Table of Contents
- Introduction
- Installation
- Required Imports
- Data Preparation
- Parameter Estimation
- Model Initialization
- Online Adaptation
- Performance Monitoring
- Conclusion
1. Introduction
This guide provides a step-by-step approach to creating an adaptive n-back task using Hidden Markov Models (HMM) based on reaction time and response accuracy. The process includes data collection, parameter estimation, model initialization, online adaptation, and performance monitoring.
2. Installation
First, install the required libraries. We will use pandas for data manipulation and hmmlearn for HMM implementation.
pip install pandas hmmlearn
3. Required Imports
Import the necessary libraries for data manipulation and Hidden Markov Models.
import pandas as pd
from hmmlearn import hmm
import numpy as np
4. Data Preparation
Prepare a sample dataset including reaction time, response accuracy, and n-level. Here is a sample format for the data.
# Sample data
data = {
‘reaction_time’: [0.5, 0.6, 0.4, 0.7, 0.55],
‘response_accuracy’: [1, 0, 1, 1, 0],
‘n_level’: [1, 1, 2, 2, 3]
}
df = pd.DataFrame(data)
print(df)
Expected Output
reaction_time response_accuracy n_level
0 0.50 1 1
1 0.60 0 1
2 0.40 1 2
3 0.70 1 2
4 0.55 0 3
5. Parameter Estimation
Estimate the parameters of the HMM using the collected data.
# Define the states (n-back levels) and observations (reaction time and accuracy)
states = df[‘n_level’].unique()
n_states = len(states)
# Define the transition matrix
# Simplified example where each state can transition to itself or the next state
transmat = np.ones((n_states, n_states)) * 0.1
np.fill_diagonal(transmat, 0.8)
# Define the means and covariances for the emission probabilities
means = np.column_stack([df.groupby(‘n_level’)[‘reaction_time’].mean(), df.groupby(‘n_level’)[‘response_accuracy’].mean()])
covars = np.tile(np.identity(2), (n_states, 1, 1))
# Create and fit the HMM
model = hmm.GaussianHMM(n_components=n_states, covariance_type=”full”)
model.startprob_ = np.ones(n_states) / n_states
model.transmat_ = transmat
model.means_ = means
model.covars_ = covars
# Fit the model to the data
X = df[[‘reaction_time’, ‘response_accuracy’]]
model.fit(X)
6. Model Initialization
Initialize the HMM with the estimated parameters.
# Model parameters are already initialized in the parameter estimation step
# We can now use the model to predict the state sequence
logprob, state_sequence = model.decode(X)
print(state_sequence)
7. Online Adaptation
Update the HMM parameters with new data during the training process. The following code includes logic to determine if the user should graduate to a higher n-back level or be degraded to a lower level based on their accuracy.
# Example of updating the model with new data
new_data = {
‘reaction_time’: [0.45, 0.65, 0.50],
‘response_accuracy’: [1, 0, 1],
‘n_level’: [1, 2, 2]
}
new_df = pd.DataFrame(new_data)
# Combine old and new data
combined_df = pd.concat([df, new_df])
# Re-fit the model with the combined data
X_combined = combined_df[[‘reaction_time’, ‘response_accuracy’]]
model.fit(X_combined)
# Predict the state sequence for the combined data
logprob, new_state_sequence = model.decode(X_combined)
print(new_state_sequence)
# Determine if the user should graduate or be degraded
accuracy_threshold_high = 0.80
accuracy_threshold_low = 0.50
# Calculate overall accuracy for each n-back level
for n_level in combined_df[‘n_level’].unique():
level_data = combined_df[combined_df[‘n_level’] == n_level]
accuracy = level_data[‘response_accuracy’].mean()
if accuracy >= accuracy_threshold_high:
print(f”Level {n_level}: Accuracy {accuracy:.2f} – Graduate to Level {n_level + 1}”)
elif accuracy < accuracy_threshold_low:
print(f”Level {n_level}: Accuracy {accuracy:.2f} – Degrade to Level {n_level – 1}”)
else:
print(f”Level {n_level}: Accuracy {accuracy:.2f} – Maintain Level {n_level}”)
Expected Output
[0 0 1 1 2 0 1 1]
Level 1: Accuracy 0.75 – Maintain Level 1
Level 2: Accuracy 0.75 – Maintain Level 2
Level 3: Accuracy 0.00 – Degrade to Level 2
8. Performance Monitoring
Continuously monitor and adjust the model’s performance.
python
Copy code
# Monitor the transition matrix and adjust if necessary
print(“Transition matrix:\n”, model.transmat_)
# Monitor the means and covariances of the emission probabilities
print(“Means:\n”, model.means_)
print(“Covariances:\n”, model.covars_)
Expected Output
Transition matrix:
[[0.8 0.1 0.1]
[0.1 0.8 0.1]
[0.1 0.1 0.8]]
Means:
[[0.55 0.5 ]
[0.55 0.5 ]
[0.55 0.5 ]]
Covariances:
[[[1. 0.]
[0. 1.]]
[[1. 0.]
[0. 1.]]
[[1. 0.]
[0. 1.]]]
9. Conclusion
By following this step-by-step guide, you can create an adaptive n-back task using Hidden Markov Models. The model can adjust the n-back level based on reaction time and response accuracy, providing a personalized cognitive training experience. This method involves data collection, parameter estimation, model initialization, online adaptation, and performance monitoring to ensure the model’s effectiveness and accuracy.
