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

Dhagash Mehta; Jingrao Lyu; Max Jarmey; Mingshu Li; Preetha Saha; Sebastian Frank; Sola Akinola; Sweet Kaur

REVIEW 3 major objections 8 minor 24 references

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

T0 review · 3 major / 8 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Private-company peers are best defined by a valuation-trained tree ensemble: importance-weighted leaf co-occurrences form a similarity metric that improves k-NN valuation over Euclidean, Gower, and text-embedding baselines in the…

desk verdict A competent application of known tree-proximity methods to private-market peer identification, but the headline improvement claim is thinner than the abstract suggests and needs stronger empirical support. read the letter →

arxiv 2608.12594 v1 pith:6JBL4QVJ submitted 2026-08-12 q-fin.ST cs.AIcs.LG

Sebastian Frank , Jingrao Lyu , Max Jarmey , Preetha Saha , Mingshu Li , Sweet Kaur , Sola Akinola , Dhagash Mehta This is my paper · ORCID

classification q-fin.STcs.AIcs.LG

keywords privatemarketscompanysimilaritysupervisedlearninggradient-boostedtreesleaf-nodeco-occurrencek-nearestneighborvaluationpost-moneypeeridentification

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that in private markets, where disclosure is sparse and transactions are infrequent, the meaning of "peer company" should be learned from market valuations rather than imposed by industry codes or text descriptions. It trains a gradient-boosted tree ensemble on 53,000 observed or derived post-money valuations and defines two companies as similar to the extent that the ensemble repeatedly routes them into the same terminal leaf, weighting each tree by its incremental reduction in training loss. That learned similarity is then used, independently of the model's own point predictions, to run k-nearest-neighbor valuation. In the evaluated industry groups the learned metric yields lower MAE and RMSE than Euclidean, Gower, and text-embedding distances, while keeping peer relationships explainable through the features that drive the splits. If the result holds, investors gain a data-driven, case-based way to define peer groups across sector, geographic, and stage boundaries.

What carries the argument

The central object is the tree-importance-weighted leaf-node co-occurrence similarity computed from an ensemble of gradient-boosted trees trained on log post-money valuation. For two companies $X_1$ and $X_2$, with $Z_{1,t}$ and $Z_{2,t}$ their terminal leaves in tree $t$, the similarity is $S(X_1,X_2)=\sum_t w_t\,\mathbb{I}[Z_{1,t}=Z_{2,t}]$, where $w_t$ is the normalized absolute reduction in training loss contributed by tree $t$; dissimilarity is $1-S(X_1,X_2)$. This turns the ensemble's splits into a pairwise geometry: firms are peers when valuation-relevant feature interactions repeatedly route them together, and the tree-boosting algorithm's handling of high-cardinality categorical variables and missing values makes the learned partitions feasible on sparse private-market data.

What would settle it

Train the identical ensemble and leaf-co-occurrence similarity on the subset of companies whose post-money valuations were directly observed, hold out the derived-valuation companies, and compare k-NN MAE and RMSE against the Euclidean, Gower, and text-embedding baselines; if the learned metric no longer dominates, or if nearest neighbors cluster by valuation-source type, the central claim is falsified.

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Extended reading notes

Core claim

The central claim is that company similarity in private markets is better modeled as an output of supervised valuation learning than as a static feature distance. After fitting a gradient-boosted tree model to log post-money valuation, the authors define the similarity of two companies as the importance-weighted frequency with which both are routed to the same terminal leaf across the ensemble; weights are each tree's absolute reduction in training loss. The complement of this score is a bounded pairwise dissimilarity that is symmetric but not necessarily metric. Using about 53,000 valuation targets drawn from a roughly 270,000-company global universe, the paper reports that k-nearest-neighbor valuation estimates built on the learned metric have lower MAE and RMSE than k-NN built on Euclidean, Gower, or text-embedding cosine distances in the evaluated industry groups, and that the neighborhoods are explainable through Shapley-value feature attributions.

Load-bearing premise

The method assumes that the 53,000 valuations used for training are economically comparable even when some are directly reported and some are reconstructed from deal terms or enterprise values; if reconstruction noise is substantial, the learned peer groups may reflect how valuations were computed rather than why companies are economic peers.

Editorial extensions

If this is right

k-nearest-neighbor valuation built on the learned similarity achieves lower MAE and RMSE than k-NN built on Euclidean, Gower, or text-embedding distances in the evaluated industry groups, without reusing the ensemble's own point predictions.
The same learned similarity matrix can support sourcing, benchmarking, and concentration risk analysis: firms that share valuation drivers appear as neighbors even when conventional sector or geography filters would separate them.
Because the similarity derives from a fixed trained ensemble, new companies can be projected into the same leaf-co-occurrence geometry, so peer relationships remain explainable by the features that drive the splits.
Valuation uncertainty and peer structure can be reported coherently from one fitted model, since conformal prediction intervals and the similarity matrix are both outputs of the same ensemble.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

An implication the authors leave implicit is that the same importance-weighted leaf co-occurrence construction transfers to any scarce-outcome private-market target, such as private-credit pricing or exit likelihood, whenever the target variable defines what economic peerhood should mean.
A testable diagnostic is to train the identical pipeline on only the directly observed post-money valuations and check whether the k-NN gains persist; if the metric no longer beats the baselines, the reported improvement is driven by construction patterns in derived valuation targets rather than economic content.
Because the training snapshot spans nearly fifty years with recency weighting, the learned geometry likely drifts with market conditions; a natural extension is to re-estimate the ensemble on rolling windows and compare k-NN error across vintages.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

You should know two things about this paper. First, the core method is not new: importance-weighted leaf-node co-occurrence from trees is Breiman proximity with a training-loss weighting, and this same group has applied it to corporate and municipal bonds. The genuine new piece is the application to private-company valuations at scale, with a focus on producing a reusable similarity matrix rather than just a prediction model. Second, the central claim of improvement over unsupervised baselines is plausible but under-supported as presented. The evaluation shows one industry group (Financial Services, 3.2k firms), gives no error bars or significance tests, and leaves out key implementation details like how the k-NN weights are computed. That is a fixable problem, not a fatal one.

The paper does several things well. The framework is clearly formalized in Eqs. 1-6, and the choice of CatBoost is sensible for high-cardinality categoricals and missing data; the use of ordered target statistics and ordered boosting shows attention to leakage. The conformal prediction intervals and SHAP analysis are nice additions that give the work practical texture. The writing is honest about what the metric is and is not (it does not satisfy the triangle inequality), and the related work is properly placed.

The soft spots are real and need to be addressed before I would trust the headline conclusion. The circularity concern is the most serious: the similarity is learned from the same post-money valuations that the k-NN evaluation uses as labels. The authors argue they do not reuse CatBoost predictions, but that misses the point. The similarity structure itself is supervised by those labels, so beating generic unsupervised distances may just mean the tree model has memorized the target well. A proper test would compare against a supervised baseline trained on a shuffled or unrelated target, or use nested cross-validation where the similarity is re-computed in each fold. The target construction heterogeneity is also a load-bearing concern. Section 4.1.1 lists four different ways to derive the post-money valuation, and these are not economically equivalent: enterprise value is not equity value, acquisition-percentage conventions vary, and deal size can include secondary shares. Because the construction method correlates with deal type and stage, the model may learn to cluster firms by how their valuation was computed rather than by economic peerhood. The stress-test note is right to flag this. A robustness check splitting the sample by direct vs. derived targets would be straightforward and should be standard.

There are also minor issues: the tree importance weighting via absolute training-loss difference is a reasonable heuristic but not deeply motivated, and the paper shows only one industry group in the k-NN experiment despite claiming multiple. The citation pattern is fine; earlier tree-proximity work is properly acknowledged.

This paper is for practitioners in private-market analytics and researchers applying tree-based ML to finance. It deserves a serious referee, not a desk reject, because the problem is important and the method is a credible adaption of known machinery. But the referee should require the authors to supply the missing robustness checks, error estimates, and code or data synthesis before publication. I would send it out, expecting at least major revision.

Referee Report

3 major / 8 minor

Summary. The manuscript proposes a supervised similarity-learning framework for private-market peer identification. The authors train a CatBoost gradient-boosted tree model on log post-money valuations of roughly 53,000 private companies and define pairwise company similarity as the tree-importance-weighted leaf-node co-occurrence frequency across the ensemble (Eqs. 1-6). They evaluate the learned dissimilarity in k-NN valuation tasks against Euclidean, Gower, and MPNet-embedding cosine baselines, reporting consistently lower MAE/RMSE in Financial Services, and also report SHAP-based and neighborhood-consistency analyses. The central claim is that the valuation-anchored similarity improves downstream k-NN valuation accuracy in the evaluated industry groups while retaining interpretability.

Significance. If the central claim holds, the framework would be a practically useful and commercially relevant extension of tree-proximity methods to private-market equity, and the paper would provide a concrete, explainable alternative to coarse-rule peer selection. The paper builds on established techniques (CatBoost, leaf-node co-occurrence, conformal prediction, SHAP) rather than introducing new theory, but the application domain and the explicit construction of a reusable pairwise similarity matrix are of potential interest to q-fin audiences. Strengths: the framework is clearly specified in closed form; the paper is candid about some limitations (dissimilarity not a metric, evaluation restricted to one industry group shown); the target construction and data provenance are described; and the design separates model fitting from test-set use. The empirical case is not yet convincing because results are shown for a single visible industry group with no uncertainty quantification.

major comments (3)

[Section 6.2 and Abstract] The central claim of improved downstream k-NN valuation over Euclidean, Gower, and MPNet baselines is supported only by a single visible figure for Financial Services (Figure 4). No other industry groups, no numeric MAE/RMSE values, no standard errors, and no significance tests are reported, so the stated claim that improvements hold 'in the evaluated industry groups' cannot be assessed. Please report per-industry-group numeric results with error bars or paired tests across all evaluated groups, or narrow the claim accordingly.
[Sections 3.4.1-3.4.2 and 6.2] The k-NN evaluation reuses as labels the same 53,000 log-valuation targets used to train the CatBoost model that defines the similarity metric (Eqs. 1-5). This is not a circular use of CatBoost predictions, but it does mean the comparison is supervised similarity against unsupervised baselines, which may largely reflect the value of supervision rather than the specific tree-weighting mechanism. To support the specific contribution, compare against an equally supervised baseline (e.g., random-forest proximity trained on the same target, or a metric learned by a deep metric-learning model), and report k-NN results with the tree-importance weights set to uniform to isolate the effect of Eq. 4.
[Sections 2.1 and 4.1.1] The target variable is assembled from four heterogeneous sources - direct post-money valuation, enterprise value, deal size divided by acquisition percentage, and pre-money value plus deal size/offering amount - that are not economically equivalent. Because source type is correlated with deal type and stage, CatBoost can in principle pick up construction-recipe signatures rather than economic peerhood, and the learned similarity could then group companies by how their valuations were computed. Please report the share of targets from each source, test whether learned neighborhoods and k-NN gains are stable within source groups, and, ideally, retrain on direct post-money valuations only as a robustness check.

minor comments (8)

[Section 3.4.1, Eqs. 3-4] The definition of training-loss improvement is a heuristic; note that because CatBoost uses ordered boosting with random permutations, training-loss differences are not variance-stabilized and the weights w_t can be dominated by noisy early iterations. A sentence acknowledging this and reporting the robustness of Eq. 5 to alternative weightings would strengthen the paper.
[Section 4.1.2 and Table 2] The descriptions of multi-label concatenation and the cardinality for 'Region and City (4,816)' are unclear; specify how multi-label deal types are combined and how the region-and-city cardinality was counted.
[Section 4.2.2] Recency-based sample weighting is described only qualitatively; provide the functional form of the weights or state explicitly that the weighting function is not disclosed.
[Section 5.2] The retransformation scaling factors of 1.74, 5.06, and 2.19 by deal type are surprisingly large; briefly explain why 'Unspecified' transactions require a factor above 5 and whether these factors are stable across folds.
[Section 5.1 and Table 4] The MAPE and MdAPE values are reported as percentages of log-space errors; clarify the definition because percentage errors are normally computed in level space, and the 0.05-0.07 values are not interpretable as conventional MAPE.
[Figures 3 and 4] The figure captions are too terse; Figure 3 and Figure 4 should state the plotted quantity, the number of companies, and the error metric used.
[Section 6.1] The claim that the learned metric shows 'mixed performance against Gower and Euclidean distances' on numerical features in Financial Services should be quantified or reconciled with the k-NN improvements in the same group.
[References] The paper cites arXiv preprint and SSRN references without DOIs or access dates; the reference list should be completed before publication.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the similarity derivation is self-contained and the k-NN evaluation is out-of-sample.

full rationale

The similarity metric (Eq. 5) is derived from CatBoost leaf co-occurrences and tree weights defined in Eqs. 3-4 from training-loss reductions; this is a standard supervised distance-learning construction and is not defined in terms of the k-NN estimates it later supports. The k-NN benchmarking (Section 6.2) evaluates test companies against a fixed training reference set, with test valuations used only in final evaluation (Section 4.2.1), so the predictions are out-of-sample. The tree-importance weighting and leaf assignments are learned from the training valuations, but the evaluation does not reuse the CatBoost point predictions; using the same training labels to build a supervised kernel and as k-NN neighbor labels is the intended supervised-learning protocol, not an equation-level identity. Self-citations to prior tree-proximity and bond/municipal similarity papers are related-work context and are not load-bearing for the derivation. The heterogeneous construction of the target valuation and the comparison against unsupervised baselines are potential validity and interpretation concerns, but they do not make the derivation circular.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the assumption that valuations are a reliable anchor, that leaf co-occurrence in a valuation model equals peerhood, and that the particular loss-based tree weighting captures the right geometry. The recency weights, feature thresholds, and winsorization are hand-set. No new physical or conceptual entities are introduced.

free parameters (4)

Recency-based training sample weights = Not specified
Section 4.2.2 states 'sample weights increase with transaction recency' but gives no formula or values; this hand-specified weighting changes the fitted trees and therefore every leaf co-occurrence.
Log-space retransformation scaling factors by deal type = Series: 1.74; Unspecified: 5.06; Other: 2.19
Section 5.2 estimates multiplicative factors on training data to correct retransformation bias. These affect the level-calibrated valuation estimates, though not the k-NN experiment.
Feature retention thresholds = 50% non-missing; zero-importance removal
Section 2.1 excludes categorical features with fewer than 50% non-missing values and removes zero-importance features. These thresholds determine the input space and hence the leaf structure.
Target winsorization percentiles = 1st and 99th
Section 4.1.1 winsorizes log valuations at the 1st and 99th percentiles, changing the target distribution used to train the similarity-defining model.

assumptions (5)

domain assumption Post-money valuation is a valid supervisory anchor for economic similarity.
Section 3.1 states valuations 'provide a market-based summary of company characteristics and future expectations.' The entire similarity definition depends on this equivalence.
domain assumption Frequent co-occurrence in leaves of a valuation prediction tree implies economic peerhood.
Section 3.2: 'firms are considered similar if they are repeatedly grouped together by the valuation model.' This is the definitional equivalence between tree geometry and peer meaning.
domain assumption CatBoost's ordered target statistics and ordered boosting eliminate target leakage into categorical encodings.
Section 3.3 claims leakage-resistant treatment; if leakage remains, the leaf structure, and hence the similarity, could be inflated by the target being predicted.
domain assumption The most recent transaction's features represent firms on a comparable footing across a 1977-2025 sample.
Section 4 uses the most recent post-money valuation as the target; Section 2 reports deal ages up to nearly 50 years with a median of 5 years. Mixing vintages without explicit regime controls is an assumption.
ad hoc to paper Training-loss improvement is the right measure of a tree's contribution to similarity.
Equations 3 and 4 define tree weights from absolute sequential training-loss reductions. No argument links loss improvement to valuation-relevant peer structure; an alternative weighting could change the metric.

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Cite this review

Pith. "Pith review of What Makes a Peer? Valuation-Anchored Similarity in Private Markets." pith.science (2026). https://pith.science/paper/6JBL4QVJ

@misc{pith2026260812594,
  author       = {Pith},
  title        = {Pith review of: What Makes a Peer? Valuation-Anchored Similarity in Private Markets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6JBL4QVJ}},
  note         = {Machine review of arXiv:2608.12594}
}

read the original abstract

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.

Figures

Figures reproduced from arXiv: 2608.12594 by the authors.

**Figure 2.** Bar Plot of Absolute Mean SHAP values 6.1 Neighborhood Analysis The objective of the similarity evaluation is to determine whether the learned metric produces economically coherent peer groups and captures meaningful relationships between private companies. We assess this both qualitatively, through neighborhood consistency, and quantitatively, through comparisons with established distance and embedding based baseli… view at source ↗

**Figure 3.** Financial Services (3.2k firms) [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: k-NN Valuation by Neighborhood Size and Distance Metric [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

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