N-back- adaptive training HMM

Adaptive n-back task using Hidden Markov Models (HMM) based on reaction time and response accuracy, follow these steps:

Process Overview

1. Data Collection:
• Reaction Time: Record the time taken for each response.
• Response Accuracy: Record whether each response is correct or incorrect.
• n-level: Keep track of the current n-back level during each trial.
2. Defining States and Observations:
• States: These represent the different n-back levels (e.g., n = 1, 2, 3, …).
• Observations: These include reaction time and response accuracy.
3. Transition Model:
• Define the probability of transitioning from one n-back level to another based on the current state’s performance metrics.
• If accuracy is between 80-100%, increase the n-back level.
• If accuracy is below 50%, decrease the n-back level.
• For intermediate accuracies, keep the current n-back level or slightly adjust based on additional metrics like reaction time.
4. Emission Model:
• Define the probability distribution of observations (reaction time and accuracy) for each n-back level.

Required Data

1. Initial Training Data:
• Collect data from a large number of trials at each n-back level to estimate the emission probabilities. This could involve thousands of trials across multiple participants to ensure robust statistics.
2. Online Adaptation:
• Continuously update the model with new data during the training process to refine transition and emission probabilities.

Steps to Develop the Algorithm

1. Data Preparation:
• Collect initial data for each n-back level to estimate initial parameters of the HMM.
• Ensure data includes a diverse set of reaction times and accuracy levels for each n-back level.
2. Parameter Estimation:
• Use the collected data to estimate the initial transition probabilities and emission probabilities for the HMM.
• Initial transition probabilities can be set based on heuristic rules (e.g., increase n-back level if accuracy > 80%).
3. Model Initialization:
• Initialize the HMM with the estimated parameters.
• Define the initial state distribution (e.g., start with n = 1).
4. Online Adaptation Mechanism:
• After each trial, update the HMM parameters using the latest reaction time and accuracy data.
• Adjust the n-back level based on the current state’s transition probabilities.
5. Performance Monitoring:
• Continuously monitor the performance of the HMM.
• Make adjustments to the transition and emission models if certain n-back levels are consistently over or under-performing.

Example Data Structure

• Reaction Time: Continuous variable representing the time taken for each response.
• Response Accuracy: Binary variable indicating correct (1) or incorrect (0) response.
• n-level: Integer representing the current n-back level during the trial.

Amount of Data Required

• Initial Training: At least a few hundred trials per n-back level, preferably more, to ensure robust estimation of emission probabilities.
• Online Adaptation: Continually collect data during each session to update the model.

Verification

• Verify the algorithm against study requirements by comparing the adaptive n-back levels and performance metrics with expected outcomes from previous research studies.
• Ensure the model’s predictions align with established cognitive training protocols and adapt dynamically based on participant performance.

By following this structured approach, you can develop an adaptive n-back task using Hidden Markov Models that adjusts based on reaction time and response accuracy.