CN107577918A - CpG Island Identification Method and Device Based on Genetic Algorithm and Hidden Markov Model - Google Patents

Abstract

The present invention relates to a kind of CpG islands recognition methods based on genetic algorithm and hidden Markov model, comprise the following steps：1）Multiple chromosomes for including gene elements are obtained, each gene elements use real number representation, and multiple Encoded Chromosomes form one group of hidden Markov model parameter；2) fitness value of each chromosome is determined using fitness function, the fitness value is used for representing chromosome quality degree；3）Using genetic algorithm, according to the fitness value, searching process is performed to the chromosome, then redefines the chromosome fitness value after optimizing again；4）Iteration is applicable step 3）, after meeting to set end condition, export optimal hidden Markov model parameter；5）Using the optimal HMM parameter of output, on the basis of given observation sequence, it is determined that the maximum probability hidden state sequence of the observation sequence is generated, for representing the position on CpG islands.

Description

CpG Island Identification Method and Device Based on Genetic Algorithm and Hidden Markov Model

technical field

The invention belongs to the field of biological information, and in particular relates to a method and a device for identifying a CpG island based on a genetic algorithm and a hidden Markov model.

Background technique

With the completion of biological gene sequencing, there are many problems and challenges in gene sequence identification. The least common dinucleotide in many genomes is CG, and the C in CG is most likely to be methylated, which causes the C to mutate into a T. But methylation is often repressed by a region of the gene called a CpG island. It is a special DNA sequence with a length of several hundred bp, in which the frequency of CG nucleotides is very high. Every discovery of a CpG island means that its sequence may contain the promoter of gene transcription and its first exon, and the identification of CpG island helps to determine the region of interest in the genome sequence. Therefore, CpG islands are of crucial importance for gene sequence recognition.

The identification of CpG islands mainly faces two problems: 1. Given a short genome sequence, how to judge whether it comes from CpG islands. 2. Given a long sequence, how to identify if it contains CpG islands.

Current research mainly focuses on the second question. Researchers believe that the region with a length greater than 200bp, a CG content of more than 50%, and a ratio of the actual CpG content to the expected CpG content greater than 0.6 is called a CpG island. The traditional CpG island identification algorithm is to define a sliding window, which is realized by calculating the CG content of the gene sequence within the window and the ratio of the actual CpG content to the expected CpG content. We can find that the setting of the window size has a great influence on the recognition effect, and the computational complexity is also great. Moreover, the proposed criteria are all artificially defined, so the identified CpG islands have little biological significance. In order to correctly identify more biologically meaningful criteria, some researchers proposed a method based on Hidden Markov Model (HMM) to identify the location of CpG islands. An HMM is a probabilistic model that consists of a sequence of hidden state changes and a sequence of observable symbols produced by that hidden state.

A Hidden Markov Model is defined by an alphabet Σ, a state set Q, a state probability matrix A, and an emission probability matrix B, where:

●∑ is an alphabet;

● Q represents the set of symbols emitted from the alphabet;

A describes the probability of HMM transitioning from state t to state t+1;

●B describes the probability of the symbol s issued by the HMM at state t;

Once a system can be described as an HMM, it can be used to solve three basic problems.

Decoding problem: Given a model and a sequence of characters, find an optimal path in the model. The path starts from the initial state, and each state in the path chooses to release a character to realize the decoding operation.

• Evaluation problem: For a given model, find the probability of generating a sequence of characters. In general, the forward algorithm is selected to calculate the probability of an observation sequence after a given HMM, and thus select the most suitable HMM.

Learning problem: Generate HMMs from sequences of observations.

The first two of these are pattern recognition problems: given the HMM, find the probability of an observation sequence (evaluation); search for the hidden state sequence that is most likely to generate an observation sequence (decoding). The third problem is to generate an HMM given a sequence of observations (learning). The third problem, and the hardest of the HMM-related problems, is to estimate a best-fit hidden Markov model given a sequence of observations (from a known set), and a set of hidden states associated with it. There are a total of eight states in HMM: {A+, G+, C+, T+, A-, G-, C-, T-}, A+ indicates that this state is inside the CpG island, and A- indicates that this state is outside the CpG island. Each base in the model corresponds to two states. In the case of a given base sequence, it cannot be determined which state value the base corresponds to. In the model, transitions between states are allowed. The Hidden Markov Model is used as follows:

First, a certain number of DNA sequences of identified CpG islands are collected, and these real data are used to train the parameters of the model, that is, the learning problem of the hidden Markov model. The parameters of the model were obtained from the training data by establishing a hidden Markov model, and the trained model was further used to identify CpG islands.

Given an HMM and a corresponding sequence of observations, we wish to find the most likely sequence of hidden states that generated this sequence. We can find the most likely hidden state by listing all possible hidden state sequences and calculating the approximate order of the corresponding observation sequence for each combination, but this method is computationally expensive.

Hidden Markov model is a time-series-based probability model, which depends on the initial state probability vector, transition probability matrix and observation probability matrix. After research, it is found that although the hidden Markov model can achieve better results in solving the overfitting problem, there are still many problems. It relies on the strong assumption that the next state is only influenced by the previous state, which is an oversimplification, so HMMs can only be made from maximum likelihood estimates if the assumptions and actual data are consistent Effective and precise identification. But usually the actual data is not only affected by the previous state. This makes HMM easy to fall into a local optimal situation, and the computational complexity is high. In order to improve the ability of HMM to recognize CpG islands, it is necessary to optimize the design of HMM parameters.

Contents of the invention

Aiming at the deficiencies in the prior art, the present invention provides a CpG island identification method based on genetic algorithm and hidden Markov model, which can comprehensively consider the solution in HMM space, so as to obtain the global optimal solution, which can be better Optimize the HMM parameters to improve the ability to identify CpG islands.

Technical scheme of the present invention is:

A method for identifying CpG islands based on genetic algorithms and hidden Markov models, comprising the following steps:

1) Obtain a plurality of chromosomes including gene elements, each gene element is represented by a real number, and a plurality of chromosomes constitute a set of Hidden Markov Model parameters;

2) Using a fitness function to determine the fitness value of each chromosome, the fitness value is used to represent the degree of chromosome pros and cons;

3) using a genetic algorithm to perform an optimization process on the chromosome according to the fitness value, and then re-determine the optimized chromosome fitness value;

4) Iteratively apply step 3), when the set termination condition is met, the optimal hidden Markov model parameters are output;

5) Using the output optimal hidden Markov model parameters, on the basis of a given observation sequence, determine the maximum probability hidden state sequence for generating the observation sequence, which is used to represent the position of the CpG island.

Wherein, we use the Viterbi algorithm to determine the maximum probability hidden state sequence that generates the observation sequence, including:

According to a local probability and a local optimal path corresponding to each base state in the observation sequence, the maximum local probability and its corresponding local optimal path at the current moment are selected through the product of the initial probability of the hidden state and the corresponding observation probability The path is backtracked according to the local optimal path at the current moment, and the position recognition result of the CpG island is obtained.

The specific formulas using the Viterbi algorithm include:

For each state i, i=1,...,n, the Viberbi algorithm is defined as:

X _i ＝(X _i1 ,X _i2 ,...,X _iT )

The local probability at time t=1 is calculated by the product of the initial probability of the hidden state and the corresponding observation probability. For other moments, each state Viterbi algorithm saves a back pointer Moreover, a local probability δ is stored in each state, the observation state is k _t , the observation probability b is, the state transition probability is a, and the probability of the nearest local path to state i is δ _t (i):

The best path to the next state can be determined by the above formula. To determine the most likely hidden state at time t=T, let it _t :

i _t = argmax(δ _T (i))

For other time it _t ,

The context of the observed sequence was best explained using the Viterbi algorithm which reduces computational complexity through recursion.

Further, the genetic algorithm includes a selection operation, a crossover operation and a mutation operation, and the chromosome is optimized by sequentially adopting the selection operation, the crossover operation and the mutation operation.

Wherein, the selection operation includes: according to the fitness value of each chromosome, select the chromosome whose fitness value meets the genetic requirement for inheritance, and delete the unselected chromosome.

If the population size is N, the chromosome is _xi and the fitness function is f( _xi ), then the probability that _xi is selected is:

q _i is used to calculate the cumulative probability of chromosome x _i (i=1,2,3….n):

Based on the above cumulative probability, we use the roulette method to select chromosomes to obtain samples that meet the genetic requirements.

Wherein, the crossover operation includes: among the chromosomes whose fitness value satisfies the genetic requirement, select some chromosomes with better fitness value as the parent generation, perform crossover operation between two adjacent parent generation chromosomes, and generate offspring chromosomes .

Similarly, in the process of selecting parent chromosomes, the roulette method is also used.

The mutation operation includes: in the chromosome of the progeny, first determine the gene variation site, and change the gene value of the gene variation site according to the set mutation rate.

Specifically, set p as the selected gene mutation site, r as a random number between [0, 1], ct as the current algebra,

mt is the total algebra, b=2, and C is the gene value after mutation. The changes in gene mutation sites are:

The mutation operation changes the value of the chromosome with a very small probability, and the generated HMM parameters are extremely close to the HMM parameters before the mutation.

Further, the fitness function is:

Further, apply step 3) iteratively, using the Baum-Welch algorithm, including:

We define the re-estimated HMM model as The left end of the above formula represents the three parameters of the re-estimated HMM model. In the formula, γ _t (j) represents the probability of being in hidden state S _j at time t, ξ _t (i, j) represents the probability of being in hidden state S _i at time t and hidden state S _j at time t+1, and O represents the observation sequence . After multiple iterations, the maximum likelihood estimation of the HMM can be obtained. The output solution is the optimal hidden Markov model parameter.

The present invention also proposes a computer storage medium, which stores a plurality of instructions, and the instructions are suitable for being loaded by a processor and performing the following processing:

1) Obtain a plurality of chromosomes including gene elements, each gene element is represented by a real number, and a plurality of coding chromosomes constitute a set of Hidden Markov Model parameters;

2) Using a fitness function to determine the fitness value of each chromosome, the fitness value is used to represent the degree of chromosome pros and cons;

3) using a genetic algorithm to perform an optimization process on the chromosome according to the fitness value, and then re-determine the optimized chromosome fitness value;

4) Iteratively apply step 3), when the set termination condition is met, the optimal hidden Markov model parameters are output;

5) Using the output optimal hidden Markov model parameters, on the basis of a given observation sequence, determine the maximum probability hidden state sequence for generating the observation sequence, which is used to represent the position of the CpG island.

The present invention also proposes a CpG island identification device based on a genetic algorithm and a hidden Markov model, including a processor for implementing instructions; and a computer storage medium for storing multiple instructions, and the instructions are suitable for use by The processor loads and performs the following processing:

1) Obtain a plurality of chromosomes including gene elements, each gene element is represented by a real number, and a plurality of coding chromosomes constitute a set of Hidden Markov Model parameters;

2) Using a fitness function to determine the fitness value of each chromosome, the fitness value is used to represent the degree of chromosome pros and cons;

3) using a genetic algorithm to perform an optimization process on the chromosome according to the fitness value, and then re-determine the optimized chromosome fitness value;

4) Iteratively apply step 3), when the set termination condition is met, the optimal hidden Markov model parameters are output;

5) Using the output optimal hidden Markov model parameters, on the basis of a given observation sequence, determine the maximum probability hidden state sequence for generating the observation sequence, which is used to represent the position of the CpG island.

Beneficial effects of the present invention:

The present invention first uses HMM to optimize parameters to improve the ability to identify CpG islands. Second, the parameters of the HMM are estimated by using a genetic algorithm. Finally, this method can obtain the maximum likelihood estimate of the HMM, which is very useful for identifying the location of the CGIS. On the basis of experiments, it is shown that the CpG island identification method combined with genetic algorithm and hidden Markov model improves the precision and recall rate.

Description of drawings

Figure 1 is a flow chart of the CpG island identification method combined with genetic algorithm and hidden Markov model;

Crossover operation in Fig. 2 genetic algorithm;

The mutation operation in the genetic algorithm of Fig. 3;

Fig. 4 genetic algorithm related parameter control;

Figure 5 corresponds to the fitness value as the number of iterations increases;

Fig. 6 HMM result combined with genetic algorithm;

Figure 7 Comparison of the ability to identify CpG islands between the HMM optimized by the genetic algorithm and the HMM;

Detailed ways:

Below in conjunction with accompanying drawing and embodiment the present invention will be further described:

It should be pointed out that the following detailed description is exemplary and intended to provide further explanation to the present application. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

It should be noted that the terminology used here is only for describing specific implementations, and is not intended to limit the exemplary implementations according to the present application. As used herein, unless the context clearly dictates otherwise, the singular is intended to include the plural, and it should also be understood that when the terms "comprising" and/or "comprising" are used in this specification, they mean There are features, steps, operations, means, components and/or combinations thereof.

As mentioned in the background art, the hidden Markov model is prone to fall into a local optimal situation in solving the overfitting problem, and the computational complexity is relatively high. In order to improve the ability of HMM to identify CpG islands, the present invention proposes a method for identifying CpG islands based on genetic algorithms and hidden Markov models, including the following steps, as shown in Figure 1:

1) Model parameter initialization: obtain multiple chromosomes including gene elements, each gene element is represented by a real number, and multiple chromosomes constitute a set of hidden Markov model parameters;

Chromosomes usually represent a string of elements, each of which is called a gene. Since the HMM parameters A, B, and Pi are three real-number matrices with high dimensions, it is difficult to implement them using binary coding. In order to directly and truly reflect the changes of model parameters, they are represented by real-number chromosome strings.

2) Using a fitness function to determine the fitness value of each chromosome, the fitness value is used to represent the degree of chromosome pros and cons;

3) using a genetic algorithm to perform an optimization process on the chromosome according to the fitness value, and then re-determine the optimized chromosome fitness value;

4) Iteratively apply step 3), when the set termination condition is met, the optimal hidden Markov model parameters are output;

5) Apply the output optimal hidden Markov model parameters to the test set, perform decoding operation on the basis of a given observation sequence, and determine the maximum probability hidden state sequence for generating the observation sequence, which is used to represent the CpG island Location.

The genetic algorithm in the present invention includes three kinds of genetic operators, which are selection operation, crossover operation and mutation operation.

The selection operation is to select excellent individuals from multiple chromosomes, and the selection mechanism simulates the survival mechanism of the fittest in natural selection. Chromosomes with high fitness values are more survivable than chromosomes with low fitness values, and chromosomes that are not selected are deleted during subsequent evolution. The method of roulette is used to determine whether it is passed on to the next generation. According to the fitness value of the chromosome itself, it corresponds to the area of different sizes. If the population size is N, the chromosome is _xi and the fitness function is f( _xi ), then the probability that _xi is selected is:

q _i is used to calculate the cumulative probability of chromosome x _i (i=1,2,3….n):

The crossover operation is the combination of recombined parental chromosomes. The selected parent is the chromosome with the largest fitness value, as shown in Figure 2. Therefore, it can be seen that this operation can cross the optimal parent to obtain a better offspring. Parents are selected based on a roulette mechanism.

Chromosomal mutations increase the variation of model parameters. By changing the value of the gene in the chromosome, the genetic algorithm has the ability of global search. It enables the genetic algorithm to restore the lost information in the initialization stage and the model parameter evolution stage, and enables the genetic algorithm to search for the optimal model parameters. Before the model parameters are changed, if the mutation rate is greater than or equal to the randomly generated probability, the mutation rate will be tested against the randomly generated probability. If the result is correct, the model parameters will be modified using single-point random mutation as shown in Figure 3. p is the original value of the gene bit selected for mutation, r is a random number between [0, 1], ct is the current algebra, mt is the total algebra, b=2, and C is the value after mutation. The mutated bits are changed to:

It is worth noting that before the mutation operation, the gene mutation site is first determined, and then the original gene of the mutation point is changed according to a certain probability. The mutation operation changes the value of the chromosome with a very small probability, and the generated HMM parameters should be extremely close to the HMM parameters before the mutation.

In this embodiment, the fitness value can reflect the performance of the genetic algorithm and is used to evaluate the adaptability of the chromosome. Each individual has a fitness score, which determines whether it is selected.

In general, if the objective function is a maximization problem, the fitness function is defined as follows:

If the objective function is a minimization problem, the fitness function is defined as follows:

where c _min (c _max ) is the correlation coefficient.

In order to reduce the complexity of the fitness function, the calculation formula of the fitness function is adopted in this method:

By adjusting the number of training data sets in the CpG island, the complexity of the fitness function can be adjusted. Therefore, the method

Effectively reduces the complexity of the fitness function.

In order to screen out the optimal hidden Markov model parameters, we use the Baum-Welch algorithm to iterate, and the specific implementation method is as follows:

We define the re-estimated HMM model as The left end of the above formula represents the three parameters of the re-estimated HMM model. In the formula, γ _t (j) represents the probability of being in hidden state S _j at time t, ξ _t (i, j) represents the probability of being in hidden state S _i at time t and hidden state S _j at time t+1, and O represents the observation sequence . After multiple iterations, the maximum likelihood estimation of the HMM can be obtained. The output solution is the optimal hidden Markov model parameter.

After obtaining the optimal model parameters, in order to verify the optimal model parameters, we apply it to the test set. For HMM and a corresponding observation sequence, we hope to find the most likely hidden state sequence that generates this sequence. That is, the decoding operation. Each base state in the DNA sequence corresponds to a local probability and a local optimal path. We can determine the global optimal path by selecting the state with the maximum local probability at this moment and its corresponding local optimal path. Using the product of the state transition probability and the corresponding observation probability, the maximum probability is selected, and the obtained probability value is the most likely hidden state sequence. In this method, the Viterbi algorithm is selected for decoding. The Viberbi algorithm can be defined as:

X _i ＝(X _i1 ,X _i2 ,...,X _iT )

The local probability at time t = 1 is calculated by the product of the initial probability of the hidden state and the corresponding observation probability. For other moments:

The most probable path to the next state can be determined by the above formula. To determine the most likely hidden state at time t=T, let it _t :

i _t = argmax(δ _T (i))

For other time it _t ,

Follow the most probable path backtracking, and the "+" state traversed in the path will correspond to a CpG island after completion. The final recognition results of CpG islands are shown in Fig. 6 and Fig. 7 .

The Viterbi algorithm reduces computational complexity through recursion, best explained by the entire context of the observed sequence. A "+" state traversed in the pathway will correspond to a CpG island. Assuming the test data set T=ATTAGCGAT, and the optimal path found by the Viterbi algorithm is the state sequence {A-, T-, T+, A+, G+C+, G+, A-, T}, it can be judged that TAGCG is a CpG island. It can be seen that HMM has great value in the field of CpG island identification.

The present invention also proposes a computer storage medium, which stores a plurality of instructions, and the instructions are loaded by a processor and perform the following processing:

1) Obtain a plurality of chromosomes including gene elements, each gene element is represented by a real number, and a plurality of coding chromosomes constitute a set of Hidden Markov Model parameters;

2) Using a fitness function to determine the fitness value of each chromosome, the fitness value is used to represent the degree of chromosome pros and cons;

3) using a genetic algorithm to perform an optimization process on the chromosome according to the fitness value, and then re-determine the optimized chromosome fitness value;

4) Iteratively apply step 3), when the set termination condition is met, the optimal hidden Markov model parameters are output;

5) Using the output optimal hidden Markov model parameters, on the basis of a given observation sequence, determine the maximum probability hidden state sequence for generating the observation sequence, which is used to represent the position of the CpG island.

Further, the present invention also proposes a CpG island identification device based on genetic algorithm and hidden Markov model, including a processor, used to implement each instruction; and a computer storage medium, used to store multiple instructions, the instructions Loaded by the processor and performs the following processing:

1) Obtain a plurality of chromosomes including gene elements, each gene element is represented by a real number, and a plurality of coding chromosomes constitute a set of Hidden Markov Model parameters;

2) Using a fitness function to determine the fitness value of each chromosome, the fitness value is used to represent the degree of chromosome pros and cons;

3) using a genetic algorithm to perform an optimization process on the chromosome according to the fitness value, and then re-determine the optimized chromosome fitness value;

4) Iteratively apply step 3), when the set termination condition is met, the optimal hidden Markov model parameters are output;

5) Using the output optimal hidden Markov model parameters, on the basis of a given observation sequence, determine the maximum probability hidden state sequence for generating the observation sequence, which is used to represent the position of the CpG island.

The present invention first uses HMM to optimize parameters to improve the ability to identify CpG islands. Second, the parameters of the HMM are estimated by using a genetic algorithm. Finally, this method can obtain the maximum likelihood estimate of the HMM, which is very useful for identifying the location of the CGIS. On the basis of experiments, it is shown that the CpG island identification method combined with genetic algorithm and hidden Markov model improves the precision and recall rate.

The above descriptions are only preferred embodiments of the present application, and are not intended to limit the present application. For those skilled in the art, there may be various modifications and changes in the present application. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of this application shall be included within the protection scope of this application.

Claims (10)

1. A CpG island identification method based on genetic algorithm and hidden Markov model, is characterized in that, comprises the following steps: 1) Obtain a plurality of chromosomes including gene elements, each gene element is represented by a real number, and a plurality of chromosomes constitute a set of Hidden Markov Model parameters; 2) Using a fitness function to determine the fitness value of each chromosome, the fitness value is used to represent the degree of chromosome pros and cons; 3) using a genetic algorithm to perform an optimization process on the chromosome according to the fitness value, and then re-determine the optimized chromosome fitness value; 4) Iteratively apply step 3), when the set termination condition is met, the optimal hidden Markov model parameters are output; 5) Using the output optimal hidden Markov model parameters, on the basis of a given observation sequence, determine the maximum probability hidden state sequence for generating the observation sequence, which is used to represent the position of the CpG island. 2. The method according to claim 1, wherein a Viterbi algorithm is used to determine the maximum probability hidden state sequence generating the observation sequence. 3. The method according to claim 2, wherein the Viterbi algorithm determines to generate the maximum probability hidden state sequence of the observation sequence comprising: According to a local probability and a local optimal path corresponding to each base state in the observation sequence, the maximum local probability and its corresponding local optimal path at the current moment are selected through the product of the initial probability of the hidden state and the corresponding observation probability The path is backtracked according to the local optimal path at the current moment, and the position recognition result of the CpG island is obtained. 4. The method according to claim 1, wherein the genetic algorithm comprises a selection operation, a crossover operation and a mutation operation, and the chromosome is optimized by sequentially adopting the selection operation, the crossover operation and the mutation operation. 5. The method according to claim 4, wherein the selecting operation comprises: according to the fitness value of each chromosome, selecting a chromosome whose fitness value meets the genetic requirement for inheritance, and deleting unselected chromosomes. 6. The method according to claim 5, wherein the crossover operation comprises: among the chromosomes whose fitness values meet the genetic requirements, select some chromosomes with better fitness values as parents, and A crossover operation is performed between two parent chromosomes to generate offspring chromosomes. 7. The method according to claim 6, wherein the mutation operation comprises: in the offspring chromosome, first determining the gene mutation site, and changing the gene mutation site according to the set mutation rate gene value. 8. The method according to claim 1, wherein the fitness function is: By adjusting the number of CpG islands in the training data set, the complexity of the fitness function can be adjusted. 9. A computer storage medium storing a plurality of instructions, wherein the instructions are adapted to be loaded by a processor and perform the following processing: 1) Obtain a plurality of chromosomes including gene elements, each gene element is represented by a real number, and a plurality of coding chromosomes constitute a set of Hidden Markov Model parameters; 2) Using a fitness function to determine the fitness value of each chromosome, the fitness value is used to represent the degree of chromosome pros and cons; 3) using a genetic algorithm to perform an optimization process on the chromosome according to the fitness value, and then re-determine the optimized chromosome fitness value; 4) Iteratively apply step 3), when the set termination condition is met, the optimal hidden Markov model parameters are output; 5) Using the output optimal hidden Markov model parameters, on the basis of a given observation sequence, determine the maximum probability hidden state sequence for generating the observation sequence, which is used to represent the position of the CpG island. 10. A CpG island identification device based on a genetic algorithm and a hidden Markov model, comprising a processor for implementing instructions; and a computer storage medium for storing multiple instructions, characterized in that: the instructions are suitable for Loaded by the processor and performs the following processing: 1) Obtain a plurality of chromosomes including gene elements, each gene element is represented by a real number, and a plurality of coding chromosomes constitute a set of Hidden Markov Model parameters; 2) Using a fitness function to determine the fitness value of each chromosome, the fitness value is used to represent the degree of chromosome pros and cons; 3) using a genetic algorithm to perform an optimization process on the chromosome according to the fitness value, and then re-determine the optimized chromosome fitness value; 4) Step 3) is applied iteratively, and when the set termination condition is satisfied, the optimal hidden Markov model parameters are output; 5) Using the output optimal hidden Markov model parameters, on the basis of a given observation sequence, determine the maximum probability hidden state sequence for generating the observation sequence, which is used to represent the position of the CpG island.