Prob & Stats Gaps: Sprinting for Closure

Prob & Stats Gap

When it comes to the mathematical underpinnings for Deep Learning, I’m extremely passionate. In fact, my perspective can be summarized succinctly:

Deep Learning – Deep Math = Deep Gap.

In reflecting upon my own mathematical credentials for Deep Learning, when it came to probability and statistics, I previously stated:

Through a number of courses in Time Series Analysis (TSA), my background affords me an appreciation for prob & stats. In other words, I have enough context to appreciate this need, and through use of quality, targeted resources (e.g., Goodfellow et al.’s textbook), I can close out the gaps sufficiently – in my case, for example, Bayes’ Rule and information theory.

Teaching to Learn

DSC02681Although I can certainly leverage quality, targeted resources, I wanted to share here a complementary approach. One reason for doing this is that resources such as Goodfellow et al.’s textbook may not be readily accessible to everyone – in other words, some homework is required before some of us are ready to crack open this excellent resource, and make sense of the prob & stats summary provided there.

So, in the spirit of progressing towards being able to leverage appropriate references such as Goodfellow et al.’s textbook, please allow me to share here a much-more pragmatic suggestion:

Tutor a few high school students in prob & stats to learn prob & stats.

Just in case the basic premise of this suggestion isn’t evident, it is: By committing to teaching prob & stats, you must be able to understand prob & stats. And as an added bonus, this commitment of tutoring each of a few students (say) once a week, establishes and reinforces a habit – a habit that is quite likely, in this case, to ensure you stick with your objective to broaden and deepen your knowledge/skills when it comes to probability and statistics.

As an added bonus, this is a service for which you could charge a fee – full rate for tutoring math at the high-school level to gratis, depending upon the value you’ll be able to offer your students … of course, a rate you could adjust over time, as your expertise with prob & stats develops.

Agile Sprints

Over recent years, I’ve found it particularly useful to frame initiatives such as this one in the form of Agile Sprints – an approach I’ve adopted and adapted from the pioneering efforts of J D Meier. To try this for yourself, I suggest the following two-step procedure:

  1. Review JD’s blog post on sprints – there’s also an earlier post of his that is both useful and relevant.
  2. Apply the annotated template I’ve prepared here to a sprint of your choosing. Because the sample template I’ve shared is specific to the prob & stats example I’ve been focused on in this post, I’ve also included a blank version of the sprint template here.


Before you go, there’s one final point I’d like to draw your attention to – and that’s lead and lag measures. Whereas lag measures focus on your (wildly) important goal (WIG), lead measures emphasize those behaviors that’ll get you there. To draw from the example I shared for addressing a math gap in prob & stats, the lag measure is:

MUST have enhanced my knowledge/skills in the area of prob & stats such that I am better prepared to review Deep Learning staples such as Goodfellow et al.’s textbook

In contrast, examples of lead measures are each of the following:

SHOULD have sought tutoring positions with local and/or online services

COULD have acquired the textbook relevant for high-school level prob & stats

With appropriately crafted lead measures then, the likelihood that your WIG will be achieved is significantly enhanced. Kudos to Cal Newport for emphasizing the importance of acting on lead measures in his Deep Work book. For all four disciplines of execution, you can have a closer look at Newport’s book, or go to the 4DX source – the book or by simply Googling for resources on “the 4 disciplines of execution”.

Of course, the approach described here can be applied to much more than a gap in your knowledge/skills of prob & stats. And as I continue the process of self-curating my Data Science Portfolio, I expect to unearth additional challenges and opportunities – challenges and opportunities that can be well approached through 4DX’d Agile Sprints.