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+---
+title: "Classification metrics on the backend"
+author: "Tyler White"
+date: "2024-12-05"
+image: thumbnail.png
+categories:
+    - blog
+    - machine learning
+    - portability
+---
+
+A review of binary classification models, metrics used to evaluate them, and
+corresponding metric calculations with Ibis.
+
+We're going explore common classification metrics such as accuracy, precision, recall,
+and F1 score, demonstrating how to compute each one using Ibis. In this example, we'll
+use DuckDB, the default Ibis backend, but we could use this same code to execute
+against another backend such as Postgres or Snowflake. This capability is useful as it
+offers an easy and performant way to evaluate model performance without extracting data
+from the source system.
+
+## Classification models
+
+In machine learning, classification entails categorizing data into different groups.
+Binary classification, which is what we'll be covering in this post, specifically
+involves sorting data into only two distinct groups. For example, a model could
+differentiate between whether or not an email is spam.
+
+## Model evaluation
+
+It's important to validate the performance of the model to ensure it makes correct
+predictions consistently and doesn’t only perform well on the data it was trained on.
+These metrics help us understand not just the errors the model makes, but also the
+types of errors. For example, we might want to know if the model is more likely to
+predict a positive outcome when the actual outcome is negative.
+
+The easiest way to break down how this works is to look at a confusion matrix.
+
+### Confusion matrix
+
+A confusion matrix is a table used to describe the performance of a classification
+model on a set of data for which the true values are known. As binary classification
+only involves two categories, the confusion matrix only contains true positives, false
+positives, false negatives, and true negatives.
+
+![](confusion_matrix.png)
+
+Here's a breakdown of the terms with examples.
+
+True Positives (TP)
+: Correctly predicted positive examples.
+
+We guessed it was a spam email, and it was. This email is going straight to the junk
+folder.
+
+False Positives (FP)
+: Incorrectly predicted as positive.
+
+We guessed it was a spam email, but it actually wasn’t. Hopefully, the recipient
+doesn’t miss anything important as this email is going to the junk folder.
+
+False Negatives (FN)
+: Incorrectly predicted as negative.
+
+We didn't guess it was a spam email, but it really was. Hopefully, the recipient
+doesn’t click any links!
+
+True Negatives (TN)
+: Correctly predicted negative examples.
+
+We guessed it was not a spam email, and it actually was not. The recipient can read
+this email as intended.
+
+### Building a confusion matrix
+
+#### Sample dataset
+
+Let's create a sample dataset that includes twelve rows with two columns: `actual` and
+`prediction`. The `actual` column contains the true values, and the `prediction` column
+contains the model's predictions.
+
+```{python}
+
+from ibis.interactive import *
+
+t = ibis.memtable(
+    {
+        "id": range(1, 13),
+        "actual": [1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1],
+        "prediction": [1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1],
+    }
+)
+
+t
+```
+
+We can use the `case` function to create a new column that categorizes the outcomes.
+
+```{python}
+
+case_expr = (
+    ibis.case()
+    .when((_.actual == 0) & (_.prediction == 0), "TN")
+    .when((_.actual == 0) & (_.prediction == 1), "FP")
+    .when((_.actual == 1) & (_.prediction == 0), "FN")
+    .when((_.actual == 1) & (_.prediction == 1), "TP")
+    .end()
+)
+
+t = t.mutate(outcome=case_expr)
+
+t
+```
+
+To create the confusion matrix, we'll group by the outcome, count the occurrences, and
+use `pivot_wider`. Widening our data makes it possible to perform column-wise
+operations on the table expression for metric calculations.
+
+```{python}
+
+cm = (
+    t.group_by("outcome")
+    .agg(counted=_.count())
+    .pivot_wider(names_from="outcome", values_from="counted")
+    .select("TP", "FP", "FN", "TN")
+)
+
+cm
+```
+
+We can plot the confusion matrix to visualize the results.
+
+```{python}
+import matplotlib.pyplot as plt
+import seaborn as sns
+
+data = cm.to_pyarrow().to_pydict()
+
+plt.figure(figsize=(6, 4))
+sns.heatmap(
+    [[data["TP"][0], data["FP"][0]], [data["FN"][0], data["TN"][0]]],
+    annot=True,
+    fmt="d",
+    cmap="Blues",
+    cbar=False,
+    xticklabels=["Predicted Positive", "Predicted Negative"],
+    yticklabels=["Actual Positive", "Actual Negative"],
+)
+plt.title("Confusion Matrix")
+plt.show()
+```
+
+Now that we've built a confusion matrix, we're able to more easily calculate a few
+common classification metrics.
+
+### Metrics
+
+Here are the metrics we'll calculate as well as a brief description of each.
+
+Accuracy
+: The proportion of correct predictions out of all predictions made. This measures the
+overall effectiveness of the model across all classes.
+
+Precision
+: The proportion of true positive predictions out of all positive predictions made.
+This tells us how many of the predicted positives were actually correct.
+
+Recall
+: The proportion of true positive predictions out of all actual positive examples. This
+measures how well the model identifies all actual positives.
+
+F1 Score
+: A metric that combines precision and recall into a single score by taking their
+weighted average. This balances the trade-off between precision and recall, making it
+especially useful for imbalanced datasets.
+
+We can calculate these metrics using the columns from the confusion matrix we created
+earlier.
+
+```{python}
+
+accuracy_expr = (_.TP + _.TN) / (_.TP + _.TN + _.FP + _.FN)
+precision_expr = _.TP / (_.TP + _.FP)
+recall_expr = _.TP / (_.TP + _.FN)
+f1_score_expr = 2 * (precision_expr * recall_expr) / (precision_expr + recall_expr)
+
+metrics = cm.select(
+    accuracy=accuracy_expr,
+    precision=precision_expr,
+    recall=recall_expr,
+    f1_score=f1_score_expr,
+)
+
+metrics
+```
+
+## A more efficient approach
+
+In the illustrative example above, we used a case expression and pivoted the data to
+demonstrate where the values would fall in the confusion matrix before performing our
+metric calculations using the pivoted data. We can actually skip this step using column
+aggregation.
+
+```{python}
+tp = (t.actual * t.prediction).sum()
+fp = t.prediction.sum() - tp
+fn = t.actual.sum() - tp
+tn = t.actual.count() - tp - fp - fn
+
+accuracy_expr = (t.actual == t.prediction).mean()
+precision_expr = tp / t.prediction.sum()
+recall_expr = tp / t.actual.sum()
+f1_score_expr = 2 * tp / (t.actual.sum() + t.prediction.sum())
+
+print(
+    f"accuracy={accuracy_expr.to_pyarrow().as_py()}",
+    f"precision={precision_expr.to_pyarrow().as_py()}",
+    f"precision={recall_expr.to_pyarrow().as_py()}",
+    f"f1_score={f1_score_expr.to_pyarrow().as_py()}",
+    sep="\n",
+)
+```
+
+## Conclusion
+
+By pushing the computation down to the backend, the performance is as powerful as the
+backend we're connected to. This capability allows us to easily scale to different
+backends without modifying any code.
+
+We hope you give this a try and let us know how it goes. If you have any questions or
+feedback, please reach out to us on [GitHub](https://github.com/ibis-project) or
+[Zulip](https://ibis-project.zulipchat.com/).
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