HMMs Pattern Recognition

HMMs Pattern Recognition Assignment 3 of Pattern recognition is on HMMs. It should contain a detailed report on HMMs. The topics covered should include: 1. An introduction to HMM and its uses. 1. Problems of HMM, their explanation and relation to prior, posterior, and evidence. 2. Solution to the problems of HMM and their algorithms. Pattern Recognition Assignment # 3 Name: Muhammad Sohaib Jamal An Introduction to HMM and its Uses A Hidden Markov Model HMM is a stochastic model which has a series of observable variable X which is generated by hidden state Y. In an indirect way HMM consist of hidden states which has output that is comprised of a set of observations. Simple Markov Model models the states are directly observables means the states are directly output while in HMM the states are hidden and different form the observables or output. HMM is very reliable model for probabilistic estimation. HMM have applications in pattern recognitions such as speech recognition, gesture and hand writing recognition, computational Bioinformatics, etc. Suppose we are considering three trails of a coin toss experiment and the person who is observing only know the results of the experiment when another person announces the result who is hidden in a closed room from the person noting the results. The result of this coin experiment can be any set of heads and tails e.g. THT, HHH, THH, TTT, THT etc. The person observing the results can get any sequence of heads and tails, and it is not possible to predict any specific sequence that will occur. The Observation Set is completely unpredictable and random. Lets assume that the third trail of coin toss experiment will produce more Head than the Tails. The resulting sequence will obviously have more number of heads then tails for this particular case. This is called Emission probability denoted by Bj(O). Now we suppose that the chance of flipping the third trail after the first and second trail is approximately zero. Then, the transition from 1st and 2nd trail to 3rd trail will be actually very small and as an outcome yields very little number heads if the person starts flipping the coin from 2nd trail to 3rd trail. This is called Transition probability denoted by aij. Assume that each trail has some probability associated with the previous trail, then the person will start the process of flipping from that particular coin. This is known to be the Initial probability denoted by à Ã¢â€š ¬i. The sequence of number of heads or tails is known to be the observables and the number of trail is said to be the state of the HMM. HMM is composed of: N number of hidden states S1, S2 à ¢Ã¢â€š ¬Ã‚ ¦Ãƒ ¢Ã¢â€š ¬Ã‚ ¦Ãƒ ¢Ã¢â€š ¬Ã‚ ¦., SN M number of observations O1, O2, à ¢Ã¢â€š ¬Ã‚ ¦Ãƒ ¢Ã¢â€š ¬Ã‚ ¦, OM The à Ã¢â€š ¬i (Initial state probability) Output Probability or Emission Probability B: P (OM | SN), where OM is observation and SN is the state. Transition probability matrix A = [ aij ]. Transition probabilities aij. Mathematically the model is represented as HMM ÃŽÂ » = {ÃŽÂ  , A, B} Problems of HMM and their explanations HMM has three basic types of problems: The Evaluation problem: Suppose we have an HMM, complete with transition probabilities aij and output probabilities bjk. We need to determine the probability that a particular sequence of observables states OT was generated by that model. The Decoding problem: The transition probabilities, output probabilities and set of observations OT is given and we want to determine the most likely sequence of hidden states ST that led to those observations. The Learning problem: In such problem the number of states and observation are given but we need to find the probabilities aij and bjk. With the given set of training observations, we will determine the probabilities aij and bjk. Relation of HMM to Prior, Posterior and evidence The à Ã¢â€š ¬i (Initial state probability) is analogous to the Prior probability. Because the initial probability is given before the set of experiments take place. This property of initial probability is identical to that of prior probability. Similarly, the output probability or emission probability B: P (OM | SN) is analogous to the posterior probability. The posterior probability is used in forward backward algorithm. In the same manner, evidence is the probability the next state is C given that the current state is state Sj. So the evidence is analogous to the transition probability A. Solution to the problems of HMM and their algorithms From the above mentioned discussion, we know that there are three different of problems in HMM. In this section we will briefly know how these problems are solved Evaluation problem, this type of problem is solved the using Forward-Backward algorithm. Decoding problem, for such type of HMM problem we use the Viterbi algorithm or posterior decoding Training problem, in case of this type of problem we have the Baun-Welch re-estimation algorithm to solve it. Forward-Backward algorithm The forward and backward steps are combined by the Forward-Backward algorithm to estimate the probability of each state for a specific time t, and repeating these steps for each t can result in the sequence having the most likely probability. This algorithm doesnt guarantee that the sequence is valid sequence because it considers every individual step. The forward algorithm has the following three steps: Initialization step Iterations Summation of overall states . Similarly, for backward algorithm we have the same steps like the forward algorithm: Initialization step Iterations Summation of overall states Viterbi algorithm Viterbi algorithm is used to find the most likely hidden states, resulting in a sequence of observed events. The relationship between observations and states can be inferred from the given image. In first step Viterbi algorithm initialize the variable In second step the process is iterated for every step In third step the iteration ends In Fourth step we track the best path Baun-Welch re-estimation algorithm Baun-Welch re-estimation algorithm is used to compute the unknown parameters in hidden Markov model HMM. Baun-Welch re-estimation algorithm can be best described using the following example. Assume we collect eggs from chicken every day. The chicken had lay eggs or not depends upon unknown factors. For simplicity assume that there are only 2 states (S1 and S2) that determine that the chicken had lay eggs. Initially we dont know about the state, transition and probability that the chicken will lay egg given specific state. To find initial probabilities, suppose all the sequences starting with S1 and find the maximum probability and then repeat the same procedure for S2. Repeat these steps until the resulting probabilities converge. Mathematically it can be References Andrew Ng (2013), an online course for Machine learning, Stanford University, Stanford, https://class.coursera.org/ml-004/class. Duda and Hart, Pattern Classification (2001-2002), Wiley, New York. http://en.wikipedia.org http://hcicv.blogspot.com/2012/07/hidden-markov-model-for-dummies.html http://www.mathworks.com/help/stats/hidden-markov-models-hmm.html http://www.comp.leeds.ac.uk/roger/HiddenMarkovModels/html_dev/viterbi_algorithm/s3_pg3.html

Happiest Day of My Life Essay

I was excited to the nerve that my father was finally in town and even more when he informed me that he has been given free tickets to the fifa world cup finals 2010 between Spain and Netherlands . i was absolutely thrilled to hear this from him. I am a huge Spain fan as I absolutely adore the club. I was very keyed up about watching Fabregas , David Villa and of course Torres in person as I am a big fan of these players. We took the flight to Johannesburg just the next morning as we had planned. We reached the marvelous place which looked even more marvelous during this FIFA season. We decided to tour the city and went to the nearest shopping mall Oriental Plaza. While on the way to the place my father informed me that this was the city where Mahatama Gandhi stayed 100 years ago. The mall was so named because it gives a taste of the orient in Africa. After this we headed to the stadium. My first impression when I arrived at the stadium was one of awe. A number of people outside the stadium appeared to be singing. I purchased a vuvuzela, got the Spanish flag painted on my face and then proceeded into the stadium and found my seat and felt content I had a good enough view of the pitch. The time for the match came and I grew extremely enthusiastic. The match had a large number of fouls, with both the teams playing equally rough. So much that although the goal scores remained 0-0, the yellow card scores kept raising. The match referee Howard Webb of England had a tough time and the final count was 14 yellow and 1 red card, Netherlands winning here 8-5. The score was 0-0 for the entire 90 minutes of the game and the first 30 minutes extra time as well, with Spain having 57% ball possession and 18 shots with 8 of them on target. Netherlands had 43% possession and 13 total shots with 5 on target. The bookings continued after the break . The dutch had a glorious chance to take the lead in the second half but Arjen Robben, comfortably his team’s strongest attacking weapon, could find no way past Spain captain Iker Casillas. I was at the edge of my seat when in the 116th minute Cesc Fabregas’s pass to the young midfielder Iniesta who struck it into the net making their captain and goal keeper Iker Casillas drop to the floor and cry out tears of joy after the final whistle. This made Spain the first team to win a World Cup after losing their opening game of the tournament. And once again the German octopus Paul Allen’s predictions came true. Then Spain was honoured with the 6. 175kg gold trophy. The Man of the Match was obvoiusly awarded to Andres Iniesta it was followed by a loud roar. And the prestigious Golden Glove Award to their captain and goalkeeper Iker Casillas. The Golden Shoe Award as well as the Best Young Player Award was given to Thomas Mueller of Germany and the Golden Ball was awarded to Diego Forlan of Uruguay.

The Deaf President Now Movement And Gallaudet University...

Introduction: The Deaf President Now movement and Gallaudet University protest did not only achieve its aims, this revolution brought unity to the Deaf Community and awareness to the general public. This revolution grew into a civil rights movement, consequently enacting legislation, the Americans with Disabilities Act of 1990 and The Telecommunications Accessibility Enhancement Act of 1988, to benefit deaf and hard of hearing citizens as well as many other disabled Americans. The events of February and March 1988 are still a great source of pride and enlightenment that are still nostalgically looked back on by this generation of deaf citizens. The Deaf community can be described as being a relatively private community, consisting of many people with various ranges of hearing loss. Like any culture, the deaf have their own community, culture, language, and essentially a separate world from the hearing majority. However, it has only been in the last few decades that there has been awareness and acc eptance of this culture, nevertheless there is not full acceptance and understanding of this community and deafness in general. Prior to this revelation, deaf people had been oppressed and ostracised throughout history. Dating back to Ancient Greece, deaf people were seen as a subordinate minority. Aristotle theorised that people could only learn through spoken language, therefore deaf people were seen as being unable to learn and were not given an education. 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Parallels between Henrik Ibsens A Dolls House and...

Parallels between Henrik Ibsen’s A Doll’s House and Ghosts Rebekah Bak Henrik Ibsen wrote a variety of controversial literature with many recurring themes appearing throughout each of them. Through his trite yet thought-provoking writing style, Ibsen presents many issues which are still discussed today. One of these controversial themes consistently appears in both A Doll’s House and Ghosts. Ibsen shows the sins of parents being passed on to their children. Primarily, in A Doll’s House, Ibsen shows the sins of parents being passed on to their children in three different ways: through Dr. Rank’s hereditary health issues, through Nora’s behavior apparently inherited from her father, and through her children’s behavior similarly†¦show more content†¦Caught in her deceit, Nora is trapped as Torvald questions her. ...And to tell me a lie into the bargain? A lie—? Didn’t you tell me no one had been here? (A Doll’s House 26) Just as Nora lies to Torvald, she instructs her children to do so also, saying, â€Å"Yes, dears, I know. But, don’t tell anyone about the stranger man. Do you hear? Not even papa† (A Doll’s House 25). In this case, Nora is leading her children toward wrongdoing. Yet it still doesn’t compare to the extent to which Torvald believes that the deceit of all women is the cause of all sin. Torvald even goes so far as to compare the deceitfulness of women to poison, saying, â€Å"Because such an atmosphere of lies infects and poisons the whole life of a home, each breath the children take in such a house is full of the germs of evil† (A Doll’s House 27). This quote shows how his contempt toward women mirrors the attitude of a child. It is like a little boy who won’t go near â€Å"girl cooties.† With the title, A Doll’s House, this childlike element adds to the entire concept of the play. Secondly, in Ghosts, Ibsen shows the sins of parents being passed on to their children through â€Å"ghosts,† or what is conceived to be the repetition of the past. Past sins repeat themselves as Oswald inadvertently mirrors some of his late father’s characteristics, which includes: smoking, drinking, suffering from syphilis, and presumably having sex with the servant girl. Oswald’s father, Mr. Alving, was perceived as aShow MoreRelatedMrs Alving in Ghosts by Ibsen1187 Words   |  5 Pagesreference to â€Å"ghosts,† Norwegian playwright Henrik Ibsen portrays a view on the rewards of duty that clashes sharply with the accepted views of the time. In his native country of Norway, and indeed all around the world in the year 1881, ‘duty’ was seen as a powerful motivator in both religion and society. The abstract concept of duty was what constrained society into ‘acceptable’ boundaries, and people without a sense of duty were often sh unned and rejected by their fellow citizens. Henrik Ibsen wasRead MoreGender Roles Of A Doll s House And Ghosts Essay2281 Words   |  10 PagesGender Roles in A Doll’s House and Ghosts Throughout much of English language literature, gender and sex are equated with specific human traits. Strength is male and weakness is female. Men are stable and women are capricious. Logic is masculine and imagination is feminine. Ibsen uses stereotypical gender attributes in his characterization of Nora and Torvald throughout A Doll House, and then abruptly reverses the stereotypes in the final moments of the play to show that inner strength and weakness