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The Hidden Markov Model or HMM is all about learning sequences.
A lot of the data that would be very useful for us to model is in sequences. Stock prices are sequences of prices. Language is a sequence of words. Credit scoring involves sequences of borrowing and repaying money, and we can use those sequences to predict whether or not you’re going to default. In short, sequences are everywhere, and being able to analyze them is an important skill in your data science toolbox.
The easiest way to appreciate the kind of information you get from a sequence is to consider what you are reading right now. If I had written the previous sentence backwards, it wouldn’t make much sense to you, even though it contained all the same words. So order is important.
While the current fad in deep learning is to use recurrent neural networks to model sequences, I want to first introduce you guys to a machine learning algorithm that has been around for several decades now - the Hidden Markov Model.
This course follows directly from my first course in Unsupervised Machine Learning for Cluster Analysis, where you learned how to measure the probability distribution of a random variable. In this course, you’ll learn to measure the probability distribution of a sequence of random variables.
You guys know how much I love deep learning, so there is a little twist in this course. We’ve already covered gradient descent and you know how central it is for solving deep learning problems. I claimed that gradient descent could be used to optimize any objective function. In this course I will show you how you can use gradient descent to solve for the optimal parameters of an HMM, as an alternative to the popular expectation-maximization algorithm.
We’re going to do it in Theano, which is a popular library for deep learning. This is also going to teach you how to work with sequences in Theano, which will be very useful when we cover recurrent neural networks and LSTMs.
This course is also going to go through the many practical applications of Markov models and hidden Markov models. We’re going to look at a model of sickness and health, and calculate how to predict how long you’ll stay sick, if you get sick. We’re going to talk about how Markov models can be used to analyze how people interact with your website, and fix problem areas like high bounce rate, which could be affecting your SEO. We’ll build language models that can be used to identify a writer and even generate text - imagine a machine doing your writing for you.
We’ll look at what is possibly the most recent and prolific application of Markov models - Google’s PageRank algorithm. And finally we’ll discuss even more practical applications of Markov models, including generating images, smartphone autosuggestions, and using HMMs to answer one of the most fundamental questions in biology - how is DNA, the code of life, translated into physical or behavioral attributes of an organism?
All of the materials of this course can be downloaded and installed for FREE. We will do most of our work in Numpy and Matplotlib, along with a little bit of Theano. I am always available to answer your questions and help you along your data science journey.
This course focuses on "how to build and understand", not just "how to use". Anyone can learn to use an API in 15 minutes after reading some documentation. It's not about "remembering facts", it's about "seeing for yourself" via experimentation. It will teach you how to visualize what's happening in the model internally. If you want more than just a superficial look at machine learning models, this course is for you.
See you in class!
All the code for this course can be downloaded from my github: /lazyprogrammer/machine_learning_examples
In the directory: hmm_class
Make sure you always "git pull" so you have the latest version!
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|Section 1: Introduction and Outline|
Introduction and Outline: Why would you want to use an HMM?Preview
Unsupervised or Supervised?Preview
Where to get the Code and Data
|Section 2: Markov Models|
The Markov PropertyPreview
The Math of Markov Chains
|Section 3: Markov Models: Example Problems and Applications|
Example Problem: Sick or Healthy
Example Problem: Expected number of continuously sick days
Example application: SEO and Bounce Rate Optimization
Example Application: Build a 2nd-order language model and generate phrases
Example Application: Google’s PageRank algorithm
|Section 4: Hidden Markov Models for Discrete Observations|
From Markov Models to Hidden Markov Models
HMMs are Doubly Embedded
How can we choose the number of hidden states?
The Forward-Backward Algorithm
Visual Intuition for the Forward Algorithm
The Viterbi Algorithm
Visual Intuition for the Viterbi Algorithm
The Baum-Welch Algorithm
Baum-Welch Explanation and Intuition
Baum-Welch Updates for Multiple Observations
Discrete HMM in Code
The underflow problem and how to solve it
Discrete HMM Updates in Code with Scaling
Scaled Viterbi Algorithm in Log Space
Gradient Descent Tutorial
Theano Scan Tutorial
Discrete HMM in Theano
|Section 5: HMMs for Continuous Observations|
Gaussian Mixture Models with Hidden Markov Models
Generating Data from a Real-Valued HMM
Continuous-Observation HMM in Code (part 1)
Continuous-Observation HMM in Code (part 2)
Continuous HMM in Theano
|Section 6: HMMs for Classification|
Generative vs. Discriminative Classifiers
HMM Classification on Poetry Data (Robert Frost vs. Edgar Allan Poe)
|Section 7: Bonus Example: Parts-of-Speech Tagging|
Data is from: http://www.cnts.ua.ac.be/conll2000/chunking/
Code is in the same repo as this course, but in the folder nlp_class2
POS Tagging with an HMM
|Section 8: Appendix|
Review of Gaussian Mixture Models
How to install Numpy, Scipy, Matplotlib, Pandas, IPython, Theano, and TensorFlow
BONUS: Where to get Udemy coupons and FREE deep learning material
I am a data scientist, big data engineer, and full stack software engineer.
For my masters thesis I worked on brain-computer interfaces using machine learning. These assist non-verbal and non-mobile persons communicate with their family and caregivers.
I have worked in online advertising and digital media as both a data scientist and big data engineer, and built various high-throughput web services around said data. I've created new big data pipelines using Hadoop/Pig/MapReduce. I've created machine learning models to predict click-through rate, news feed recommender systems using linear regression, Bayesian Bandits, and collaborative filtering and validated the results using A/B testing.
I have taught undergraduate and graduate students in data science, statistics, machine learning, algorithms, calculus, computer graphics, and physics for students attending universities such as Columbia University, NYU, Humber College, and The New School.