Experimental and comparative oncology: zebrafish, dogs, elephants

One of the exciting things about mathematical oncology is that thinking about cancer often forces me to leave my comfortable arm-chair and look at some actually data. No matter how much I advocate for the merits of heuristic modeling, when it comes to cancer, data-agnostic models take second stage to data-rich modeling. This close relationship between theory and experiment is of great importance to the health of a discipline, and the MBI Workshop on the Ecology and Evolution of Cancer highlights the health of mathematical oncology: mathematicians are sitting side-by-side with clinicians, biologists with computer scientists, and physicists next to ecologists. This means that the most novel talks for me have been the ones highlighting the great variety of experiments that are being done and how they inform theory.In this post I want to highlight some of these talks, with a particular emphasis on using the study of cancer in non-humans to inform human medicine.
Read more of this post

Colon cancer, mathematical time travel, and questioning the sequential mutation model.

On Saturday, I arrived in Columbus, Ohio for the the MBI Workshop on the Ecology and Evolution of Cancer. Today, our second day started. The meeting is an exciting combination of biology-minded mathematicians and computer scientists, and math-friendly biologist and clinicians. As is typical of workshops, the speakers of the first day had an agenda of setting the scope. In this case, the common theme was to question and refine the established model as embodied by Hannah & Weinberg’s (2000) hallmarks of cancer outlined. For an accessible overview of these hallmarks, I recommend Buddhini Samarasinghe’s series of posts. I won’t provide a full overview of the standard model, but only focus on the aspects at issue for the workshop participants. In the case of the first two speakers, the standard picture in question was the sequential mutation model. In the textbook model of cancer, a tumour acquires the hallmark mutations one at a time, with each subsequent mutation sweeping to fixation. Trevor Graham and Darryl Shibata presented their work on colon cancer, emphasizing tumour heterogeneity, and suggesting that we might have to rewrite the sequential mutation page of our Cancer 101 textbooks to better discuss the punctuated model.
Read more of this post

Defining empathy, sympathy, and compassion

PaulBloomWhen discussing the evolution of cooperation, questions about empathy, sympathy, and compassion are often close to mind. In my computational work, I used to operationalize-away these emotive concepts and replace them with a simple number like the proportion of cooperative interactions. This is all well and good if I want to confine myself to a behaviorist perspective, but my colleagues and I have been trying to move to a richer cognitive science viewpoint on cooperation. This has confronted me with the need to think seriously about empathy, sympathy, and compassion. In particular, Paul Bloom‘s article against empathy, and a Reddit discussion on the usefulness of empathy as a word has reminded me that my understanding of the topic is not very clear or critical. As such, I was hoping to use this opportunity to write down definitions for these three concepts and at the end of the post sketch a brief idea of how to approach some of them with evolutionary modeling. My hope is that you, dear reader, would point out any confusion or disagreement that lingers.
Read more of this post

Transcendental idealism and Post’s variant of the Church-Turing thesis

KantPostOne of the exciting things in reading philosophy, its history in particular, is experiencing the tension between different schools of thought. This excitement turns to beauty if a clear synthesis emerges to reconcile the conflicting ideas. In the middle to late 18th century, as the Age of Enlightenment was giving way to the Romantic era, the tension was between rationalism and empiricism and the synthesis came from Immanuel Kant. His thought went on to influence or directly shape much of modern philosophy, and if you browse the table of contents of philosophical journals today then you will regularly encounter hermeneutic titles like “Kant on <semi-obscure modern topic>”. In this regard, my post is in keeping with modern practice because it could have very well been titled “Kant on computability”.

As stressed before, I think that it is productive to look at important concepts from multiple philosophical perspectives. The exercise can provide us with an increased insight into both the school of thought that is our eyes, and the concept that we behold. In this case, the concept is the Church-Turing thesis that states that anything that is computable is computable by a Turing machine. The perspective will be of (a kind of) cognitivism — thought consists of algorithmic manipulation of mental states. This perspective that can often be read directly into Turing, although Copeland & Shagrir (2013) better described him as a pragmatic noncognitivist. Hence, I prefer to attribute this view to Emil Post. Also, it would be simply too much of a mouthful to call it the Post-Turing variant of the Church-Turing thesis.
Read more of this post

Weapons of math destruction and the ethics of Big Data

CathyONeilI don’t know about you, dear reader, but during my formal education I was never taught ethics or social consciousness. I even remember sitting around with my engineering friends that had to take a class in ethics and laughing at the irrelevance and futility of it. To this day, I have a strained relationship with ethics as a branch of philosophy. However, despite this villainous background, I ended up spending a lot of time thinking about cooperation, empathy, and social justice. With time and experience, I started to climb out of the Dunning-Kruger hole and realize how little I understood about being a useful member of society.

One of the important lessons I’ve learnt is that models and algorithms are not neutral, and come with important ethical considerations that we as computer scientists, physics, and mathematicians are often ill-equipped to see. For exploring the consequences of this in the context of the ever-present ‘big data’, Cathy O’Neil’s blog and alter ego mathbabe has been extremely important. This morning I had the opportunity to meet Cathy for coffee near her secret lair on the edge of Lower Manhattan. From this writing lair, she is working on her new book Weapons of Math Destruction and “arguing that mathematical modeling has become a pervasive and destructive force in society—in finance, education, medicine, politics, and the workplace—and showing how current models exacerbate inequality and endanger democracy and how we might rein them in”.

I can’t wait to read it!

In case you are impatient like me, I wanted to use this post to share a selection of Cathy’s articles along with my brief summaries for your browsing enjoyment:
Read more of this post

Falsifiability and Gandy’s variant of the Church-Turing thesis

RobinGandyIn 1936, two years after Karl Popper published the first German version of The Logic of Scientific Discovery and introduced falsifiability; Alonzo Church, Alan Turing, and Emil Post each published independent papers on the Entscheidungsproblem and introducing the lambda calculus, Turing machines, and Post-Turing machines as mathematical models of computation. The years after saw many more models, all of which were shown to be equivalent to each other in what they could compute. This was summarized in the Church-Turing thesis: anything that is computable is computable by a Turing machine. An almost universally accepted, but also incredibly vague, statement. Of course, such an important thesis has developed many variants, and exploring or contrasting their formulations can be very insightful way to understand and contrast different philosophies.

I believe that the original and most foundational version of the thesis is what I called Kleene’s purely mathematical formulation. Delving into this variant allowed us explore the philosophy of mathematics; Platonism; and the purpose, power and limitations of proof. However, because of the popularity of physicalism and authority of science, I doubt that Kleene’s is the most popular variant. Instead, when people think of the Church-Turing thesis, they often think of what is computable in the world around them. I like to associate this variant with Turing’s long time friend and student — Robin Gandy. I want to explore Gandy’s physical variant of the Church-Turing thesis to better understand the philosophy of science, theory-based conceptions, and the limits of falsifiability. In particular, I want to address what seems to me like the common misconception that the Church-Turing thesis is falsifiable.
Read more of this post

A Theorist’s Apology

Gadfly of ScienceAlmost four months have snuck by in silence, a drastic change from the weekly updates earlier in the year. However, dear reader, I have not abandoned TheEGG; I have just fallen off the metaphorical horse and it has taken some time to get back on my feet. While I was in the mud, I thought about what it is that I do and how to label it. I decided the best label is “theorist”, not a critical theorist, nor theoretical cognitive scientist, nor theoretical biologist, not even a theoretical computer scientist. Just a theorist. No domain necessary.

The problem with a non-standard label is that it requires justification, hence this post. I want to use the next two thousand words to return to writing and help unify my vision for TheEGG. In the process, I will comment on the relevance of philosophy to science, and the theorist’s integration of scientific domains with mathematics and the philosophy of science. The post will be a bit more personal and ramble more than usual, and I am sorry for that. I need this moment to recall how to ride the blogging horse.
Read more of this post

Useful delusions, interface theory of perception, and religion

As you can guess from the name, evolutionary game theory (EGT) traces its roots to economics and evolutionary biology. Both of the progenitor fields assume it impossible, or unreasonably difficult, to observe the internal representations, beliefs, and preferences of the agents they model, and thus adopt a largely behaviorist view. My colleagues and I, however, are interested in looking at learning from the cognitive science tradition. In particular, we are interested in the interaction of evolution and learning. This interaction in of itself is not innovative, it has been a concern for biologists since Baldwin (1886, 1902), and Smead & Zollman (2009; Smead 2012) even brought the interaction into an EGT framework and showed that rational learning is not necessarily a ‘fixed-point of Darwinian evolution’. But all the previous work that I’ve encountered at this interface has made a simple implicit assumption, and I wanted to question it.

It is relatively clear that evolution acts objectively and without regard for individual agents’ subjective experience except in so far as that experience determines behavior. On the other hand, learning, from the cognitive sciences perspective at least, acts on the subjective experiences of the agent. There is an inherent tension here between the objective and subjective perspective that becomes most obvious in the social learning setting, but is still present for individual learners. Most previous work has sidestepped this issue by either not delving into the internal mechanism of how agents decide to act — something that is incompatible with the cognitive science perspective — or assuming that subjective representations are true to objective reality — something for which we have no a priori justification.

A couple of years ago, I decided to look at this question directly by developing the objective-subjective rationality model. Marcel and I fleshed out the model by adding a mechanism for simple Bayesian learning; this came with an extra perk of allowing us to adopt Masel’s (2007) approach to looking at quasi-magical thinking as an inferential bias. To round out the team with some cognitive science expertise, we asked Tom to join. A few days ago, after an unhurried pace and over 15 relevant blog posts, we released our first paper on the topic (Kaznatcheev, Montrey & Shultz, 2014) along with its MatLab code.
Read more of this post

Models, modesty, and moral methodology

In highschool, I had the privilege to be part of a program that focused on the humanities and social sciences, critical thinking, and building research skills. The program’s crown was a semester of grade eleven (early 2005) dedicated to working on independent research for a project of our own design. For my project, I poured over papers and books at the University of Saskatchewan library, trying to come up with a semi-coherent thesis on post-cold war religious violence. Maybe this is why my first publications in college were on ethnocentrism? It’s a hard question to answer, but I doubt that the connection was that direct. As I was preparing to head to McGill, I had ambition to study political science and physics, but I was quickly disenchanted with the idea, and ended up focusing on theoretical computer science, physics, and math. When I returned to the social sciences in late 2008, it was with the arrogance typical of a physicist first entering a new field.

In the years since — along with continued modeling — I have tried to become more conscious of the types and limitations of models and their role in knowledge building and rhetoric. In particular, you might have noticed a recent trend of posts on the social sciences and various dangers of Scientism. These are part of an on-going discussions with Adam Elkus and reading the Dart-Throwing Chimp. Recently, Jay Ulfelder shared a fun quip on why skeptics make bad pundits:

First Rule of Punditry: I know everything; nothing is complicated.

First Rule of Skepticism: I know nothing; everything is complicated.

Which gets at an important issue common to many public-facing sciences, like climate, social, or medicine, among others. Academics are often encouraged to be skeptical, both of their work and others, and precise in the scope of their predictions. Although self-skepticism and precision is sometimes eroded away by the need to publish ‘high-impact’ results. I would argue that without factions, divisions, and debate, science would find progress — whatever that means — much more difficult. Academic rhetoric, however, is often incompatible with political rhetoric, since — as Jay Ulfelder points out — the latter relies much more on certainty, conviction, and the force with which you deliver your message. What should a policy oriented academic do?
Read more of this post

Cross-validation in finance, psychology, and political science

A large chunk of machine learning (although not all of it) is concerned with predictive modeling, usually in the form of designing an algorithm that takes in some data set and returns an algorithm (or sometimes, a description of an algorithm) for making predictions based on future data. In terminology more friendly to the philosophy of science, we may say that we are defining a rule of induction that will tell us how to turn past observations into a hypothesis for making future predictions. Of course, Hume tells us that if we are completely skeptical then there is no justification for induction — in machine learning we usually know this as a no-free lunch theorem. However, we still use induction all the time, usually with some confidence because we assume that the world has regularities that we can extract. Unfortunately, this just shifts the problem since there are countless possible regularities and we have to identify ‘the right one’.

Thankfully, this restatement of the problem is more approachable if we assume that our data set did not conspire against us. That being said, every data-set, no matter how ‘typical’ has some idiosyncrasies, and if we tune in to these instead of ‘true’ regularity then we say we are over-fitting. Being aware of and circumventing over-fitting is usually one of the first lessons of an introductory machine learning course. The general technique we learn is cross-validation or out-of-sample validation. One round of cross-validation consists of randomly partitioning your data into a training and validating set then running our induction algorithm on the training data set to generate a hypothesis algorithm which we test on the validating set. A ‘good’ machine learning algorithm (or rule for induction) is one where the performance in-sample (on the training set) is about the same as out-of-sample (on the validating set), and both performances are better than chance. The technique is so foundational that the only reliable way to earn zero on a machine learning assignments is by not doing cross-validation of your predictive models. The technique is so ubiquotes in machine learning and statistics that the StackExchange dedicated to statistics is named CrossValidated. The technique is so…

You get the point.

If you are a regular reader, you can probably induce from past post to guess that my point is not to write an introductory lecture on cross validation. Instead, I wanted to highlight some cases in science and society when cross validation isn’t used, when it needn’t be used, and maybe even when it shouldn’t be used.
Read more of this post

Follow

Get every new post delivered to your Inbox.

Join 2,293 other followers