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Machine Learning Algorithms

Machine Learning Algorithms

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Machine Learning Algorithms

Machine Learning Algorithms

Overview of this book

Machine learning has gained tremendous popularity for its powerful and fast predictions with large datasets. However, the true forces behind its powerful output are the complex algorithms involving substantial statistical analysis that churn large datasets and generate substantial insight. This second edition of Machine Learning Algorithms walks you through prominent development outcomes that have taken place relating to machine learning algorithms, which constitute major contributions to the machine learning process and help you to strengthen and master statistical interpretation across the areas of supervised, semi-supervised, and reinforcement learning. Once the core concepts of an algorithm have been covered, you’ll explore real-world examples based on the most diffused libraries, such as scikit-learn, NLTK, TensorFlow, and Keras. You will discover new topics such as principal component analysis (PCA), independent component analysis (ICA), Bayesian regression, discriminant analysis, advanced clustering, and gaussian mixture. By the end of this book, you will have studied machine learning algorithms and be able to put them into production to make your machine learning applications more innovative.
Table of Contents (24 chapters)
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Title Page
Dedication
Packt Upsell
Contributors
Preface
Index

Gaussian mixture


Let's suppose that we have a dataset made up of nm-dimensional points drawn from a data generating process, pdata

In many cases, it's possible to assume that the blobs (that is, the densest and most separated regions) are symmetric around a mean (in general, the symmetry is different for each axis), so that they can be represented as multivariate Gaussian distributions. Under this assumption, we can imagine that the probability of each sample is obtained as a weighted sum of k (the number of clusters) multivariate Gaussians parametrized by the mean vector, μj and the covariance matrix, Σi:

This model is called Gaussian mixture and can be employed either as a soft- or a hard-clustering algorithm. The former option is clearly the native way because each point is associated with a probability vector representing the membership degree with respect to each cluster (that is, each Gaussian distribution). However, in many cases, it's preferable to apply an argmax(•) function to...

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