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==Naive Bayes==
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Lecture and Tutorial:
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</html>
 +
 
 +
<br />
 +
==Projects portfolio==
 +
 
 +
 
 +
<br />
 +
==Data Analytics courses==
 +
 
 +
 
 +
<br />
 +
==Possible sources of data==
 +
 
 +
 
 +
<br />
 +
==What is data==
 +
 
 +
 
 +
<br />
 +
===Qualitative vs quantitative data===
 +
 
 +
 
 +
<br />
 +
====Discrete and continuous data====
 +
 
 +
 
 +
<br />
 +
===Structured vs Unstructured data===
 +
 
 +
 
 +
<br />
 +
===Data Levels and Measurement===
 +
 
 +
 
 +
<br />
 +
===What is an example===
 +
 
 +
 
 +
<br />
 +
===What is a dataset===
 +
 
 +
 
 +
<br />
 +
===What is Metadata===
 +
 
 +
 
 +
<br />
 +
==What is Data Science==
 +
 
 +
 
 +
<br />
 +
===Supervised Learning===
 +
 
 +
 
 +
 
 +
<br />
 +
===Unsupervised Learning===
 +
 
 +
 
 +
<br />
 +
===Reinforcement Learning===
 +
 
 +
 
 +
<br />
 +
==Some real-world examples of big data analysis==
 +
 
 +
 
 +
<br />
 +
==Statistic==
 +
 
 +
 
 +
<br />
 +
==Descriptive Data Analysis==
 +
 
 +
 
 +
<br />
 +
===Central tendency===
 +
 
 +
 
 +
<br />
 +
====Mean====
 +
 
 +
 
 +
<br />
 +
=====When not to use the mean=====
 +
 
 +
 
 +
<br />
 +
====Median====
 +
 
 +
 
 +
<br />
 +
====Mode====
 +
 
 +
 
 +
<br />
 +
====Skewed Distributions and the Mean and Median====
 +
 
 +
 
 +
<br />
 +
====Summary of when to use the mean, median and mode====
 +
measures-central-tendency-mean-mode-median-faqs.php
 +
 
 +
 
 +
<br />
 +
===Measures of Variation===
 +
 
 +
 
 +
<br />
 +
====Range====
 +
 
 +
 
 +
<br />
 +
====Quartile====
 +
 
 +
 
 +
<br />
 +
====Box Plots====
 +
 
 +
 
 +
 
 +
<br />
 +
====Variance====
 +
 
 +
 
 +
<br />
 +
====Standard Deviation====
 +
 
 +
 
 +
<br />
 +
==== Z Score ====
 +
 
 +
 
 +
<br />
 +
===Shape of Distribution===
 +
 
 +
 
 +
<br />
 +
====Probability distribution====
 +
 
 +
 
 +
<br />
 +
=====The Normal Distribution=====
 +
 
  
Note, on all the Naive Bayes examples given, the Performance operator is Performance (Binomial Classification)
+
<br />
 +
====Histograms====
  
  
 
<br />
 
<br />
'''Naïve Bayes''' is a classification technique that uses data about prior events to derive a probability of future events.
+
====Skewness====
  
'''Bayesian classifiers''' utilize training data to calculate an observed probability for each class based on feature values. When such classifiers are later used on unlabeled data, they use those observed probabilities to predict the most likely class, given the features in the new data. It is a very simple idea, but it gives us a classification method that often delivers results on par with more sophisticated algorithms.
 
  
'''The Naïve Bayes algorithm''' is named as such because it makes a couple of naïve assumptions about the data. In particular, it assumes that all of the features in a data-set are equally important and independent. These assumptions are rarely true of most of the real-world applications. However, in most cases when these assumptions are violated, Naïve Bayes still performs fairly well. This is true even in extreme circumstances where strong dependencies are found among the features. Due to the algorithm's versatility and accuracy across many types of conditions, Naïve Bayes is often a strong first candidate for classification learning tasks.
+
<br />
 +
====Kurtosis====
  
  
 
<br />
 
<br />
'''Bayesian classifiers are typically best applied to''' problems in which the information from numerous attributes should be considered simultaneously in order to estimate the probability of an outcome.
+
====Visualization of measure of variations on a Normal distribution====
  
While many algorithms ignore features that have weak effects, Bayesian methods utilize all available evidence to subtly change the predictions.
 
  
If a large number of features have relatively minor effects, taken together their combined impact could be quite large.
+
<br />
Bayesian probability theory is rooted in the idea that the estimated likelihood of an event should be based on the evidence at hand.
+
==Simple and Multiple regression==
  
  
 
<br />
 
<br />
'''Bayesian classifiers have been used for:'''
+
===Correlation===
* Text classification, such as spam filtering, author identification, and topic modeling
 
:* A common application of the algorithm uses the frequency of the occurrence of words in past emails to identify junk email.
 
  
* In weather forecast, the chance of rain describes the proportion of prior days with similar measurable atmospheric conditions in which precipitation occurred. A 60 percent chance of rain, therefore, suggests that in 6 out of 10 days on record where there were similar atmospheric conditions, it rained.
 
  
* Intrusion detection and anomaly detection on computer networks
+
<br />
 +
====Measuring Correlation====
  
* Diagnosis of medical conditions, given a set of observed symptoms.
+
 
 +
<br />
 +
=====Pearson correlation coefficient - Pearson s r=====
  
  
 
<br />
 
<br />
===Probability Primer===
+
=====The coefficient of determination <math>R^2</math>=====
'''Events''' are possible outcomes, such as sunny and rainy weather, a heads or tails result in a coin flip, or spam and not spam email messages.
 
  
A '''trial''' is a single opportunity for the event to occur, such as a day's weather, a coin flip, or an email message.
 
Naive Bayes
 
  
 +
<br />
 +
====Correlation <math>\neq</math> Causation====
  
The probability of an event can be estimated from observed data by dividing the number of trials in which an event occurred by the total number of trials.
 
  
* For instance, if it rained 3 out of 10 days, the probability of rain can be estimated as 30 percent.
+
<br />
* Similarly, if 10 out of 50 email messages are spam, then the probability of spam can be estimated as 20 percent.
+
====Testing the "generalizability" of the correlation ====
* The notation P(A) is used to denote the probability of event A, as in P(spam) = 0.20
 
  
  
 
<br />
 
<br />
====Independent and dependent events====
+
===Simple Linear Regression===
If the two events are totally unrelated, they are called '''independent events'''. For instance, the outcome of a coin flip is independent of whether the weather is rainy or sunny.
 
  
On the other hand, a rainy day depends and the presence of clouds are '''dependent events'''. The presence of clouds is likely to be predictive of a rainy day. In the same way, the appearance of the word Viagra is predictive of a spam email.
 
  
If all events were independent, it would be impossible to predict any event using data about other events. Dependent events are the basis of predictive modeling.
+
<br />
 +
===Multiple Linear Regression===
  
  
 
<br />
 
<br />
====Mutually exclusive and collectively exhaustive====
+
===RapidMiner Linear Regression examples===
<!-- Events are '''mutually exclusive''' and '''collectively exhaustive'''. -->
 
  
In probability theory and logic, a set of events is '''Mutually exclusive''' or '''disjoint''' if they cannot both occur at the same time. A clear example is the set of outcomes of a single coin toss, which can result in either heads or tails, but not both. https://en.wikipedia.org/wiki/Mutual_exclusivity
 
  
A set of events is '''jointly''' or '''collectively exhaustive''' if at least one of the events must occur. For example, when rolling a six-sided die, the events 1, 2, 3, 4, 5, and 6 (each consisting of a single outcome) are collectively exhaustive, because they encompass the entire range of possible outcomes. https://en.wikipedia.org/wiki/Collectively_exhaustive_events
+
<br />
 +
==K-Nearest Neighbour==
  
  
If a trial has n outcomes that cannot occur simultaneously, such as heads or tails, or spam and ham (non-spam), then knowing the probability of n-1 outcomes reveals the probability of the remaining one.
+
<br />
 +
==Decision Trees==
  
In other words, if there are two outcomes and we know the probability of one, then we automatically know the probability of the other.
+
 
For example, given the value P(spam) = 0.20 , we are able to calculate P(ham) = 1 – 0.20 = 0.80
+
<br />
 +
===The algorithm===
  
  
 
<br />
 
<br />
====Joint Probability====
+
====Basic explanation of the algorithm====
Joint Probability (Independence)
 
  
  
Often, we are interested in monitoring several non-mutually exclusive events for the same trial. If some other events occur at the same time as the event of interest, we may be able to use them to make predictions.
+
<br />
 +
====Algorithms addressed in Noel s Lecture====
  
In the case of spam detection, consider, for instance, a second event based on the outcome that the email message contains the word Viagra.
 
For most people, this word is only likely to appear in a spam message. Its presence in a message is therefore a very strong piece of evidence that the email is spam.
 
  
We know that 20 percent of all messages were spam and 5 percent of all messages contained the word "Viagra". Our job is to quantify the degree of overlap between these two probabilities. In other words, we hope to estimate the probability of both spam and the word "Viagra" co-occurring, which can be written as P(spam ∩ Viagra).
+
<br />
 +
=====The ID3 algorithm=====
  
If we assume that P(spam) and P(Viagra) are '''independent''', we could then easily calculate P(spam ∩ Viagra) - the probability of both events happening at the same time (note that they are not independent, however!).
 
  
Because 20 percent of all messages are spam, and 5 percent of all emails contain the word Viagra, we could assume that 5 percent of 20 percent (0.05 * 0.20 = 0.01 ), or 1 percent of all messages are spam contain the word Viagra.
+
<br />
 +
=====The C5.0 algorithm=====
  
More generally, for any two independent events A and B, the probability of both happening is:
 
P(A ∩ B) = P(A) * P(B)
 
  
In reality, it is far more likely that P(spam) and P(Viagra) are highly '''dependent''', which means that this calculation is incorrect. So we need to employ '''conditional probability'''.
+
<br />
 +
===Example in RapidMiner===
  
  
 
<br />
 
<br />
 +
==Random Forests==
 +
https://www.youtube.com/watch?v=J4Wdy0Wc_xQ&t=4s
  
====Conditional probability - The Bayes' Theorem====
+
 
Thomas Bayes (1763): An essay toward solving a problem in the doctrine of chances, Philosophical Transactions fo the Royal Society, 370-418.
+
<br />
 +
==Naive Bayes==
  
  
The relationship between dependent events can be described using Bayes' Theorem, as shown in the following equation.
+
<br />
 +
===Probability===
  
  
<math>
+
<br />
P(A|B)= \frac{P(A \cap B)}{P(B)} = \frac{P(B|A)P(A)}{P(B)}
+
===Independent and dependent events===
</math>
 
  
  
The notation P(A|B) can be read as the probability of event A given that event B occurred. This is known as conditional probability, since the probability of A is dependent or '''conditional''' on the occurrence of event B.
+
<br />
 +
===Mutually exclusive and collectively exhaustive===
  
  
 
<br />
 
<br />
 +
===Marginal probability===
 +
The marginal probability is the probability of a single event occurring, independent of other events. A conditional probability, on the other hand, is the probability that an event occurs given that another specific event has already occurred. https://en.wikipedia.org/wiki/Marginal_distribution
 +
  
====Prior Probability====
+
<br >
Suppose that you were asked to guess the probability that an incoming email was spam. Without any additional evidence, the most reasonable guess would be the probability that any prior message was spam (that is, 20 percent in the preceding example). This estimate is known as the prior probability.
+
===Joint Probability===
  
  
 
<br />
 
<br />
====Posterior Probability====
+
===Conditional probability===
Now suppose that you obtained an additional piece of evidence. You are told that the incoming email contains the word 'Viagra'.
 
  
By applying Bayes' theorem to the evidence, we can compute the posterior probability that measures how likely the message is to be spam.
 
  
In the case of spam classification, if the posterior probability is greater than 50 percent, the message is more likely to be spam than ham, and it can potentially be filtered out.
+
<br />
 +
====Kolmogorov definition of Conditional probability====
  
The following equation is the Bayes' theorem for the given evidence:
 
  
 +
<br />
 +
====Bayes s theorem====
  
[[File:BayesTheorem-Posterior_probability.png|500px|thumb|center|]]
+
 
 +
<br />
 +
=====Likelihood and Marginal Likelihood=====
  
  
 
<br />
 
<br />
====Applying Bayes' Theorem - Example====
+
=====Prior Probability=====
We need information on how frequently Viagra has occurred as spam or ham. Let's assume these numbers:
 
  
{| class="wikitable"
 
|+
 
!
 
! colspan="2" |Viagra
 
!
 
|-
 
|'''Frequency'''
 
|'''Yes'''
 
|'''No'''
 
|'''Total'''
 
|-
 
|Spam
 
|4
 
|16
 
|20
 
|-
 
|Ham
 
|1
 
|79
 
|80
 
|-
 
|'''Total'''
 
|5
 
|95
 
|100
 
|}
 
  
 +
<br />
 +
=====Posterior Probability=====
  
* The likelihood table reveals that P(Viagra|spam) = 4/20 = 0.20,  indicating that the probability is 20 percent that a spam message contains the term Viagra.
+
 
* Additionally, since the theorem says that P(B|A) x P(A) = P(A ∩ B), we can calculate P(spam ∩ Viagra) as P(Viagra|spam) x  P(spam) = (4/20) x (20/100) = 0.04.
+
<br />
* This is four times greater than the previous estimate under the faulty independence assumption.
+
===Applying Bayes' Theorem===
  
  
To compute the posterior probability we simply use:
+
<br />
 +
====Scenario 1 - A single feature====
  
  
<math>  
+
<br />
P(spam|Viagra) = \frac{P(Viagra|spam)P(spam)}{P(Viagra)} = \frac{4/20 \times 20/10}{5/100} = \frac{0.2 \times 0.2}{0.05} = 0.8
+
====Scenario 2 - Class-conditional independence====
</math>
 
  
  
* Therefore, the probability is 80 percent that a message is spam, given that it contains the word "Viagra".
+
<br />
* Therefore, any message containing this term should be filtered.
+
====Scenario 3 - Laplace Estimator====
  
  
 
<br />
 
<br />
====Applying Bayes' Theorem - Example====
+
===Naïve Bayes - Numeric Features===
  
* Let's extend our spam filter by adding a few additional terms to be monitored: "money", "groceries", and "unsubscribe".
 
* We will assume that the Naïve Bayes learner was trained by constructing a likelihood table for the appearance of these four words in 100 emails, as shown in the following table:
 
  
 +
<br />
 +
===RapidMiner Examples===
  
[[File:ApplyingBayesTheorem-Example.png|800px|thumb|center|]]
 
  
 +
<br />
 +
==Perceptrons - Neural Networks and Support Vector Machines==
  
As new messages are received, the posterior probability must be calculated to determine whether the messages are more likely to be spam or ham,  given the likelihood of the words found in the message text. For example, suppose that a message contains the terms '''Viagra''' and '''Unsubscribe''', but does not contain either '''Money''' or '''Groceries'''. Using Bayes' theorem, we can define the problem as shown in the equation on the next slide, which captures the probability that a message is  spam, given that the words 'Viagra' and Unsubscribe are present and that the words 'Money' and  'Groceries' are not.
 
  
As mentioned on the previous slide, using Bayes' theorem, we can define the problem as shown in the equation below, which captures the probability that a message is spam, given that the words 'Viagra' and Unsubscribe are present and that the words 'Money' and  'Groceries' are not.
+
<br />
 +
==Boosting==
  
  
<math>
+
<br />
P(Spam|Viagre \cap \urcorner Money \cap \urcorner Groceries \cap Unsubscribe) = \frac{P(Viagra \cap \urcorner Money \cap \urcorner Groceries \cap Unsubscribe | spam)P(spam)}{P(Viagra \cap \urcorner Money \cap \urcorner Groceries \cap Unsubscribe)}
+
===Gradient boosting===
</math>
 
  
  
For a number of reasons, this is computationally difficult to solve. As additional features are added, tremendous amounts of  memory are needed to store probabilities for all of the possible intersecting events.
+
<br />
 +
==K Means Clustering==
  
  
 
<br />
 
<br />
====Class-Conditional Independence====
+
===Clustering class of the Noel course===
  
The work becomes much easier if we can exploit the fact that Naïve Bayes assumes independence among events. Specifically, Naïve Bayes assumes '''class-conditional independence''', which means that events are independent so long as they are conditioned on the same class value.
 
  
Assuming conditional independence allows us to simplify the equation using the probability rule for independent events, which you may recall is P(A ∩ B) = P(A) * P(B). This results in a much easier-to-compute formulation:
+
<br />
 +
====RapidMiner example 1====
  
  
[[File:ApplyingBayesTheorem-ClassConditionalIndependance.png|800px|thumb|center|]]
+
<br />
 +
==Principal Component Analysis PCA==
  
  
Using the values in the likelihood table, we can start filling numbers in these equations. Because the denominatero si the same in both cases, it can be ignored for now. The overall likelihood of spam is then:
+
<br />
 +
==Association Rules - Market Basket Analysis==
  
  
<math>
+
<br />
\frac{4}{20} \times \frac{10}{20} \times \frac{20}{20} \times \frac{12}{20} \times \frac{20}{100} = 0.012
+
===Association Rules example in RapidMiner===
</math>
 
  
  
While the likelihood of ham given the occurrence of these words is:
+
<br />
 +
==Time Series Analysis==
  
  
<math>
+
<br />
\frac{1}{80} \times \frac{60}{80} \times \frac{72}{80} \times \frac{23}{80} \times \frac{80}{100} = 0.002
+
==[[Text Analytics|Text Analytics / Mining]]==
</math>
 
  
  
Because 0.012/0.002 = 6, we can say that this message is six times more likely to be spam than ham. However, to convert these numbers to probabilities, we need one last step.
+
<br />
 +
==Model Evaluation==
  
  
The probability of spam is equal to the likelihood that the message is  spam divided by the likelihood that the message is either spam or  ham:
+
<br />
 +
===Why evaluate models===
  
  
<math>
+
<br />
\frac{0.012}{(0.012 + 0.002)} = 0.857
+
===Evaluation of regression models===
</math>
 
  
  
The probability that the message is spam is 0.857. As this is over the threshold of 0.5, the message is classified as spam.
+
<br />
 +
===Evaluation of classification models===
  
  
 
<br />
 
<br />
====Naïve Bayes - Problems====
+
===References===
Suppose we received another message, this time containing the terms: Viagra, Money, Groceries, and Unsubscribe. The likelihood table of spam is:
+
Landis JR, Koch GG. The measurement of observer agreement for categorical data. Biometrics. 1977 Mar;33(1):159-174. DOI: 10.2307/2529310.
  
  
<math>
+
<br />
\frac{4}{20} \times \frac{10}{20} \times \frac{0}{20} \times \frac{12}{20} \times \frac{20}{100} = 0
+
==[[Python for Data Science]]==
</math>
 
  
  
Surely this is a misclassification? right?. This problem might arise if an event never occurs for one or more levels of the class. for instance, the term Groceries had never previously appeared in a spam message. Consequently, P(spam|groceries) = 0%
+
<br />
 +
===[[NumPy and Pandas]]===
  
Because probabilities in Naïve Bayes are multiplied out, this 0% value causes the posterior probability of spam to be zero, giving the presence of the word Groceries the ability to effectively nullify and overrule all of the other evidence.
 
  
Even if the email was otherwise overwhelmingly expected to be spam, the zero likelihood for the word Groceries will always result in a probability of spam being zero.
+
<br />
 +
===[[Data Visualization with Python]]===
  
  
 
<br />
 
<br />
====Naïve Bayes -  Laplace Estimator====
+
===[[Text Analytics in Python]]===
A solution to this problem involves using something called the '''Laplace estimator''', named after the French mathematician Pierre-Simon Laplace. The Laplace estimator essentially adds a small number to each of the counts in the frequency table, which ensures that each feature has a nonzero probability of occurring with each class.
 
  
Typically, the Laplace estimator is set to 1, which ensures that each class-feature combination is found in the data at least once. The Laplace estimator can be set to any value and does not necessarily even have to be the same for each of the features.
 
  
Using a value of 1 for the Laplace estimator, we add one to each numerator in the likelihood function. The sum of all the 1s added to the numerator must then be added to each denominator. The likelihood of spam is therefore:
+
<br />
 +
===[[Dash - Plotly]]===
  
  
<math>
+
<br />
\frac{5}{24} \times \frac{11}{24} \times \frac{1}{24} \times \frac{13}{24} \times \frac{20}{100} = 0.0004
+
===[[Scrapy]]===
</math>
+
 
 +
 
 +
<br />
 +
==[[R]]==
 +
 
  
 +
<br />
 +
===[[R tutorial]]===
  
While the likelihood of ham is:
 
  
 +
<br />
 +
==[[RapidMiner]]==
  
<math>
 
\frac{2}{84} \times \frac{15}{84} \times \frac{9}{84} \times \frac{24}{84} \times \frac{80}{100} = 0.0001
 
</math>
 
  
This means that the probability of spam is 80 percent and the probability of ham is 20 percent; a more plausible result that the one obtained when Groceries alone determined the result.
+
<br />
 +
==Assessments==
  
  
 
<br />
 
<br />
====Naïve Bayes -  Numeric Features====
+
===Diploma in Predictive Data Analytics assessment===
Because Naïve Bayes uses frequency tables for learning the data, each feature must be categorical in order to create the combinations of class and feature values comprising the matrix.
 
  
Since numeric features do not have categories of values, the preceding algorithm does not work directly with numeric data.
 
  
One easy and effective solution is to discretize numeric features, which simply means that the numbers are put into categories knows as bins. For this reason, discretization is also sometimes called '''binning'''.
+
<br />
 +
==Notas==
  
This method is ideal when there are large amounts of training data, a common condition when working with Naïve Bayes.
 
  
There is also a version of Naïve Bayes that uses a '''kernel density estimator''' that can be used on numeric features with a normal distribution.
+
<br />
 +
==References==
  
  
 
<br />
 
<br />

Latest revision as of 21:50, 10 March 2021



aver


Contents

Projects portfolio


Data Analytics courses


Possible sources of data


What is data


Qualitative vs quantitative data


Discrete and continuous data


Structured vs Unstructured data


Data Levels and Measurement


What is an example


What is a dataset


What is Metadata


What is Data Science


Supervised Learning


Unsupervised Learning


Reinforcement Learning


Some real-world examples of big data analysis


Statistic


Descriptive Data Analysis


Central tendency


Mean


When not to use the mean


Median


Mode


Skewed Distributions and the Mean and Median


Summary of when to use the mean, median and mode

measures-central-tendency-mean-mode-median-faqs.php



Measures of Variation


Range


Quartile


Box Plots


Variance


Standard Deviation


Z Score


Shape of Distribution


Probability distribution


The Normal Distribution


Histograms


Skewness


Kurtosis


Visualization of measure of variations on a Normal distribution


Simple and Multiple regression


Correlation


Measuring Correlation


Pearson correlation coefficient - Pearson s r


The coefficient of determination


Correlation Causation


Testing the "generalizability" of the correlation


Simple Linear Regression


Multiple Linear Regression


RapidMiner Linear Regression examples


K-Nearest Neighbour


Decision Trees


The algorithm


Basic explanation of the algorithm


Algorithms addressed in Noel s Lecture


The ID3 algorithm


The C5.0 algorithm


Example in RapidMiner


Random Forests

https://www.youtube.com/watch?v=J4Wdy0Wc_xQ&t=4s



Naive Bayes


Probability


Independent and dependent events


Mutually exclusive and collectively exhaustive


Marginal probability

The marginal probability is the probability of a single event occurring, independent of other events. A conditional probability, on the other hand, is the probability that an event occurs given that another specific event has already occurred. https://en.wikipedia.org/wiki/Marginal_distribution



Joint Probability


Conditional probability


Kolmogorov definition of Conditional probability


Bayes s theorem


Likelihood and Marginal Likelihood


Prior Probability


Posterior Probability


Applying Bayes' Theorem


Scenario 1 - A single feature


Scenario 2 - Class-conditional independence


Scenario 3 - Laplace Estimator


Naïve Bayes - Numeric Features


RapidMiner Examples


Perceptrons - Neural Networks and Support Vector Machines


Boosting


Gradient boosting


K Means Clustering


Clustering class of the Noel course


RapidMiner example 1


Principal Component Analysis PCA


Association Rules - Market Basket Analysis


Association Rules example in RapidMiner


Time Series Analysis


Text Analytics / Mining


Model Evaluation


Why evaluate models


Evaluation of regression models


Evaluation of classification models


References

Landis JR, Koch GG. The measurement of observer agreement for categorical data. Biometrics. 1977 Mar;33(1):159-174. DOI: 10.2307/2529310.



Python for Data Science


NumPy and Pandas


Data Visualization with Python


Text Analytics in Python


Dash - Plotly


Scrapy


R


R tutorial


RapidMiner


Assessments


Diploma in Predictive Data Analytics assessment


Notas


References