IEEE Systems, Man and Cybernetics Magazine - April 2021 - 14

computing system has a very simple structure, and it can
be initiated by any known optimization algorithm, including the most primitive ones, such as random search algorithms. This article introduces the UFO and shows why the
system is so important to cybernetic applications.
Performance Criteria
Cybernetics is defined as the " science of governance " [1].
Let's refer to Figure 1. For technical systems, the most
popular language used to explain and build a model is
mathematics. It employs a transfer function, or a set of
them, to transform input variables into one or multiple
output variables. In ML and deep learning (DL), this process is known as function approximation, where the goal
is to find a direct relationship between the input variables (also called predictors) and the output variables
(also called responses and targets) of a given data set.
Today, there are many ML computing systems, such as
linear regression (LR), non-LR (NLR), decision trees,
SR, SVMs, ANNs, and so on. Each has strengths and

weaknesses and is thus used for specific applications. The
good approximation of a system should fulfill both the precision/accuracy and the explainability/interpretability performance criteria. Figure 2 reveals an important fact:
state-of-the-art ML algorithms have highly accurate
approximations, but their explanations are very weak; the
opposite is true for classical ML algorithms. The question
that must be asked here is: Can both performance criteria
be satisfied?
Current ML Tools
As stated in the preceding section, there are many ML
algorithms. Let's focus on the following ones.
LR
Refer to Figure 1. LR can be used to explain data sets' variability by expressing the input variables as linear or polynomial equations. Suppose there is an actual output
variable denoted by y. Then, its estimated value (yt ) can
be mathematically expressed as follows:
◆◆ Linear equation:
yt = b 0 + b 1 x, (1)

y1
y2
Model

xn

ym

where bs are the model coefficients.
Outputs

Inputs

	
x1
x2

◆◆ Polynomial equation:

	

d

yt = | b l x l = b 0 + b 1 x + b 2 x 2 + g + b d x d . (2)
l=0

◆◆ Multiple LR (MLR):

Figure 1. The mathematical foundations of

yt = b 0 + b 1 x 1 + b 2 x 2 + g + b n x n . (3)

	

cybernetics [1].

DL

Statistical AOGs
Models
SVMs

Graphical
Models
Bayesian
Belief Networks
SRL
CRFs HBNs
MLNs
Markov
Models

Ensemble
Methods
Random
Forests

Prediction Accuracy

NNs

Decision
Trees
Explainability
(b)

(a)
Figure 2. The explainability versus the accuracy of ML algorithms: (a) ML algorithms and (b) accuracy

versus explainability. SRL: statistical relation learning; CRFs: conditional random fields; HBNs: hyperbolic batch
normalizations; MLNs: Markov logic networks; AOG: And-Or graph.

14	

IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE Apri l 2021



IEEE Systems, Man and Cybernetics Magazine - April 2021

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