Design Framework for Robust House-Price Prediction Model
Company: Citadel
Role: Data Scientist
Category: Machine Learning
Difficulty: hard
Interview Round: Technical Screen
##### Scenario
Deep-dive on model robustness and feature engineering for house-price prediction.
##### Question
In linear regression, how do you detect and handle outliers and influential points? Explain Cook's distance and high-leverage diagnostics. In Random Forests, how can you prune trees and compute variable importance? Design a modelling framework to predict a city's house prices. Which factors would you include and why? When the number of predictors is huge, how can you compute or update the β coefficients of a linear regression in mini-batches without loading all data at once?
##### Hints
Discuss leverage-residual plots, robust loss, OOB importance, incremental least squares or SGD.
Overview: Evaluates robust house-price prediction modeling across diagnostics, features, scale, and validation. Strong answers cover linear regression diagnostics, Cook's distance, leverage, Random Forest complexity controls and variable importance, housing-market feature engineering, leakage prevention, large-scale training, and time-geography validation.
Design a Framework for a Robust House-Price Prediction Model
You are building and evaluating a supervised model to predict residential house prices in a city. The interview focuses on linear-model diagnostics, Random Forests, feature engineering, and large-scale regression training.
Constraints & Assumptions
Treat this as a modeling-framework question, not a request to train a model live.
Include both predictive performance and robustness.
Discuss diagnostics, feature choices, model alternatives, and scalability.
Avoid leakage from future sale information.
Clarifying Questions to Ask Guidance
Is the target sale price, appraised price, log price, or price per square foot?
What prediction time matters: listing, offer, appraisal, or sale closing?
Is interpretability required for business or regulatory reasons?
How large is the dataset and how frequently must the model refresh?
Part 1 - Linear Regression Diagnostics
In linear regression, how do you detect and handle outliers and influential points? Explain Cook's distance and high-leverage diagnostics.
What This Part Should Cover Guidance
Residuals, standardized residuals, leverage, hat matrix, Cook's distance, and practical thresholds.
How to investigate, correct, transform, winsorize, robustly model, or exclude points with justification.
Part 2 - Random Forests
How can you control complexity in Random Forests, and how do you compute and interpret variable importance?
What This Part Should Cover Guidance
Tree depth, minimum samples per leaf, number of features per split, number of trees, out-of-bag validation, and pruning-like controls.
Impurity-based importance, permutation importance, bias warnings, and interpretation limits.
Part 3 - House-Price Modeling Framework
Design a modeling framework to predict a city's house prices. Which factors and features would you include?
Feature preprocessing, missing values, spatial effects, time splits, and leakage prevention.
Part 4 - Large-Scale Linear Regression
When the dataset is very large, how would you train and evaluate linear regression efficiently?
What This Part Should Cover Guidance
Sparse features, regularization, stochastic or mini-batch optimization, distributed training, feature hashing, incremental updates, and scalable validation.
Metrics such as RMSE, MAE, MAPE, calibration by segment, and residual diagnostics.
What a Strong Answer Covers Guidance
A strong answer connects statistical diagnostics with production modeling: it handles outliers, chooses robust features, compares linear and tree models, scales training, and evaluates generalization across time and geography.
Follow-up Questions Guidance
How would you handle homes in neighborhoods with few recent sales?
What if Random Forest performs better but stakeholders need interpretability?
How would you detect model drift in a changing housing market?