Evaluation Metrics for Hyperlattices

Probabilistic Hyperlattice Models

There are several common evaluation metrics for probabilistic hyperlattice models, depending on the specific application and the type of data. Here are some examples:

1. Log-likelihood: The log-likelihood measures how well the model fits the data, by computing the log-probability of the observed data under the model. A higher log-likelihood indicates a better fit to the data.

2. Accuracy: The accuracy measures the proportion of correctly classified instances in a classification task. It is defined as the number of correct predictions divided by the total number of predictions.

3. Precision and recall: Precision measures the proportion of true positives among the instances predicted as positive, while recall measures the proportion of true positives among the instances that are actually positive. These metrics are commonly used in binary classification tasks.

4. F1 score: The F1 score is the harmonic mean of precision and recall, and provides a balanced measure of the model’s performance in binary classification tasks.

5. Mean squared error: The mean squared error measures the average squared difference between the predicted and actual values in a regression task. A lower mean squared error indicates a better fit to the data.

6. Receiver operating characteristic (ROC) curve: The ROC curve plots the true positive rate against the false positive rate for different threshold values in a binary classification task. It provides a visual representation of the trade-off between sensitivity and specificity of the model.

7. Area under the curve (AUC): The AUC measures the area under the ROC curve, and provides a single number that summarizes the overall performance of the model in a binary classification task.

These evaluation metrics can be computed on a held-out test set, or using cross-validation to estimate the generalization performance of the model. In addition, it is important to consider the interpretability and complexity of the model, and to compare it to other models and baselines in the same task and domain.

Implementing Evaluation Metrics for Probabilistic Hyperlattice Models in Common Lisp

Here are some examples of evaluation metrics for probabilistic hyperlattices that can be implemented in Common Lisp:

1. Log-likelihood: The log-likelihood measures how well the model fits the data, by computing the log-probability of the observed data under the model. This can be computed using the log-probability function, which takes as input the hyperlattice model and the observed data, and returns the log-probability of the data under the model.

2. Accuracy: The accuracy measures the proportion of correctly classified instances in a classification task. This can be computed using the accuracy function, which takes as input the hyperlattice model, the test data, and the class labels, and returns the proportion of correctly classified instances.

3. Precision and recall: Precision measures the proportion of true positives among the instances predicted as positive, while recall measures the proportion of true positives among the instances that are actually positive. These can be computed using the precision and recall functions, which take as input the hyperlattice model, the test data, the class labels, and the threshold value, and return the precision and recall values for the given threshold.

4. F1 score: The F1 score is the harmonic mean of precision and recall, and provides a balanced measure of the model’s performance in binary classification tasks. This can be computed using the f1-score function, which takes as input the precision and recall values, and returns the F1 score.

5. Mean squared error: The mean squared error measures the average squared difference between the predicted and actual values in a regression task. This can be computed using the mean-squared-error function, which takes as input the hyperlattice model, the test data, and the target values, and returns the mean squared error.

These evaluation metrics can be implemented using Common Lisp functions and libraries, such as the cl-mathstats library for statistical computations, and the cl-ml library for machine learning algorithms. The choice of the evaluation metrics depends on the specific application and the type of data, and should be validated using appropriate validation techniques and statistical tests.