you folks do; it was great to hear about heart arrhythmias and neuron chemistry and asthma and actin and myosin and all the rest! I hope it was also fun for the CAMBAM folks to hear about my models of floral morphology and pollen dispersal and reproductive isolation. Mathematical biology contains such a diversity of ideas!

The second was Dr. Otto’s CAMBAM talk, “Inferring the past for traits that alter speciation and extinction rates”. The talk was about a method called BiSSE (“Binary-State Speciation and Extinction”) for estimating evolutionary parameters given information about extant species. For example, suppose you have a set of related species – a “clade”, like primates – and you know the value of some binary trait for all of these species – whether they live in trees or on the ground, for example. Suppose you also have a phylogenetic tree for your clade: based upon genetic sequences, probably, you have a tree that expresses which species are most closely related and long long ago their common ancestor lived, all the way back to the ancestor that the whole clade descends from. BiSSE (and related methods) will allow you to answer questions about the evolution of that clade and the way that it is related to the binary trait of interest. For example, what is the speciation rate and the extinction rate over the clades’ history, and do those rates differ significantly between lineages that live in trees and lineages that live on the ground? What is the rate of evolutionary transition from tree-living to ground-living, and vice-versa? And was the common ancestor of the clade tree-living (and thus ground-living was a later evolutionary innovation), or ground living (making tree-living the more recent development)?

The really neat thing about her talk, to me, was that she didn’t just present the method as “received wisdom”; she showed us exactly how the likelihood equations underlying it were derived, based upon an analysis of the ways that the binary states of lineages could change over infinitesimal time intervals. Once you understand how a model like BiSSE is constructed, you can construct your own models with additional constraints or additional parameters – traits that are not just binary, ancestral morphological states constrained by fossils, all sorts of possibilities. The power of this sort of method is immense – you can use information about extant species to tease apart what happened millions of years ago as those species evolved and diverged!

Today Dr. Otto has been giving a workshop on modeling in ecology and evolution; we’ve got more than 50 participants at that, so that’s a wonderful success. Tomorrow (Thursday December 5th), don’t forget that Dr. Otto will be giving a talk at the Redpath Museum’s auditorium, on “The Evolutionary Enigma of Sex”, at 3:00, with a wine and cheese social afterwards. I hope to see you there!

**References:**

*(the original paper on BiSSE:)*

Maddison, W., P. Midford, and S. Otto. 2007. Estimating a binary character’s effect on speciation and extinction. Systematic Biology 56:701–710. doi: 10.1080/10635150701607033

*(a paper on a later related method, BISSE-ness, that develops the primate example I used above, with fascinating results:)*

Magnuson-Ford, K., and S. Otto. Linking the Investigations of Character Evolution and Species Diversification. 2012. American Naturalist 180:225–245. doi: 10.1086/666649

]]>