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Welcome to today's topic: Big Data for Small Minds, where we will try to wrap our heads around the notion of bigness of big data; hopefully, by the end, we will convince ourselves that it involves a bit more than raw size, and that such "bigness" has non-trivial implications for how we work with, and reason about, problems in which such datasets arise. I am Ishanu Chattopadhyay, Assistant Professor of Medicine, and in my research group, we aim to solve hard questions in biomedicine and the social sciences, particularly where such problems are associated with large and complex datasets. We spend a lot of time thinking about how to analyze such data, how we can use such data to answer important questions, and if such data can point us to questions that we have not yet thought to ask.

So lets begin at the beginning. What is data? As I think about about it, data is a collection of shallow, mechanically gathered systematic record of information. By shallow I mean, individual datapoints do not necessarily have much meaning, but as an aggregate they convey an emergent picture.

Now, that datasets are important, this notion is not new. Going back to the Roman empire, there were tabularia which were fancy buildings housing extensive records of business transactions, with the goal of analyzing the state of commerce in the city and the empire. And in science, large datasets have time and again been instrumental. Tycho Brahe is perhaps the most obvious example. In the 16th century, he spend his life gathering precise astronomical observations, position of starts, motion of planets, and while he is credited with some important astronomical discoveries, his biggest contribution was amassing this dataset, which was then used by J. Kepler to derive the three Kepler's of planetary motion, which directly influences or enabled Newton to formulate the universal law of gravitation.

A couple of centuries later, detailed pollination experiments on pea plants led Mendel to formulate the laws of Mendelian genetics, laying the foundation of modern biology. He carried out some 30 thousand meticulous experiments to come up with his laws. Now the question is that "big data", or for that matter, Tycho Brahe's voluminous collection of astronomical data: is that "big data"?

Lets think about this. Note that these data sets led to "simple explanations". Three laws of planetary motion,. or the law of universal gravitation, or the Mendelian laws of genetics. In essence these datasets were "simple", large no doubt, but simple. The way I think about "bigness" of data, is its intrinsic complexity, where we might fail to obtain simple representations of such datasets. Hold that thought for moment,

Lets think about what is the purpose of data, in general. Document phenomena, forecast, predict, optimize decisions, and in general, formulate scientific theories. That leads us to ask, what then is a scientific theory? Well, one way to think of scientific theories are that they are collection of equations, principles, which are compressed representation of data about the physical world. Note that scientific theories -- famous scientific theories -- in physics and biology are always simple. After all the equations of quantum mechanics can be written down on the back of an envelope, and the equation of Einstein's relativity, using the right notation, is even simpler. Why is that so? Maybe nature is like that: when looked at with the right abstraction, and when asked the right questions, the answers are simple. And there is some reasoning that supports that conclusion. However, it may also be that we have uncovered simple equation and simple principles, because that is what we are able to comprehend, that's what we looked for, and the complex phenomena were , well too complex, that we haven't stumbled on them yet.

And this is a very real possibility. Think about how the scientific method works. We start with some experiments, which produces data, that data is used to formulate hypotheses (equations, principles, laws), and then we do more experiments to validate those laws, and if there is a mismatch, we update our hypotheses.. leading to this eternal dialogue with nature. Is there subjectivity build into this process -- why yes off course.. its the capacity of the human mind that determines these hypotheses. Is this possible that really complex processes requires hypotheses so complicated that we generally don't consider them as valid theories within this classical cyclical process.

That is not only plausible, that is actually likely. In fact most questions of interest in biology, bio medicine and the social sciences fall in this category. Who believes that we we can write down an equation which outlines the detailed operation of cellular machinery. These are emergent phenomena, where clean first principle "laws" either don't exist or are too complex.

What are some examples? Pandemics.. how they manifest, and respond to countermeasures. How novel pathogens emerge.. why are some spillover events result in epidemics and pandemics, while other don't? How do we model social dynamics? Are events like crime predictable? How do we screen for complex diseases, diseases which are shaped by the interaction of hundreds of thousands of genes, and uncharted epigenetic effects, it is almost obvious that there phenomena do not have "simple" explanations, and the data about them are not compressible by a a few laws.. they are intrinsically complex.

So what now? Clearly this cyclic approach will not work? Can we salvage it? Yes, we have to reinterpret what we mean by "understanding". We can make broad hypotheses, but some part of the "model" that we infer, will always be not "simple" or "understandable" in the classical sense. The complexity has to go somewhere, since simple laws do not exist, the inherent complexity of the phenomena must be represented somewhere. And we have to be OK with that, because it appears that some problems or phenomena in nature are like that... they have emergent complexity, and to reason about them, or answer questions about them, we need to work with that irreducible complexity.

How do we do it? Well a popular approach is machine learning. We have inputs and outputs and the tools of ML will tell you how the inputs connect with the outputs. What goes on in that jumble of connections might not be understandable, but that's OK, that is what capturing the irreducible complexity of the phenomena you are trying to study.

Lets look at some concrete example.

plan

• Tycho Brahe was in essensce the first dat ascientist. Collected precise astronomical observations, with instruments he himself developed (teh sextant), and amassed data that enabled Keplar to come up with his laws of planetary motion.
• Johannes Kepler is best known for his three laws of planetary motion. These laws are: Planets move in orbits shaped like an ellipse. A line between a planet and the Sun covers equal areas in equal times.

defn of data

• When we reference data today, we are speaking about very shallow, very specific, and very unambiguous observations. Consider a buoy out at sea. One data point from the buoy will tell you the sea temperature, elevation, and direction of the ocean current at a very specific GPS location at 2:05:05 PM on June 22nd, 2015. In fact, the information is so shallow, that we need to take these data points and combine them with many others to get a bigger picture. This is precisely why the word data is almost always encountered in the plural. It could be said that a datum is only valuable when it is combined into data (it’s about as valuable as a single pant that’s not joined into pants).
• data is shallow, mechanically-gathered, systematic information that is recorded in an inanimate device.
• we can add another constraint: data is self-consciously gathered – it does not result from another activity. Noe tthat this does not always apply, for example EHR data. In ancient Rome they had tabularia – storehouses of receipts from individual purchases that gave the Romans vision into the state of commerce within the city.

• Mendel

Johann Gregor Mendel (1822–1884) was a lifelong learner, teacher, scientist, and man of faith. As a young adult, he joined the Augustinian Abbey of St. Thomas in Brno in what is now the Czech Republic. Supported by the monastery, he taught physics, botany, and natural science courses at the secondary and university levels. In 1856, he began a decade-long research pursuit involving inheritance patterns in honeybees and plants, ultimately settling on pea plants as his primary model system (a system with convenient characteristics that is used to study a specific biological phenomenon to gain understanding to be applied to other systems). In 1865, Mendel presented the results of his experiments with nearly 30,000 pea plants to the local natural history society. He demonstrated that traits are transmitted faithfully from parents to offspring in specific patterns. In 1866, he published his work, Experiments in Plant Hybridization,1 in the proceedings of the Natural History Society of Brünn.

Mendel’s work went virtually unnoticed by the scientific community, which incorrectly believed that the process of inheritance involved a blending of parental traits that produced an intermediate physical appearance in offspring. This hypothetical process appeared to be correct because of what we know now as continuous variation. Continuous variation is the range of small differences we see among individuals in a characteristic like human height. It does appear that offspring are a “blend” of their parents’ traits when we look at characteristics that exhibit continuous variation. Mendel worked instead with traits that show discontinuous variation. Discontinuous variation is the variation seen among individuals when each individual shows one of two—or a very few—easily distinguishable traits, such as violet or white flowers. Mendel’s choice of these kinds of traits allowed him to see experimentally that the traits were not blended in the offspring as would have been expected at the time, but that they were inherited as distinct traits. In 1868, Mendel became abbot of the monastery and exchanged his scientific pursuits for his pastoral duties. He was not recognized for his extraordinary scientific contributions during his lifetime; in fact, it was not until 1900 that his work was rediscovered, reproduced, and revitalized by scientists on the brink of discovering the chromosomal basis of heredity.