Question

I want to use HMM with Viterbi Algorithm to correct typographical errors, I calculated the required probability but when I apply Viterbi algorithm I got very bad results, I checked the code line by line and I couldn’t find the error

public ForwardViterbi(string[] states, string[] observations, double[] startProbability, double[,] transitionProbability, double[,] emissionProbability, double scaleFactor)
        {

            this.states = states;
            this.observations = observations;
            this.startProbability = startProbability;
            this.transitionProbability = transitionProbability;
            this.emissionProbability = emissionProbability;
            this.scaleFactor = scaleFactor;

        }

        //----------------------------------------------------------------------
        //The Methods

        public void Process(int[] problem)
        {

            double[,] T = new double[states.Length, 3];  //We will store the probability sequence for the Viterbi Path
            vPath = new int[problem.Length];
            vProbs = new double[problem.Length];

            //initialize T
            //------------------------------------------------------------------    
            for (int state = 0; state < states.Length; state++)
            {
                T[state, 0] = startProbability[state];
                T[state, 1] = state;
                T[state, 2] = startProbability[state];
            }

            for (int output = 0; output < problem.Length; output++)
            {

                double[,] U = new double[states.Length, 3];  //We will use this array to calculate the future probabilities

                Console.WriteLine("\nTesting hypothesis {0} ({1})", output, observations[problem[output]]);
                double highest = 0;

                for (int nextState = 0; nextState < states.Length; nextState++)
                {
                    double total = 0;
                    double argMax = 0;
                    double valMax = 0;

                    Console.WriteLine("  Estimating probability for future state {0} ({1})", nextState, states[nextState]);
                    for (int state = 0; state < states.Length; state++)
                    {
                        Console.WriteLine("    The testing state is {0} ({1})", states[state], state);
                        double prob = T[state, 0];
                        double v_path = T[state, 1];
                        double v_prob = T[state, 2];
                        double p = emissionProbability[state, problem[output]] * transitionProbability[state, nextState] * scaleFactor;
                        prob *= p;
                        v_prob *= p;
                        total += prob;

                        if (v_prob > valMax)
                        {
                            valMax = v_prob;
                            argMax = nextState;
                        }

                        Console.WriteLine("    VProbability of {0} is {1} with scale {2}^{3}", states[nextState], v_prob, scaleFactor, output + 1);

                        if (v_prob > highest)
                        {
                            highest = v_prob;
                            vPath[output] = nextState;
                            vProbs[output] = v_prob;
                        }
                    }

                    U[nextState, 0] = total;
                    U[nextState, 1] = argMax;
                    U[nextState, 2] = valMax;
                }
                T = U;
                Console.WriteLine("The highest probability was {0} in state {1} (scale factor of {2}^{3})", highest, states[vPath[output]], scaleFactor, output + 1);
            }


            //Apply SumMax
            double Total = 0;
            double ValMax = 0;

            for (int state = 0; state < states.Length; state++)
            {
                double prob = T[state, 0];
                double v_path = T[state, 1];
                double v_prob = T[state, 2];

                Total += prob;
                if (v_prob > ValMax)
                {
                    ValMax = v_prob;
                }
            }

            Console.WriteLine("\nAnalysis: Total probability (sum of all paths) for the given state is :: {0}\nThe Viterbi Path Probability is :: {1}", Total, ValMax);
            Console.WriteLine("The above results are presented with a scale factor of {0}^{1}", scaleFactor, problem.Length);

        }

Answer 1

I’ve just checked this implementation and the one published on wikipedia.
This one doesn’t seem to work. The one on wikipedia does work.
If you want – you can compare them, but I’m lazy to do this.

(I’ve implemented solution for exactly your problem as described here)