What Makes a Peer? Valuation-Anchored Similarity in Private Markets

As more investors contemplate private markets and contend with limited transparency, sparse disclosures, and infrequent transactions, identifying economically meaningful peer companies for comparison is a fundamental challenge for valuation, due diligence, portfolio construction, and risk management. We propose an ensemble tree-based supervised similarity learning framework that defines company similarity through the lens of market valuation rather than static feature matching or semantic descriptions. Specifically, we train a CatBoost gradient-boosted decision tree model on observed private company valuations and derive a valuation-aware similarity metric from importance-weighted leaf-node co-occurrences across the ensemble. The similarity metric captures shared valuation drivers while accommodating nonlinear relationships, mixed data types, and pervasive missing data common in private markets. Using a global private-market universe of approximately 270,000 companies, including more than 53,000 firms with observed or derivable post-money valuations spanning multiple industries, geographies, and deal stages, we demonstrate that the proposed similarity framework improves upon traditional distance-based and text-embedding-based approaches in downstream k-nearest-neighbor valuation tasks in the evaluated industry groups, while retaining case-based explainability.

Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification

Data valuation, the task of quantifying the contribution of individual data points to model performance, has emerged as a fundamental challenge in machine learning. Game-theoretic approaches, such as the Banzhaf value, offer principled frameworks for fair data valuation; however, they suffer from exponential computational complexity. We address this challenge by developing efficient algorithms specifically tailored for computing Banzhaf values in $k$-nearest neighbor ($k$NN) classifiers. We first establish the theoretical hardness of the problem by proving that it is \#P-hard. Despite this intractability, we exploit the locality properties of $k$NN classifiers to develop practical exact algorithms. Our main contribution is a dynamic programming framework that achieves significant computational improvements: we present a pseudo-polynomial algorithm with $O(Wkn^2)$ time complexity for weighted $k$NN classifiers, where $W$ is the maximum sum of top-$k$ weights, and a specialized algorithm for unweighted $k$NN that achieves $O(nk^2)$ time complexity, that is, linear in the number of data points. We also offer efficient Monte Carlo estimation methods. Extensive experiments on real-world datasets demonstrate the practical efficiency of our approach and its effectiveness in data valuation applications.