Machine Learning Hidden Markov Model

Darshana PathakUniversity of North Carolina at Chapel Hill

Research Seminar – November 14, 2012

Disclaimer

All the information in the following slides assumes that

“There is a GREAT human mind behind every computer

program.”

What is Machine Learning?

• Make Computers learn from a given task and experience.

• “Field of study that gives computers the ability to learn without being explicitly programmed”.

- Arthur Samuel (1959)

Why Machine Learning?

• Human Learning is terribly slow! (?)o 6 years to start school, around 20 more years to

become cognitive /computer scientist...o Linear programming, calculus, Gaussian models,

optimization techniques and so on…

Why Machine Learning?

• No copy process in human beings - ‘one-trial learning’ in computers.

• Computers can be programmed to learn – Both human and computer programs make errors, error is predictable for computer, we can measure error.

Some more reasons…

• Growing flood of electronic data – Machines can digest huge amounts of data which is not possible for human.

• Supporting computational power is also growing!

• Data mining – to help improve decisionsoMedical records study for diagnosis o Speech/handwriting/face recognitiono Autonomous driving, robots

Important Distinction

• Machine learning focuses on prediction, based on known properties learned from the training data.

• Data mining focuses on the discovery of (previously) unknown properties on the data.

• Example: Purchase history/behavior of a customer.

Hidden Markov Model

Hidden Markov Model - HMM

• A Markov model with hidden states.

• Markov Model – Stochastic Model that assumes Markov property.

• Stochastic model – A system with stochastic process (random process).

HMM – Stochastic model

• Stochastic process vs. Deterministic process.– SP is probabilistic counterpart of DP.

• Examples:– Games involving dice and cards, coin toss.– Speech, audio, video signals– Brownian motion– Medical data of patients– Typing behavior (Related to my project)

HMM – Markov Model

• Markov Model – Stochastic Model that assumes Markov property.

• Markov property Memory-less property – Future states of the process depend only

upon the present state, –And not on the sequence of events that

preceded it.

Funny example of Markov chain

• 0 – Home; 4 – Destination• 1,2,3 corners;

Hidden Markov Model - HMM

• A Markov model with hidden states – Partially observable system.

Simple Markov Model Hidden Markov Model

Every state is directly visible to the observer.

The state is not directly visible, but the output, dependent upon the state is visible.

The only parameters are state transition probabilities.

Each state has a probability distribution over possible o/p tokens.

HMM

• Markov process is hidden, we can see sequence of output symbols (observations).

HMM - Conditional Dependence

HMM: Simple Example

• Determine the average annual temperature at a particular location over a series of years (Past when thermometers were not invented).

• 2 annual temperatures, Hot – H and Cold - C.• A correlation between the size of tree growth

rings and temperature.• We can observe Tree ring size.• Temperature is unobserved – hidden.

HMM – Formation of problem

• 2 hidden states – H and C • 3 observed states – tree ring sizes.

Small – S, Medium – M, Large – L.• The transition probabilities, observation matrix

and initial state distribution.

• All matrices are row stochastic.

HMM – Formation of problem

• Consider a 4 year sequence. • We observe the series of tree rings S;M; S; L.

O = (0, 1, 0, 2)• We need to determine temperature (H or C)

for these 4 years i. e. Most likely state sequence of Markov process given observations.

HMM – Formation of problem

• X = (x0, x1, x2, x3)

• O = (O0, O1, O2, O3)

• A = State transition probability (aij)

• B = Observation probability matrix (bij)

HMM – Formation of problem

• aij = P(state qj at t + 1 | state qi at t)• Bj(k) = P(observation k at t | state qj at t)

• P(X) = πx0 * bx0(O0) * ax0,x1 * bx1(O1) * ax1,x2 * bx2(O2) * ax2,x3bx3(O3)

• P(HHCC) = 0.6(0.1)(0.7)(0.4)(0.3)(0.7)(0.6)(0.1) = 0.000212

Applying HMM to Error Generation

• Erroneous data in real-world data sets• Typing errors are very common.– Insertion– Deletion– Replace

• Is there any way to determine most probable sequence or patterns of errors made by typist?

Applying HMM to Error Generation• Examples:

1. BRIDGETT and BRIDGETTE2. WILLIAMS and WILIAMS

3. LATONYA and LATOYA 4. FREEMAN and FREEMON

Applying HMM to Error Generation

• Sequence of characters/Alignment Problem

W I L L I A M S

W

I

L

L

L

I

M

HMM & Error Generation

• Hidden states: Pointer positions• Observations: Output character sequence• Problems:

o Finding Path - Given an input, output character sequence and HMM model, determine most probable operation sequence?

o Training - Given n pairs of input and output sequences, what is the model that maximizes probability of output?

o Likelihood - Given input, output and the model, determine likelihood of observed sequence.

References

• Why should machines learn? – Herbert A. Simon, Department of Computer Science and Psychology, Carnegie-Mellon University, C.I.P. # 425

• http://en.wikipedia.org/wiki/Machine_learning

• http://en.wikipedia.org/wiki/Hidden_Markov_model

• A Revealing Introduction to Hidden Markov Models – Mark Stamp, Department of Computer Science, San Jose State University

THANK YOU!