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.

Doing well with less! On Sampling Techniques for Empirical Pairwise Loss Estimation/Minimization

Many machine learning problems, including similarity learning, ranking, and clustering, rely on empirical pairwise loss functions whose quadratic computational cost quickly becomes prohibitive at scale. We demonstrate how a frugal approach that retains only a fraction of the available information on pairs can achieve estimation or optimization performance comparable to that obtained by using all pairs, by leveraging survey sampling techniques. A central finding, supported by both theory and experiments, is that such sampling plans must target pairs directly rather than individual observations. In particular, for pairwise losses between high-dimensional vectors such as embeddings in vision or graph learning, assigning higher inclusion probabilities to informative pairs using suitable auxiliary information yields performance close to full pairwise evaluation, providing a principled and theoretically grounded trade-off between accuracy and computational cost.