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2018 | OriginalPaper | Buchkapitel

7. Principles of Data Science: Advanced

verfasst von : Jeremy David Curuksu

Erschienen in: Data Driven

Verlag: Springer International Publishing

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Abstract

This chapter covers advanced analytics principles and applications. Let us first back up on our objectives and progress so far. In Chap. 6, we defined the key concepts underlying the mathematical science of data analysis. The discussion was structured in two categories: descriptive and inferential statistics. In the context of a data science project, these two categories may be referred to as unsupervised and supervised modeling respectively. These two categories are ubiquitous because the objective of a data science project is always (bear with me please) to better understand some data or else to predict something. Chapter 7 thus again follows this binary structure, although some topics (e.g. computer simulation, Sect. 7.3) may be used to collect and understand data, forecast events, or both.

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Vorheriges Kapitel Principles of Data Science: Primer
Nächstes Kapitel Principles of Strategy: Primer
Fußnoten
1
Note that in this example the two variables are so correlated that one could have ignored the other variable from the beginning and thereby bypass the process of coordinate mapping altogether. Coordinate mapping becomes useful when the trend is not just a 50/50 contribution of two variables (which corresponds to a 45° correlation line in the scatter plot) but some more subtle relationship where maximum variance lies along an asymmetrically weighted combination of the two variables.
 
2
This assertion is only true under certain conditions, but for most real-world applications where observations are made across a finite set of variables in a population, these conditions are fulfilled.
 
3
The word Eigen comes from the German for characteristic.
 
4
The equation used to find eigenvectors and eigenvalues for a given matrix when they exist is det(A − λI) = 0. Not surprisingly, it is referred to as the matrix’s characteristic equation.
 
5
Quantum theory teaches us that everything in the universe is periodic! But describing the dynamics of any system except small molecules at a quantum level would require several years of computations even on last-generation supercomputers. And this is assuming we would know how to decompose the signal into a nearly exhaustive set of factors, which we generally don’t. Hence an harmonic analysis in practice requires periodic features to be detected at a scale directly relevant to the analysis in question; this defines macroscopic in all circumstances. For example, a survey of customer behaviors may apply Fourier analysis if a periodic feature is detected in a behavior or any factor believed to influence a behavior.
 
6
k can be fixed in advance or refined recursively based on a distance metric threshold.
 
7
It is standard practice in calculus to truncate a Taylor expansion after second order derivative because higher order term tend to be insignificant.
 
8
The idea that stable states are exponentially more likely than unstable states extends much beyond the confines of physical systems. This Boltzmann distribution law has a different name in different fields, such as the Gibbs Measure, the Log-linear response or the Exponential response (to name a few), but the concept is always the same: There is an exponential relationship between the notions of probability and stability.
 
9
The general concept of inference was introduced in Sect. 6.1.2 – Long story short: it indicates a transition from a descriptive to a probabilistic point of view.
 
10
Categorical variables also include non-ordinal numbers, i.e. numbers that don’t follow a special order and instead correspond to different labels. For example, to predict whether customers will choose a product identified as #5 or one identified as #16, the response is presented by two numbers (5 and 16) but they define a qualitative variable since there is no unit of measure nor zero value for this variable.
 
11
Bootstrap refers to successive sampling of a same dataset by leaving out some part of the dataset until convergence of the estimated quantity, in this case a decision tree.
 
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Metadaten
Titel
Principles of Data Science: Advanced
verfasst von
Jeremy David Curuksu
Copyright-Jahr
2018
Buch
Data Driven

Print ISBN: 978-3-319-70228-5

Electronic ISBN: 978-3-319-70229-2

Copyright-Jahr: 2018

DOI
https://doi.org/10.1007/978-3-319-70229-2_7

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