# Instrumentation & Measurement Magazine 24-2 - 85

```spectrometer [5] which is more mobile and affordable, and directly measures the chemical makeup of the food such as the
per-100-gram amount of protein, saturated fats, glucose, etc.
On top of that, if we also directly measure the food's weight,
we can then indirectly measure the total calories of the food
based on the said chemical makeup and weight. Today, such
indirect measurements are widely used in domains as diverse
as oil refinery, chemical industry, air conditioning systems, automobiles, semiconductor production, and manufacturing [6].
There are two ways to determine the functional relationship f: analytical modeling and data-driven modeling.
Analytical modeling is done by domain experts who use the
laws of science, such as a physical phenomenon, to create a
model that gives the relationship between the directly measured variables and the measurand. In the food spectrometer
example, if near-infrared spectroscopy is used, then the designers can use the laws of chemistry and physics to detect the
chemical makeup of certain food ingredients from the spectra
resulting from the ingredients' molecules' absorption of the
near-infrared light waves. Once we know the ingredients, we
can calculate the calories by using the weight and standard calorie tables for those ingredients.
On the other hand, data-driven modeling estimates the
functional relationship f by statistical analysis and curve fitting of a sufficient number of existing direct measurements of
the said variables and the measurand, all of which are collected
in a dataset. Today, ML methods are the most commonly-used
data-driven modeling tools, and in many applications, they
are easier to design and sometimes even more accurate than
using an analytical model [1]. The process of estimating f in
ML is known as " training " the model. In this process, the ML
model is trained with the given dataset to find an fˆ, referred
to as hypothesis or estimator, which estimates f. Once the model
is trained, tested and approved, it is deployed in the measurement system. If we input the aforementioned vector x to
this ML model, it gives the output yˆ = fˆ(x) as an estimation of
y. To understand this, let's go back to our food calorie measurement example. Instead of using a spectrometer, we could
install an app on our smartphone that gives the smartphone
virtual instrumentation capabilities [7] to perform Vision Based
Measurement (VBM) [8] on the food's image taken with the
smartphone's camera. In this specific example, the app has an
ML model that can recognize, from the image of the food, individual food ingredients, their volume, and their mass [9], [10],
because the ML model has been trained with a food image dataset. Once we have the ingredients and their mass, the system
calculates the total calories with standard calorie tables that are
already programmed into the app. Here, we did not use any
physical or chemical laws as we did with the spectrometer; instead, we used a mathematical model that resulted from a best
fit to a dataset. For readers who are not familiar with VBM, we
note that VBM is by default indirect measurement, where the
direct measurement component of the experiment (gray box
in Fig. 1) happens when the camera captures the image and
measures the value (RGB or YUV) of each pixel at cartesian position (a, b) in the image. The quantities R, G, B, Y, U, and V are
April 2021

ordinal quantities and therefore compliant with measurement
standards [11, 1.26].
The accuracy of the ML model depends on (1) the specific
ML method used, e.g., SVM, Deep Learning, etc.; (2) how well
f is estimated by fˆ; and (3) the quality and size of the food image dataset. In addition, looking at Fig. 1, we can see that each
of the direct measurement component and the ML component
could separately contribute to the total error of the measurement system. In this article, we are interested in the latter:
the ML component's contribution to measurement error and
quantifying the resulting uncertainty, which will be discussed
at length in Part 2.

ML in I&M: Handle with Care!
It is rather easy to get confused with seemingly similar terminology when applying ML to an I&M system, so in this section
we describe the terminology similarities and differences between the two to help both I&M and ML practitioners avoid
confusion. Let's start that with Fig. 2, in which a bullseye represents the true value in I&M and in ML, while a black dot
represents a single measurement in I&M and the total estimation outcome in ML over an entire dataset. There are multiple
black dots in each bullseye diagram, representing multiple repeated measurements of the same measurand in I&M, and
multiple outcomes of the same ML model over different data-sets of the same size [12, Fig. 6] as is done in ML cross validation or ML bootstrap sampling, for example. The distance
between a black dot and the center of the bullseye represents
the error: measurement error in I&M and training error (value
of the loss function a.k.a. cost function) in ML. Fig. 2(i) shows
a commonly-used visualization in the I&M community illustrating systematic error (the part of measurement error that
remains constant or varies in a predictable manner) which affects trueness (the closeness to the bullseye of the average of
the repeated measurements of the same measurand) versus
random error (the part of measurement error that varies in a
random way) which affects precision (the closeness of those repeated measurements to each other). On the other hand, Fig.
2(ii) shows a commonly-used visualization in the ML community illustrating bias (deviation of the expected value of the
estimator from the bullseye) versus variance (fluctuations in
the estimator's output).
We can see that the visuals are quite similar, and it looks as if
there might be a relationship between systematic error in I&M
and bias in ML, and between random error in I&M and variance in ML. But, as the proverb goes, " looks can be deceiving "
and the reality is more complicated, as explained in the next 3
subsections.
1) The two parts of the figure represent totally different
situations: Fig. 2(i) relates to run time when we are taking repeated measurements of the same measurand and getting a
different result each time due to measurement error, whereas
Fig. 2(ii) relates not to run time (a.k.a. prediction time or estimation time in ML) but to training time, with each black dot
indicating the outcome of the ML model trained with a different dataset, Dj, with all datasets being of the same size S. At run

IEEE Instrumentation & Measurement Magazine	85

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# Instrumentation & Measurement Magazine 24-2

## Table of Contents for the Digital Edition of Instrumentation & Measurement Magazine 24-2

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