Points of Inflection in Machine Learning

Points of Inflection: That Moment When Everything Changes

Gain first-mover advantage with intel from meaningful change.

One morning, I looked out the window at a bird flying gracefully towards a backyard bird feeder. Seemingly in an instant, the bird changed direction and “aborted” his landing on the feeder, taking refuge in a nearby tree. His arrival disturbed other birds, some of which took flight. I found myself wondering about what went on in the mind of the bird. Did it make a rational, conscious decision, or was this change some sort of reflex or instinct? What about the other birds? Was there some broader environmental stimulus, such as an unseen threat, or just an unfortunate gust of wind? Imagine I had video (and audio) of the event. Might I find that exact instant when the bird went from landing to veering off? If so, studying what happened immediately before this “point of inflection” and the implications to the surrounding environment would be interesting and perhaps informative. Such is the case with points of inflection. In math, they are easily predictable if we know the underlying function describing a graph – just basic Calculus. In life, it’s not so simple. What can we learn as data scientists by thinking about points of inflection as we try to do our best in a world that is increasingly awash in new data, new technology, new laws, new opportunities, and new risks? Can we do better than simply acting out of reflex?

What can we learn as data scientists by thinking about points of inflection as we try to do our best in a world increasingly awash in new data, technology, laws, opportunities, and risks?

College Colleagues Collaborate: What I learned in college 

For me, transitioning from High School to College was a point of inflection. I went from having a schedule given to me to making a schedule of the classes that I wanted to take. I went from pursuing an interest, to possibly pursuing a career. I learned as much from my professors at times as I did from fellow students trying to grapple with the same change, but with different perspectives. At the same time, I was exposed to disciplines where there was no exact “answer” either due to the nature of the subject matter (e.g. Calculus vs. discrete mathematics) or because research was still being done (fundamental computer science vs. artificial intelligence).


Somewhere in this journey, I was exposed to the concepts of points of inflection, in math, history, and other disciplines. The terminology was often different, but the concept was the same. There was always some point where things changed in an instant: the seemingly magical moments when things switch from where they were going to where they are going. I realized a few aspects of points of inflection that stay with me today:

  • VALUE: The point of inflection often contains some very useful information that can be very powerful if you know how to recognize it.
  • PERSPECTIVE: Recognizing a point of inflection (in all but math) often requires some historical perspective. Points of inflection are often difficult to see in the moment, and often more difficult to see when you are embedded in the changing environment. Any insight must be considered in the context of perspective.
  • PROPAGATION: Sometimes, the causes for inflection are critical incidents; other times they are the culmination of events and conditions that reach a certain saturation where inflection is possible.
  • IMPLICATION: The mere fact that inflection has occurred does not guarantee that trends will continue in the new direction. In many cases, the inflection causes changes in behavior that bring about further inflection.

As a data scientist, looking for points of inflection in behavior or other complex systems, especially where the data are not easily describable with an underlying function, can be very powerful if considered from carefully-chosen dimensions, such as value, perspective, propagation, and implication.

Making Sense: Everything is the same… until something changes

There is a tremendous amount of focus lately on artificial intelligence (AI). Of course, many of the techniques of machine learning and other inference have been around for a very long time, but we are now at a point where computing power and data availability make possible inference that was never before possible. Somewhere along the line, we seem to have passed a point of inflection. The once possible is now part of the daily experience. 

This new normal, where technologies are available to approach old problems in new ways and to take on new challenges, can be a wonderful opportunity if we act thoughtfully. For example, consider machine learning. There are multiple methods, including supervised (based on training from typical data), unsupervised (based on more complex combination of data and curation), and reinforcement methods (based on observation).

If we know, for example, that we just had a major shift and the future looks very different from the past, we should challenge using certain data as “training” data from the past if we intend to project certain assumptions into this certainly new future. The current advent of privacy regulations is a good example.

We might consider which methods would be appropriate in the context of points of inflection. Using the frames above, here is what our analysis might look like:

VALUE: We recognize that the change in regulation must bring about changes in behavior and interaction and that understanding the change in behavior and interaction could inform decisions about risk and opportunity.

PERSPECTIVE: Armed with our hypothesis of value, we consider perspective. Sociologists use two terms which are very helpful: “emic” and “etic.” If we are emic, we are often part of the system we are studying. If we are etic, we are observing it from an external perspective. If we are emic in this situation, we may not be able to see all of the data required to understand the changes in the system. For example, certain parties may no longer share information because of privacy considerations. Similarly, if we are etic, we may consider that the regulations might limit our ability to observe the system because of new sources that are not yet available. The point is to consider the bias that is introduced and how it may inform our analysis.

PROPAGATION: Having established our experiment and considered a method to observe, and informed by our assessment of bias, we now construct appropriate measures to collect (or observe) information about the system, looking for the value that comes about from this important point of inflection. Do certain transactions become riskier? Are there new types of white space opening up that did not exist because of the changes in the system behavior? Many questions can be posited and tested by observing the data in the system from the perspective of inflection.

IMPLICATION: This is the point where we start to ask what our analysis and observation mean. How can we take action that is appropriate? Often, the true meaning will only come from further experimentation. Very likely, multiple methods will be required (no simple push-of-the-button exercise in this uncharted territory). The good news is that, armed with a rational perspective, it is possible to make very valuable observations, even if a complete understanding of the system is still elusive.

Applying a formal methodology that focuses on points of inflection can yield first-mover advantages to practitioners that study these phenomena in a structured and empirical way.

Data science has the opportunity to inform our understanding of old things in new ways. New technologies and newly-available data also can lead us to recognize previously unseen challenges, and to better understand the implications of actions in a more agile, actionable way. The key to approaching abstract concepts is to avoid the temptation to “solve” immediately. By applying even a simple structure, we can inform data discovery, curation and synthesis that allow us to navigate the critical path from where we were going to where we are going now at critical points of inflection, informed by a far better understanding of what it all means.

This article also appears on LinkedIn.