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This Edureka PPT on Introduction To Markov Chains will help you understand the basic idea behind Markov chains and how they can be modelled as a solution to real-world problems.
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Markov Chains | Edureka
1.
2. WHAT IS A MARKOV CHAIN?
UNDERSTANDING MARKOV CHAINS WITH AN EXAMPLE
MARKOV CHAIN IN PYTHON
MARKOV CHAIN APPLICATIONS
TRANSITION MATRIX & TRANSISTION STATE DIAGRAM
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4. A stochastic process containing random variables, transitioning from one state to another
depending on certain assumptions and definite probabilistic rules.
What Is A Markov chain?
Markov Property states that the calculated probability of a random process transitioning to the
next possible state is only dependent on the current state and time and it is independent of the
series of states that preceded it.
Let the random process be, { π π , m=0,1,2 β¦ }
This process is a Markov chain only if,
π π π+1 = Θπ π π = β , π πβ1 = β πβ1, β¦ , π0 = β 0 = π π π+1 = Θπ π π = β
πππ = π π π+1 = Θπ π π = β
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6. A Markov Model is a stochastic model that models random variables in such a manner that the variables
follow the Markov property.
β’ Keys denote the unique words in the sentence, i.e., 5 keys (one, two, hail, happy, edureka)
β’ Tokens denote the total number of words, i.e. 8 tokens.
one edureka two edureka hail edureka happy edureka
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7. A Markov Model is a stochastic model that models random variables in such a manner that the variables
follow the Markov property.
one
edureka
two
hail
happy
1
4
1
1
1
Keys Frequencies
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8. A Markov Model is a stochastic model that models random variables in such a manner that the variables
follow the Markov property.
one
edureka
two
hail
happy
1
4
1
1
1
Weighted distributions:
1. 'edureka' is 50% (4/8)
2. (one, two, hail, happy)
is β 13% (1/8)
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9. Start one edureka two edureka hail edureka happy edureka end
one
edureka
two
hail
happy
1
4
1
1
1
start
end
1
1
Keys Frequencies
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14. In a Markov Process, we use a matrix to represent the transition probabilities from one state to
another. This matrix is called the Transition or probability matrix. It is usually denoted by P.
What Is A Transition Matrix?
π11 π12 π1π
π21 π22 π2π
π21 π22 π2π
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P =
ΰ·
π=1
π
πππ = ΰ·
π=1
π
π π π+1 = Θπ π π = β
Note, πij β₯ 0, and 'i' for all values is,
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15. Consider a Markov chain with three states 1, 2, and 3.
Transition Matrix & State Diagram Example
Transition matrix
1/4 0 3/4
P = 1/2 0 1/2
1/4 1/2 1/4
1 2
3
1/4
3/4
1/2
1/2
1/4
1/2
1/4
State Transition Diagram
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18. To apply Markov Property and create a Markov Model that can generate text simulations by
studying Donald Trump speech data set.
Problem Statement
Apply Markov property
Generate Text Simulations
Donald Trump speeches
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