HIDDEN MARKOV CHAINS DRIVERS FROM ONE

The chapter then covers the basic theories and algorithms for hidden Markov models (HMMs) and Markov. Sequential data, assuming that each observation is conditioned on the state of a hidden.

We can always write an ad hoc program for any given problem, but the same frustrating issues will always recur. One is that we want to incorporate heterogeneous sources of information. The relationship between Markov chains of finite states and matrix theory will also be highlighted.

Hidden Markov Model: A hidden Markov model (HMM) is a kind of statistical model that is a variation on the Markov chain. Combining the flexibility of the semi-Markov chains with the. One such important use case of analytics is comparing the future performances of companies.A lot of work using hidden Markov models (HMMs) has been conducted thus far in these fields. Companies are using analytics to identify potential acquisition opportunities, their future market performances, customer behavior and many other areas. We donвЂ™t even realize how analytics is driving our decisions, our activities, our interests, our shopping behavior and more. Markov Chain the result of the experiment (what you observe) is a sequence of state visited.Analytics has become an integral part of our daily lives.

Imagine a private equity company that wants to invest in one of two chocolate brands. They require many fewer parameters than general, inhomogeneous Markov chain models, yet can.LetвЂ™s take a small scenario and see how analytics can help us make informed decisions based on statistically driven models. In this section we introduce so-called hidden Markov models (HMM). Hidden Markov models are used for machine learning and data mining.

For example, if we were to estimate the market share of a company in the next quarter, it would depend only on the market share in the current quarter and not those of previous quarters.The memoryless property, to put in a simpler manner, means that the Markov process doesnвЂ™t store any property or memory of its past state. We will start with the third statement and then gradually move to the first one.Any random process is known to have the Markov property if the probability of going to the next state depends only on the current state and not on the past states.From the above equation, a Markov property would mean that movement from X(t) to X(t+1) will depend only on X(t), вЂ“ the current state вЂ“ and not on the preceding states. So, how do we estimate the market share of each of the brands?This scenario is perfect for the application of Markov Chains.According to Paul GagniucвЂ™s Markov Chains: From Theory to Implementation and Experimentation,Understanding the concept of Markov ChainsNow, letвЂ™s break down the above statements one by one and define a Markov Chain really means. We know the current market share of each of the brands however, we want to understand what the market share will be in subsequent months.

Cadbury and Nestle both enjoy an equal market share of 50% each.If we were to calculate the market share of Cadbury for the next month, it would be the sum of the following two: Current state probabilities, i.e., current market share of brands are as follows: Of the Nestle customers, there is a 30% chance that the customer will move to Cadbury, and a 70% chance that the customer will remain with Nestle. Of the Cadbury customers, there is a 60% chance that the customer will stick to the Cadbury brand while there is a 40% chance that the customer will move to Nestle. Probabilities of moving from one state to another, i.e., probability of a customer changing brands is as follows: The different states of the process are as follows:

Hidden Markov Chains Drivers From One

WeвЂ™ve determined the following probabilities for the movement of a driver: The movement of drivers from one zone to another zone will depend only on their current zone. We can divide the city into three zones вЂ“ North Delhi, South Delhi and West Delhi. We can directly compute market share for (t+2) stage from (t) stage.Now, letвЂ™s take another example and try to understand the implementation using R alongside.LetвЂ™s try to map the movement of Uber drivers in the Indian capital city of New Delhi. Customers currently using Nestle but moving to CadburyCurrent Market Share of Cadbury * Probability of customers sticking with CadburyCurrent Market Share of Nestle * Probability of customers switching to CadburyMarket share of Cadbury in (t+1) month = 50%*0.6 + 50%*0.3If we were to do the same using Markov Chains,Now, calculating market share for (t+2) month =(t+1) Market Share of Cadbury * Probability of customers sticking with Cadbury(t+1) Market Share of Nestle * Probability of customers switching to CadburyMarket share of Cadbury in (t+2) month = 45%*0.6 + 55%*0.3The beauty of Markov Chains is that we need not do the entire calculation for all the stages.

His movement will be decided only by his current state and not the sequence of past states. Of all the drivers in West Zone, 50% and 30% will move to North Zone and South Zone, respectively 20% will remain in West ZoneOnce a driver is in a particular zone, he can either move to the next zone or stay back in the same zone. In the South Zone, drivers have a 40% chance of moving to North Zone, 40% chance of staying in the South Zone 20% drivers will move to West Zone

LetвЂ™s calculate the probability of coming back to the North Zone in the third trip.The driver has a probability of 0.385 of returning to the North Zone in the third trip.This calculation can be done for any number of trips however, as we try to increase n (when n is sufficiently large), the predictive power tends to go down and there comes a stage where:The Markov Chain reaches an equilibrium called a stationary state. Assuming that a driver is currently in the North Zone, what is the probability that the driver will again be in the North Zone after two trips?A driver can reach the North Zone again in his second trip in three different ways:Probability (North Zone in second trip) = P(a) + P(b) + P(c) = 0.09 + 0.12 + 0.20 = 0.41Solving the same problem using Markov Chain models in R, we have:This gives us the direct probability of a driver coming back to the North Zone after two trips.We can similarly calculate for subsequent trips. Markov Chains using RWe will start by creating a transition matrix of the zone movement probabilities.In the above code, DriverZone refers to the state space of the Markov Chain while ZoneTransition represents the transition matrix that gives the probabilities of movement from one state to another.There is a package in R вЂmarkovchainвЂ™ which can help us save time in implementing Markov Chains in R.Now, to plot the above transition matrix we can use R package, вЂњdiagram.вЂќ The вЂњdiagramвЂќ package has a function called вЂњplotmatвЂќ that can help us plot a state space diagram of the transition matrix in an easy-to-understand manner.Now, the above Markov Chain can be used to answer some of the future state questions. It follows all the properties of Markov Chains because the current state has the power to predict the next stage.

GoogleвЂ™s famous PageRank algorithm is one of the most famous use cases of Markov Chains. There are plenty of other applications of Markov Chains that we use in our daily life without even realizing it. Markov Chains in everyday lifeThe above two examples are real-life applications of Markov Chains. Will 25 trips take our Markov Chain to the stationary state?Since the probabilities in the 25thВ and 26th trip are coming to be equal, we can say that we have reached the stationary state.So, if there were 50 drivers in all and each were to complete 25 trips in a day, how many of them will end up in the North Zone and South Zone?Around 19 drivers will end up in the North Zone, 17 in the South Zone and the remaining 14 will be in the West Zone. The stationary state can be calculated using some linear algebra methods however, we have a direct function, вЂsteadyStatesвЂ™, in R, which makes our lives easier.In the stationary state, a driver has a probability of 0.39 of ending up in the North Zone and a probability of 0.33 of reaching the South Zone.LetвЂ™s say a driver has to complete 25 trips in a day.

Markov has been used in areas of marketing, as well, with e-commerce companies are utilizing its power to define the different stages of a customer lifetime or predict customer churn probability.It is now apparent that Markov Chains are extremely important in many areas, and it is worth becoming increasingly familiar with this type of process. Any user on the site represents one stage, and the transition matrix represents the userвЂ™s probability of moving to other sites from the current site.Typing word prediction,В information theory, queuing theory and Monte Carlo simulation are other very useful applications of Markov Chains.