5 Machine Learning for IoT
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like large processing systems or databases for data scientists. On the other hand,
data scientists are concerned with utilizing statistical analysis and advanced
mathematics to extract insights from data.
5.1.2 Review of Probability Theory
Probability plays a key role in machine learning because most learning algorithms
rely on the probabilistic assumption of the data. Therefore, a basic understanding
of probability theory is essential in learning and understanding machine learning
techniques. Probability theory is the mathematical study of uncertainty. Below, we
introduce some basic concepts in probability theory that will familiarize readers
with the language used in machine learning [4].
5.1.2.1 Random Variable
A random variable is a set of possible values from a random experiment. Assume
that we toss a coin, the outcome X of a coin toss can be either head (1) or tail (2). If
the coin is fair, both outcomes X = 1 or X = 2 are equally likely to occur; hence we
would see a probability of 0.5 in the outcome of such experiments. We could state
that the probability of seeing heads when flipping a coin is ½. Note that a random
variable denotes a whole set of outcomes, which means it can take on any of those
values, randomly [5].
5.1.2.2 Distribution
Given a random variable, we can further characterize the probabilities associated
with the random values it can take. If the random variable is discrete (i.e., it can
have only a finite number of values), then this probability assignment is called
a probability mass function (PMF). By definition, a PMF must be non-negative
and must sum to one. Let us take coin flipping example again; if tails and heads
are equally likely, then the random variable X takes values of +1 and −1 with
probability 0.5 each. This can be described as
Pr (X = +1) = 0.5
Pr (X = −1) = 0.5
247
like large processing systems or databases for data scientists. On the other hand,
data scientists are concerned with utilizing statistical analysis and advanced
mathematics to extract insights from data.
5.1.2 Review of Probability Theory
Probability plays a key role in machine learning because most learning algorithms
rely on the probabilistic assumption of the data. Therefore, a basic understanding
of probability theory is essential in learning and understanding machine learning
techniques. Probability theory is the mathematical study of uncertainty. Below, we
introduce some basic concepts in probability theory that will familiarize readers
with the language used in machine learning [4].
5.1.2.1 Random Variable
A random variable is a set of possible values from a random experiment. Assume
that we toss a coin, the outcome X of a coin toss can be either head (1) or tail (2). If
the coin is fair, both outcomes X = 1 or X = 2 are equally likely to occur; hence we
would see a probability of 0.5 in the outcome of such experiments. We could state
that the probability of seeing heads when flipping a coin is ½. Note that a random
variable denotes a whole set of outcomes, which means it can take on any of those
values, randomly [5].
5.1.2.2 Distribution
Given a random variable, we can further characterize the probabilities associated
with the random values it can take. If the random variable is discrete (i.e., it can
have only a finite number of values), then this probability assignment is called
a probability mass function (PMF). By definition, a PMF must be non-negative
and must sum to one. Let us take coin flipping example again; if tails and heads
are equally likely, then the random variable X takes values of +1 and −1 with
probability 0.5 each. This can be described as
Pr (X = +1) = 0.5
Pr (X = −1) = 0.5