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Which Way Will the Scale Tip?

Given the weight and distance on each side, does the scale tip left, tip right or balance? There's a simple rule behind it, so you can see whether a model finds it.

Use caseSciencePredictionModel evaluation

The table

625 set-ups of a balance scale, with weight and distance on each side, labelled left, right or balanced. It's in Welt's research catalogue as Balance Scale, 625 rows by 5 columns, licensed CC BY 4.0. The catalogue measures its signal at 0.51. At 625 rows and 4 features, TabICLv2, Kumo Tabular Medium and Mitra-v2 take the table as it is. The others can't take a table this size, so the walkthrough leaves them out.

Walkthrough

  1. Load it from the catalogue

    Find the table, read its recorded target and print the column names.

    import pandas as pd
    from welt import Client
    
    with Client() as client:
        item = client.research_datasets(q="balance scale", limit=1)["items"][0]
        info = client.research_dataset(item["id"])
        data = client.load_research_dataset(item["id"])
    
    target = info["targets"][0]
    target = target["name"] if isinstance(target, dict) else target
    print([column["name"] for column in info["schema"]], target)
  2. Pick the rows

    Set aside 20 rows to predict at the end, and keep the rest for the models to learn from.

    known = data.dropna(subset=[target])
    new_rows = known.sample(20, random_state=1)
    table = known.drop(new_rows.index)
  3. Compare the models and predict

    The models compete on the same folds against a simple guess, then the top-ranked one is fitted on the whole table. ROC AUC runs from 0.5, a coin toss, to 1, a perfect ranking, and a lower Brier score means the probabilities can be trusted more. The last table puts each prediction next to the real answer.

    with Client() as client:
        evaluation = client.evaluate(table, target, task="classification", seed=7,
                                     models=["tabicl-v2", "kumo-medium", "mitra-v2"])
        model = evaluation.fit()
    
    print(evaluation.summary()[["name", "rank", "roc_auc_mean", "brier_mean"]])
    features = new_rows.drop(columns=target)
    print(pd.DataFrame({"actual": new_rows[target].values, "predicted": model.predict(features),
                        "probability": model.predict_proba(features).max(axis=1)}))

What you get

A result per set-upWith a probability for each outcome.
A known ruleCheck the model against the physics.
Small data handledThree of the four models take all 625 set-ups.

Try it

Use Open with to run the research datasets notebook in Colab, Kaggle or Jupyter and search for "balance scale", or run the code above after pip install "welt-client[parquet]".