Analytics: A Technical Overview

Analytics may be broadly divided into descriptive analytics, predictive analytics and prescriptive analytics. (Alternatively, what-is/what-if/what-now, where “what” corresponds to the output of a computational process.)

This short post touches on what they are how they relate to each other.

Descriptive Analytics

Descriptive analytics relates to making sense of situations. It is most commonly associated with business intelligence tasks like data aggregation and visualisation. Also included are statistical inference methods where parameters of interest are identified based on data and a data generating model.

When one sees a dashboard that displays organisation-level KPIs and “drills down” to individual contributor KPIs is seeing, in each chart, the product of data aggregation (filtering/grouping/summarising data records/etc.) and the visual encoding of the resulting information.

A Typical Performance Dashboard

Statistical inference in descriptive analytics is extremely broad. Here are some exampleSuppose we have data on the behaviour of a large number of people. We attempt to identify sub-groups and their characteristics to the end of market segmentation.

A (Likely Synthetic) Clustering/Segmentation Example

Or we might have experimental data where participants are presented multiple pairs of products and indicate which they prefer, and we use that to identify the “value” of individual product features (e.g.: leather seats, swivelling side mirrors, etc.) to support product design.

A Conjoint Analysis Example

Predictive Analytics

Predictive analytics relates to making projections using methods that lie on a continuum of model-based (causal structure) to data-driven (“model-free”). Technically, it reflects: (i) a computational process encoding the elements and interactions of a model; and/or (ii) an approximation of the input/output relationship underlying data and the usage of that approximation to estimate an outcome. This is most commonly associated with simulations and machine learning.

Less “technically”, predictive analytics supports what-if analysis (counterfactual analysis), which is a workhorse of planning.

That was rather abstract, so here are some examples. We will start with simulation and then go to machine learning.

Suppose that we had the below a model of a queueing system.

A Queueing Model that May Be Implemented in Simulation

Often, when realistic rules are introduced (priority classes, variable service loads), it becomes analytically intractable (or very difficult) to accurately determine performance. Instead of hiring an expensive team of PhDs (with no assurance of performance), why not put a conscientious undergraduate intern with domain experts to build a simulation that encodes system elements and their interactions, and then play forward the system dynamics with simulation to determine the outcomes. Formally, simulation is equivalent to a pen and paper dry run. Where systems include uncertainty, that is modelled as randomness. Instead of computing a single outcome, we compute a large enough sample and consider their statistics.

What have we not heard about machine learning? It is another very diverse domain. You may have heard of how you can train a Convolutional Neural Network to recognise cats. But consider a different example.

Suppose a (web) customer arrives (virtually) at your (web) store. Somehow (cookies/user profile) you have information about him/her/them (?). You are interested in whether that customer will buy or not buy your expensive product. Based on past information, you have learnt a that associates information on users with whether or not they buy. We will consider a situation which is one better, where we get an estimated probability of buying. If that is high or low, we might not intervene. But if the user had a middling probability of buying, we might intervene with a promotion (discount/bundle/gift/etc.) to push them off the fence. (And the choice of intervention may itself be another analytics example.)

Customers with Characteristics (encoded in x/y position) in the Lighter Areas Might Be “On the Fence”

Prescriptive Analytics

Prescriptive analytics relates to obtaining recommendations for courses of actions. This form of analytics is tied with optimisation wherein (i) measure of effectiveness or objective function (to maximise or minimise), (ii) decisions to be made, and (iii) constraints on the available descriptions. This is most commonly associated with mathematical optimisation (mathematical programming) and constraint optimisation (constraint programming).

Example Depiction of an Objective Function: Get to the Top of the Hill

There is the Objective Function, and there are Constraints

There are many possible application examples: identifying a matching of service providers and customers to maximise some measure of compatibility; generating a roster that respects approved leave applications, business holidays and resource availability while minimising project duration; creating a multi-stage implementation plan given multiple possible contingencies.

Remarks

The various families and their methods are often used in supporting ways. For example:

• Model parameters may be estimated with statistical inference (descriptive) and used in simulation (predictive)
• Data aggregation (descriptive) might be applied to compute the parameters of an optimisation model (prescriptive)
• Relationships obtained from machine learning (predictive) may be used to formulate optimisation models (prescriptive)
• Simulations (predictive) may be used as a component of simulation-based optimisation (prescriptive)
• Optimisation methods (most associated with prescriptive analytics) are a vital component supporting machine learning (most associated with predictive analytics)

Note: Some vendors insert intermediate levels for marketing purposes. For example, “diagnostic analytics” is a form of descriptive analytics where the tools used are closer to those used in predictive analytics.