Lost in Hyperspace

Engineer at most 300 features from 5×5×5×6 hypercube arrays so a fixed linear regression predicts three properties with low RMSE.

Regression (feature engineering)

The task

This task follows on from the at-home Save the Factory task. You have been promoted to Principal Engineering Detective and handed a set of Glowing Hypercubes. Each one is a 5 × 5 × 5 × 6 numeric array full of symmetries, and the statement says it shares traits with the at-home widget data.

You have to predict three numeric properties for every hypercube. The model is fixed: plain scikit-learn LinearRegression with no hyperparameter changes and at most 300 input features per property, so all the work goes into designing features. Each property may use its own feature set.

Each property is scored by RMSE, multiplied by a per-property weight, and the three weighted errors are averaged into one score. Feature generation, training and inference must fit in 5 minutes per property on a standard non-GPU Colab instance. Supervised models may not serve as feature extractors, pretrained models and AutoML are banned, and the validation split may not be used for training.

Abridged by SOTA from the official materials. The official statement has the exact rules, and it wins wherever this summary differs.

At a glance

You get

A pickle (ml_data_onsite_start.pickle) holding X and y for train and validation splits plus an unlabelled live_test split, where each sample is a 5×5×5×6 array with three target properties; a separate pickle (ml_data_onsite_final_test.pickle) holds the final test inputs. Split sizes are not stated.

You submit

Predictions of all three properties for the final test set, plus the Colab notebook. The statement text asks for files ml_feature_0.txt, ml_feature_1.txt and ml_feature_2.txt, while the notebook's helper code writes a CSV with columns ID, y1, y2, y3.

Scoring

Root mean square error for each property, multiplied by SCALING_WEIGHTS = [100/15, 100/8, 100/100], then averaged over the three properties into a single score.

Rules

Only scikit-learn LinearRegression may be used as the model, with no hyperparameter changes
At most 300 features per property
Feature generation, training and inference must take no more than 5 minutes per property on a standard non-GPU Colab instance (data analysis and feature search are not time-limited)
Supervised models (neural networks, LDA, boosting trees, etc.) may not be used as feature extractors; simpler supervised models may be used for feature selection only
Unsupervised learning, including autoencoders, is allowed
No pretrained models, AutoML, or libraries that automatically search over approaches
Validation data may not be used for training
If reproducibility or time limits are in doubt, the jury may use the notebook's own outputs and keep the lower score

Format

Scientific round, on-site stage (teams had 8 hours for the three on-site tasks)

Lost in Hyperspace

The task

At a glance

Links

Statement

Notebook

Data

Solutions

Results

Source files

Details