Supervised behavior. item Association Problems: The intention

Supervised machine learning algorithms:
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item Linear regression (regression problems).
item Random forest (classification problems).
item Support vector machines (classification problems).
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extbf{Supervised learning problems fall into:}
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item Classification Problem: The output variable (Y) is a category, such as compliant taxpayer or non compliant taxpayer.
item Regression Problem: The output variable is a real value, such as the amount of tax yield from tax audit.
end{itemize}
subsubsection{Unsupervised Machine Learning}
Unsupervised learning, means that the algorithm is provided only with input variables (X) without the corresponding outputs variables (Y).

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The goal of the algorithm is to learn the underlying structure or distribution in the data. There are no correct answers and no teacher, its a self-learning process.

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ewline extbf{ extit Unsupervised learning problems fall into:}

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egin{itemize}
item Clustering Problems: The intention is to discover the inherent groupings in the data, such as grouping taxpayers by compliance behavior.
item Association Problems: The intention is to discover rules that describe large portions of the data, such whether taxpayers that do not file tax returns on time also tend stop filing returns.
end{itemize}
Examples of unsupervised learning algorithms are:
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item k-means for clustering problems.
item A-priori algorithm for association rule learning problems.
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subsubsection{Semi-Supervised Machine Learning}
Problems where you have a large amount of input variables (X) and only some of the data is labeled (Y) are called semi-supervised learning problems. A good example is the taxpayers audit yield where only few of the taxpayers have been audited and the majority are unaudited.

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Many of the real world machine learning problems fall into this category. It is very time consuming and costly to label data with the services of experts, while unlabeled data is readily available at no extra cost.

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The unsupervised learning techniques are used to discover and learn the structure in the input variables. They can be used to make best guess predictions for the unlabeled data, feed that data back into the supervised learning algorithm as training data and use the model to make predictions on new unseen data.
chapter{Approach}
A semi-supervised learning model exploits the unlabeled data to learn to infer latent features and pairs these with labels to learn an associate classifier.

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extbf{A hidden (Latent) feature discriminative model (Model 1): }

The model provides an embedding or feature representation of the data of all taxpayers. The features are then used to train a separate classifier. The information acquired allows for the clustering of related features in a hidden space.

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A deep generative model of both audited and not audited taxpayers data provides a more robust set of hidden(latent) features. The generative model used is:

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