> ## Documentation Index > Fetch the complete documentation index at: https://arize-ax.mintlify.dev/docs/llms.txt > Use this file to discover all available pages before exploring further. # All Functions > Aggregate and metric function syntax ## Functions Overview This page provides a reference of all available functions by **aggregation functions** and **metric functions**. Click the linked model type for documentation on a particular model. 1. [Aggregation functions](/ax/machine-learning/machine-learning/how-to-ml/custom-metrics-api/custom-metric-syntax/all-functions#agg_func) 2. [Metric functions](/ax/machine-learning/machine-learning/how-to-ml/custom-metrics-api/custom-metric-syntax/all-functions#metric-functions) ## Aggregation functions Every User Defined Metric must have one or more aggregation functions or metrics\*\*.\*\* | Function | Description | Type | | ---------------------------------- | --------------------------------------------------------------------------------------------------- | ------- | | `COUNT(*)` | Counts the number of rows | n/a | | `APPROX_COUNT_DISTINCT(exprs)` | Counts the unique values of exprs | String | | `SUM(exprs)` | Sums the value of the expression across rows | Numeric | | `AVG(exprs)` | Averages the value of the expression across rows | Numeric | | `APPROX_QUANTILE(exprs,)` | Approximate quantile of expres. Second argument must be a numeric literal between 0 and 1 inclusive | Numeric | | `MIN(exprs)` | Minimum of the value of the expression across rows | Numeric | | `MAX(exprs)` | Maximum of the value of the expression across rows | Numeric | ## Metric functions Metric functions leverage existing metrics in Arize for use in your custom metric. They also allow you to customize the way existing metrics are calculated. Metric functions can take both positional arguments and keyword arguments. When using both, positional arguments must come before keyword arguments. Keyword arguments can be specified in any order. For classification metrics, the model's configured positive class is the default value, we will refer to this as defaultPositiveClass in this doc. Note that these functions need actual (a.k.a. ground truth) data to produce results. ### **True Positive** ``` TP(actual=categoricalActualLabel, predicted=categoricalPredictionLabel, pos_class=defaultPositiveClass) ``` **Model Type:** Score Categorical Computes the true positive rate, using the positive class. If `pos_class=` is omitted, then the positive class configured for the model is used. ### **False Positive** ``` FP(actual=categoricalActualLabel, predicted=categoricalPredictionLabel, pos_class=defaultPositiveClass) ``` **Model Type:** Score Categorical Computes the false positive rate, using the positive class. If `pos_class=` is omitted, then the positive class configured for the model is used. ### **True Negative** ``` TN(actual=categoricalActualLabel, predicted=categoricalPredictionLabel, pos_class=defaultPositiveClass) ``` **Model Type:** Score Categorical Computes the true negative rate, using the positive class. If `pos_class=` is omitted, then the positive class configured for the model is used. ### **False Negative** ``` FN(actual=categoricalActualLabel, predicted=categoricalPredictionLabel, pos_class=defaultPositiveClass) ``` **Model Type:** Score Categorical Computes the false negative rate, using the positive class. If `pos_class=` is omitted, then the positive class configured for the model is used. ### **Precision** ``` PRECISION(actual=categoricalActualLabel, predicted=categoricalPredictionLabel, pos_class=defaultPositiveClass) ``` **Model Type:** Score Categorical Computes precision, using the positive class. If `pos_class=` is omitted, then the positive class configured for the model is used. ### **Recall** ``` RECALL(actual=categoricalActualLabel, predicted=categoricalPredictionLabel, pos_class=defaultPositiveClass) ``` **Model Type:** Score Categorical Computes recall, using the positive class. If `pos_class=` is omitted, then the positive class configured for the model is used. ### **F1** ``` F1(actual=categoricalActualLabel, predicted=categoricalPredictionLabel, pos_class=defaultPositiveClass) ``` **Model Type:** Score Categorical Compute the F1 score, also known as balanced F-score or F-measure. If `pos_class=` is omitted, then the positive class configured for the model is used. ### **F\_BETA** ``` F_BETA(actual=categoricalActualLabel, predicted=categoricalPredictionLabel, pos_class=defaultPositiveClass, beta=1) ``` **Model Type:** Score Categorical Computes F-score with optional `beta=` parameter for re-weighting precision and recall. Beta is defaulted to `1`, which produces the same result as the F-1 score. When `beta=0`, F-score equals precision, when beta goes to infinity, F-score equals recall. Commonly used values for `beta=` are `2`, which weighs recall higher than precision, and `0.5`, which weighs recall lower than precision. If `pos_class=` is omitted, then the positive class configured for the model is used. ### **LOG\_LOSS** ``` LOG_LOSS(actual=categoricalActualLabel, predicted_score=scorePredictionLabel, pos_class=defaultPositiveClass) ``` **Model Type:** Score Categorical Computes log loss of the model. Note that `actual=` is a string column while `predicted=` is a numeric column. ### ACCURACY ``` ACCURACY(actual=categoricalActualLabel, predicted=categoricalPredictionLabel) ``` **Model Type:** Score Categorical Computes accuracy of the model. ### MAE ``` MAE(actual=scoreActualLabel, predicted=scorePredictionLabel) ``` **Model Type:** Numeric, Score Categorical Computes mean absolute error. ### MAPE ``` MAPE(actual=scoreActualLabel, predicted=scorePredictionLabel) ``` **Model Type:** Numeric, Score Categorical Computes mean absolute percentage error. ### MSE ``` MSE(actual=scoreActualLabel, predicted=scorePredictionLabel) ``` **Model Type:** Numeric, Score Categorical Computes mean squared error. ### RMSE ``` RMSE(actual=scoreActualLabel, predicted=scorePredictionLabel) ``` **Model Type:** Numeric, Score Categorical Computes root mean square error. ### AUC ``` AUC(actual=scoreActualLabel, predicted=scorePredictionLabel) ``` **Model Type:** Score Categorical Computes the (ROC) AUC. ### NDCG ```python theme={null} NDCG(ranking_relevance=relevance, prediction_group_id=predictionGroupId, rank=rank, omit_zero_relevance=True, k=10) ``` **Model Type:** Ranking Computes the Normalized Discounted Cumulative Gain of a ranking model. In order to control the behavior of whether rows with 0-relevance are included or not, use `omit_zero_relevance` since this will impact the averaging that is implicit in this metric. ### MAX\_PRECISION ```java theme={null} MAX_PRECISION(pos_class=positive_class, actual=scoreActualLabel, predicted=scorePredictionLabel group_by_column = 'column_to_group_by') ``` **Model Type**: Score Categorical Groups the data by the group\_by\_column and selects only the rows with the highest prediction score in each group. Calculates precision using only those rows. ### ECE ``` ECE(predicted=categoricalPredictionLabel, actual=categoricalActualLabel, predicted_score=categoricalPredictionScore) ``` **Model Type**: Score Categorical Computes the Expected Calibration Error (ECE) for categorical predictions. Accepts positional or keyword arguments. Defaults to system-configured predicted and actual labels if unspecified.