BLOG POST by Dr. Poomjai Nacaskul, Faculty Member at the Chulalongkorn School of Integrated Innovation. Poomjai.N@chula.ac.th
2022.7.25

Humans are predictive animals. In fact, many, if not most, animals are predictive animals. But what do I mean by that? By saying that humans are predictive animals, I mean humans survive and thrive by way of predicting (in the most general sense). Of course, predict = pre + dict. If you looked up \"pre-\", \"dict\", and \"predict\" in www.etymonline.com, you’d be directed to this:

The Latin word was active in forming verbs. Also see prae-. Sometimes in Middle English muddled with words in pro- or per-.

dicte (n.) >>> also dict, \"a saying, maxim, statement,\" late 14c., from Latin dictum \"a thing said\" (see dictum). A word long obsolete, but it figures in what is probably the first book printed in English, Caxton\'s issue of Anthony Woodville\'s \"Dictes and Sayings of the Philosophers.\"

predict (v.) >>> 1620s (implied in predicted), \"foretell, prophesy, declare before the event happens,\" a back formation from prediction or else from Latin praedicatus, past participle of praedicere \"foretell, advise, give notice,\" from prae \"before\" (see pre-) + dicere \"to say\" (from PIE root *deik- \"to show,\" also \"pronounce solemnly\"). Related: Predicted; predicting.

Here, when I say humans predict, I don’t mean outcome of an election, war, or long-term survivability of the human species on this planet. I mean when I see clouds darkening, I make the statement (\"dicte\") about rain before (\"pre-\") water droplets fall from the sky and hit the ground I’m standing on. I mean when I hear someone paying another person a compliment, I say (probably just to myself) that that would make the second person feel good about herself/himself.

In the grand scheme of things, ability to predict ahead could have been one amongst a myriad of attributes that gave our evolutionary ancestors the evolutionary edge over the other competing hominids over the evolutionary time span of a few hundred thousand years or so.\"

Much, much more personal, your ability to predict better—meaning faster, more accurately, more consistently so (hopefully all three)—is ultimately what would give you the competitive edge, let’s say, in business, in innovation, in innovative business, or in the business of innovation.

My thesis here is that to predict something, anything, you need to know two kinds of things: the what and the how. The \"what\" is the specific given at the time you’re trying to make prediction of some kind. The \"why\" is the general mechanism that enables you to make prediction given your knowledge of said specific.

In short, y = f(x). The \"dependent variable\" y refers to our predicted value. The \" independent variable\" x is the specific value given to you. The \"function\" f is the general mechanism that tells you how to say y whenever you see or are given x. By paraphrasing \"making a prediction\" with a mathematical equation, I sneaked one detail by you. Equation, if you take the meaning literally, means the \"left-hand-side\" (of the equality sign) is identical to or otherwise quantitatively indistinguishable from the \"right-hand-side\" (of the equality sign). The one detail I sneaked in is the fact that there is an \"order of information arrival\" at play here.

Let’s revisit the \"chicken-and-egg\" conundrum, except this time the question is: what comes first, y or f or x, and what comes second? Now, whenever we make prediction, for sure the \"right-hand-side\" comes before the \"left-hand-side\", so we know y must come last. But between f and x, what comes first? Here we say that of course f comes first, as it’s the general mechanism by which any specific x that comes by this way gets \"transformed\" or \"mapped\" into y. In summary, to predict y, you need to first know the function f — in fact, strictly speaking, you’d need to pick yourself one such function from an infinite possibility of such \"univariate\" functions, then you need to get the value of provided to you as \"information\".

Before we go on, let’s altogether be cognizant of the fact that, in life, you you’d never be able to achieve perfect results. In reality, all your predictions will most likely be \"a little bit off\". Having said that, in practical terms, if you are \"not off by much\" — how much is \"not much\" or \"not by much\" depends on whether you are trying to land an artillery barrage or administering drug intravenously, then you’d be fine. Perhaps more to the point, if you are \"off by less\" (i.e. more accurate) than your competitors could manage, then de facto you are golden.

So how do you make better (fast, accurate, consistently fast/accurate) prediction? By having the \"best/most suitable\" function f from the world of mathematics applied to the \"most accurate/precise/reliable\" information as to the true value of x, and by having the \"fastest/least error-prone\" computational platform for performing the calculation f(x).

Let’s assign jobs. Let the mathematicians create/accumulate/populate the \"catalog\" of functions and give us the \"menu\" to pick and choose from. Let the data professionals make sure we have necessary and sufficient information when we need it. Let the computer scientists/engineers/programmers invent/innovate as well as research/develop the computational platform for best speed and reliability under cost constraints.

Which brings us to the modern world, one driven by Artificial Intelligence, Machine Learning, Quantitative Models, and Data Analytics. At the end of the day, all these strive to achieve better f in combination w/ better x. Now, assuming the mathematicians, data professionals, and computer scientists/engineers/programmers have done their part, our task as analyst-—data scientists if you want to be fancy about it-—is to construct f from having observed the (x, y) pairings. This is called modelling, or model-building, or building a model. Put another way, mathematicians have furnished all kinds of possibilities regarding y = f(x) in the most generic/generalisable way possible, and we can count on the quality/quantity of data providing the right kind of information, as well as being able to do the necessary computation in time. Now it is up to us to narrow down from amongst infinite possibilities the best combination of f and x working together.

The choice is infinite, but here I have groups them into the following:  

• Multi-variate model – where x = {x₁, … , x_n}.
• Affine model – where x = {x₁, … , x_n}, f(x) = Ax + b, and A is an m-by-n matrix (in particular, m = n).
• Time-Series model – where y = v(t) and x = {v(s), s < t}
• Dynamic model (ordinary differential equation) – where y = v(t) and x = {v₀ , v\'(t), v\'\'(t), ..}
• Dynamic model (partial differential equation) – where y = {v_i(t)} and x = {{v_i0 , v_i\'(t), v_i\'\'(t), ..}, i = 1, … , n}
• Probabilistic model – where y is a probabilistic statement about some quantity x that we expect to be able to observe, but cannot be absolutely certainty beforehand what that observed value would be.
• Stochastic model (stochastic differential equation) – kind of like introducing probabilistic element of probabilistic modelling into a differential equation!
• Machine Learning model – where f is not hand-picked, but rather a parametric form f(x|θ) is provided to a computer algorithm that successively alter/fine-tune θ so that {(x, f(x|θ))} closely resemble actual (x, y) of some the dataset {(x, y)}.
• AI-driven model – machine learning model whereby the \"learning\" algorithm mimics humans’ cognitive learning process, and so (hopefully) the resultant f retains some of that \"intuitive/flexible\" attribute associated with human reasoning. Also, in a much narrower sense, f that enables digital application to \"interact naturally\" w/ humans, for instance, when x = “Alexa, how are you?” elicits y = “Fine thank you, and you?” in response.

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