---
id: "monks-problems-2"
slug: "monks-problems-2"
name: "Monks Problems 2"
domain: "Data Science & Artificial Intelligence"
taskType: "binary_classification"
numRows: 601
numColumns: 7
targetColumn: "is_target_concept_met"
primaryMetric: "1 - AUC Error"
primaryScore: "0.0000"
parquetUrl: "https://huggingface.co/datasets/carlahq/demo-tabular-benchmarks/resolve/main/data/monks-problems-2/monks-problems-2.parquet"
spreadsheetUrl: "https://docs.google.com/spreadsheets/d/13TFQ2RLxYn_ixRQUDJz4jif8e3g5x1WGQwAktEfRwzQ/edit?usp=sharing"
canonicalUrl: "https://carlahq.eu/datasets/monks-problems-2"
---

# Dataset: Monks Problems 2 (monks-problems-2)

> The MONK's Problems 2 benchmark dataset comprises 601 records evaluated across 6 discrete categorical features to determine whether an entity satisfies an exact non-linear combinatorial condition. It serves as a foundational machine learning benchmark for evaluating algorithm capability in learning complex logical parity-like interactions.

## Dataset Overview

| Attribute | Value |
| :--- | :--- |
| **Task Type** | `binary_classification` |
| **Business Domain** | Data Science & Artificial Intelligence |
| **Target Column** | `is_target_concept_met` |
| **Rows (Instances)** | 601 |
| **Features (Columns)** | 7 |
| **Primary Evaluation Metric** | 1 - AUC Error |
| **Best Benchmark Score** | **0.0000** |

## Business Decision Context
**Context:** Conceived at the 2nd European Summer School on Machine Learning (Corsendonk Priory) to compare inductive learning paradigms, the MONK-2 task tests an algorithm's capability to learn non-linear logical interactions without manual feature engineering across discrete feature dimensions.
**Objective:** Predict binary classification status ('class' = 1 vs 0) based on whether exactly two of the six discrete attributes equal 1.
**Decision Impact:** Provides definitive diagnostic validation of model inductive biases; standard decision tree ensembles struggle with high-order XOR/parity-like interactions, leading to costly model selection errors and degraded real-world rule extraction.

## Feature Schema
| Column Name | Data Type | Role | Distinct Values | Missing Values (%) | Description |
| :--- | :--- | :--- | :--- | :--- | :--- |
| `is_target_concept_met` | `numeric` | target | 2 | 0 | Binary target outcome indicating whether exactly two of the six attributes equal 1 (1 = True, 0 = False). |
| `attribute_1_head_shape` | `numeric` | feature | 3 | 0 | Discrete categorical feature representing head shape with 3 discrete values (1: round, 2: square, 3: octagon). |
| `attribute_2_body_shape` | `numeric` | feature | 3 | 0 | Discrete categorical feature representing body shape with 3 discrete values (1: round, 2: square, 3: octagon). |
| `attribute_3_is_smiling` | `numeric` | feature | 2 | 0 | Discrete binary feature indicating facial expression (1: smiling, 2: not smiling). |
| `attribute_4_holding_object` | `numeric` | feature | 3 | 0 | Discrete categorical feature indicating held object (1: sword, 2: balloon, 3: flag). |
| `attribute_5_jacket_color` | `numeric` | feature | 4 | 0 | Discrete categorical feature denoting jacket color (1: red, 2: yellow, 3: green, 4: blue). |
| `attribute_6_has_tie` | `numeric` | feature | 2 | 0 | Discrete binary feature denoting tie presence (1: yes, 2: no). |

## Empirical Benchmark Leaderboard
| Rank | Algorithm / Model | Model Family | Runtime | Accuracy | ROC AUC | F1-Score |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- |
| 1 | **Carla Engine (TabICLv2 WebGPU)** | Tabular Foundation Model | Browser | **100.00%** | 1.0000 | 1.0000 |
| 2 | **Streaming nanotabicl** | Tabular Foundation Model | PyTorch/Python | **100.00%** | 1.0000 | 1.0000 |
| 3 | **nanotabicl Vanilla** | Tabular Foundation Model | PyTorch/Python | **100.00%** | 1.0000 | 1.0000 |
| 4 | **Full TabICLv2 (PyTorch Reference)** | Tabular Foundation Model | PyTorch/Python | **100.00%** | 1.0000 | 1.0000 |
| 5 | **TabPFN v3** | Tabular Foundation Model | PyTorch/Python | **100.00%** | 1.0000 | 1.0000 |
| 6 | **Google TabFM v1.0** | Tabular Foundation Model | PyTorch/Python | **100.00%** | 1.0000 | 1.0000 |
| 7 | **FilteredClassifier MultiSearch SMO RBFKernel** | Support Vector Machine (SVM) | Python | **100.00%** | 1.0000 | 1.0000 |
| 8 | **FilteredClassifier MultilayerPerceptron** | Neural Network (MLP) | Python | **100.00%** | 1.0000 | 1.0000 |
| 9 | **MultilayerPerceptron** | Neural Network (MLP) | Python | **100.00%** | 1.0000 | 1.0000 |
| 10 | **Bagging MultilayerPerceptron** | Neural Network (MLP) | Python | **100.00%** | 1.0000 | 1.0000 |
| 11 | **FilteredClassifier MultiSearch MultilayerPerceptron** | Neural Network (MLP) | Python | **100.00%** | 1.0000 | 1.0000 |
| 12 | **EXAONE Tabular** | Tabular Foundation Model | PyTorch/Python | **99.48%** | 1.0000 | 0.9926 |
| 13 | **BFTree** | Decision Tree | Python | **97.50%** | 0.9958 | 0.9752 |
| 14 | **SimpleCart** | Machine Learning Model | Python | **96.84%** | 0.9986 | 0.9686 |
| 15 | **ClassificationViaRegression M5P** | Decision Tree | Python | **95.84%** | 0.9873 | 0.9586 |

### Repeated Cross-Validation Fold Scores (TabICLv2 Reference)
| Fold | Train Samples | Test Samples | Metric Score | Latency |
| :--- | :--- | :--- | :--- | :--- |
| Fold 0 | 400 | 201 | 0.0000 | 655ms |
| Fold 1 | 401 | 200 | 0.0000 | 589ms |
| Fold 2 | 401 | 200 | 0.0000 | 601ms |
| Fold 0 | 400 | 201 | 0.0000 | 596ms |
| Fold 1 | 401 | 200 | 0.0000 | 605ms |
| Fold 2 | 401 | 200 | 0.0000 | 577ms |
| Fold 0 | 400 | 201 | 0.0000 | 604ms |
| Fold 1 | 401 | 200 | 0.0000 | 586ms |
| Fold 2 | 401 | 200 | 0.0000 | 604ms |
| Fold 0 | 400 | 201 | 0.0000 | 593ms |
| Fold 1 | 401 | 200 | 0.0000 | 604ms |
| Fold 2 | 401 | 200 | 0.0000 | 600ms |
| Fold 0 | 400 | 201 | 0.0000 | 602ms |
| Fold 1 | 401 | 200 | 0.0000 | 585ms |
| Fold 2 | 401 | 200 | 0.0000 | 601ms |
| Fold 0 | 400 | 201 | 0.0000 | 586ms |
| Fold 1 | 401 | 200 | 0.0000 | 596ms |
| Fold 2 | 401 | 200 | 0.0000 | 596ms |
| Fold 0 | 400 | 201 | 0.0000 | 616ms |
| Fold 1 | 401 | 200 | 0.0000 | 587ms |
| Fold 2 | 401 | 200 | 0.0000 | 600ms |
| Fold 0 | 400 | 201 | 0.0000 | 581ms |
| Fold 1 | 401 | 200 | 0.0000 | 616ms |
| Fold 2 | 401 | 200 | 0.0000 | 591ms |
| Fold 0 | 400 | 201 | 0.0000 | 603ms |
| Fold 1 | 401 | 200 | 0.0000 | 598ms |
| Fold 2 | 401 | 200 | 0.0000 | 610ms |
| Fold 0 | 400 | 201 | 0.0000 | 589ms |
| Fold 1 | 401 | 200 | 0.0000 | 599ms |
| Fold 2 | 401 | 200 | 0.0000 | 587ms |
| Fold 0 | 400 | 201 | 0.0000 | 603ms |
| Fold 1 | 401 | 200 | 0.0000 | 586ms |
| Fold 2 | 401 | 200 | 0.0000 | 604ms |
| Fold 0 | 400 | 201 | 0.0000 | 589ms |
| Fold 1 | 401 | 200 | 0.0000 | 601ms |
| Fold 2 | 401 | 200 | 0.0000 | 598ms |
| Fold 0 | 400 | 201 | 0.0000 | 601ms |
| Fold 1 | 401 | 200 | 0.0000 | 580ms |
| Fold 2 | 401 | 200 | 0.0000 | 626ms |
| Fold 0 | 400 | 201 | 0.0000 | 591ms |
| Fold 1 | 401 | 200 | 0.0000 | 603ms |
| Fold 2 | 401 | 200 | 0.0000 | 588ms |
| Fold 0 | 400 | 201 | 0.0000 | 592ms |
| Fold 1 | 401 | 200 | 0.0000 | 591ms |
| Fold 2 | 401 | 200 | 0.0000 | 611ms |
| Fold 0 | 400 | 201 | 0.0000 | 611ms |
| Fold 1 | 401 | 200 | 0.0000 | 600ms |
| Fold 2 | 401 | 200 | 0.0000 | 594ms |
| Fold 0 | 400 | 201 | 0.0000 | 620ms |
| Fold 1 | 401 | 200 | 0.0000 | 592ms |
| Fold 2 | 401 | 200 | 0.0000 | 607ms |
| Fold 0 | 400 | 201 | 0.0000 | 586ms |
| Fold 1 | 401 | 200 | 0.0000 | 604ms |
| Fold 2 | 401 | 200 | 0.0000 | 597ms |
| Fold 0 | 400 | 201 | 0.0000 | 594ms |
| Fold 1 | 401 | 200 | 0.0000 | 592ms |
| Fold 2 | 401 | 200 | 0.0000 | 604ms |
| Fold 0 | 400 | 201 | 0.0000 | 582ms |
| Fold 1 | 401 | 200 | 0.0000 | 608ms |
| Fold 2 | 401 | 200 | 0.0000 | 592ms |

## Provenance & Downloadable Artifacts
- **Dataset Parquet File:** [Direct Parquet Download](https://huggingface.co/datasets/carlahq/demo-tabular-benchmarks/resolve/main/data/monks-problems-2/monks-problems-2.parquet)
- **Google Sheets Interactive Demo:** [Open in Google Sheets](https://docs.google.com/spreadsheets/d/13TFQ2RLxYn_ixRQUDJz4jif8e3g5x1WGQwAktEfRwzQ/edit?usp=sharing)
- **OpenML Source:** [OpenML Dataset](https://www.openml.org/d/334)
- **Academic Paper / Citation:** [Read Research Paper](https://archive.ics.uci.edu/dataset/70/monk+s+problems)
- **Canonical HTML Page:** [https://carlahq.eu/datasets/monks-problems-2](https://carlahq.eu/datasets/monks-problems-2)