Principled Federated Random Forests for Heterogeneous Data

Aur\'elien Bellet; Erwan Scornet; Julie Josse; R\'emi Khellaf

arxiv: 2602.03258 · v2 · submitted 2026-02-03 · 📊 stat.ML · cs.LG

Principled Federated Random Forests for Heterogeneous Data

R\'emi Khellaf , Erwan Scornet , Aur\'elien Bellet , Julie Josse This is my paper

Pith reviewed 2026-05-16 07:54 UTC · model grok-4.3

classification 📊 stat.ML cs.LG

keywords federated learningrandom forestsheterogeneous datadecision treessplit selectionimpurity criterionpersonalization

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The pith

FedForest approximates centralized random forest splits by aggregating local client statistics even when data distributions differ across clients.

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

Random forests are powerful for tabular data but resist standard federated learning because their splits are chosen by impurity measures rather than gradients. FedForest solves this by having each client compute and transmit a small set of statistics about potential splits, which the server combines to pick the split that nearly matches the one a centralized algorithm would choose. The paper proves this approximation holds under several forms of heterogeneity, including shifts in outcomes as well as features. The same mechanism also permits splits that depend on which client an observation came from, giving a built-in non-parametric way to personalize predictions. The result is a forest that performs close to a centralized model while exchanging only compact summaries instead of raw records.

Core claim

The paper establishes that a splitting procedure based on aggregating carefully chosen client statistics closely approximates the split that would be selected by a centralized random forest algorithm. Furthermore, by allowing splits on client indicators, FedForest introduces a non-parametric personalization mechanism absent from previous federated random forest approaches. The method accommodates various heterogeneity types including covariate and outcome shifts.

What carries the argument

The aggregation of local counts or impurity contributions from each client to select tree splits that optimize the global criterion.

If this is right

The federated forest achieves predictive performance close to a centralized random forest across heterogeneous benchmarks.
Only summary statistics are exchanged, keeping communication low.
Splits on client indicators enable non-parametric personalization without extra parameters.
The procedure handles both simple covariate shifts and more complex outcome-shift mechanisms.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The approach could be directly useful for tabular prediction tasks in privacy-sensitive settings such as clinical data where central pooling is restricted.
Similar aggregation ideas might be tested on other non-differentiable models like gradient-boosted trees.
Empirical checks on regimes with hundreds of clients or very high-dimensional features would reveal where the approximation begins to degrade.

Load-bearing premise

The local client statistics remain sufficient to recover near-optimal splits even under complex outcome shifts without the approximation error growing too large.

What would settle it

A high-dimensional dataset with strong outcome shifts across clients where the splits chosen by FedForest differ markedly from centralized splits and produce substantially worse held-out accuracy.

read the original abstract

Random Forests (RF) are among the most powerful and widely used predictive models for centralized tabular data, yet few methods exist to adapt them to the federated learning setting. Unlike most federated learning approaches, the piecewise-constant nature of RF prevents exact gradient-based optimization. As a result, existing federated RF implementations rely on unprincipled heuristics: for instance, aggregating decision trees trained independently on clients fails to optimize the global impurity criterion, even under simple distribution shifts. We propose FedForest, a new federated RF algorithm for horizontally partitioned data that naturally accommodates diverse forms of client data heterogeneity, from covariate shift to more complex outcome shift mechanisms. We prove that our splitting procedure, based on aggregating carefully chosen client statistics, closely approximates the split selected by a centralized algorithm. Moreover, FedForest allows splits on client indicators, enabling a non-parametric form of personalization that is absent from prior federated random forest methods. Empirically, we demonstrate that the resulting federated forests closely match centralized performance across heterogeneous benchmarks while remaining communication-efficient.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

FedForest gives a clean aggregation rule for federated RF splits plus client-indicator personalization, but the approximation's error under strong outcome shifts still needs explicit bounds.

read the letter

The main advance is a splitting procedure that pools selected local client statistics to approximate the global impurity reduction, plus the option to split on client indicators for built-in personalization. This moves past the usual heuristic of training separate trees and averaging them, which the abstract notes fails to optimize the joint criterion even under simple shifts. The proof sketch that the aggregated choice stays close to the centralized one is the core technical piece, and the client indicators add a non-parametric handle on heterogeneity without extra modeling assumptions. The method also claims to stay communication-efficient by sending only the needed counts rather than full data or gradients. Empirically the abstract reports performance close to a centralized forest across heterogeneous benchmarks, which would be useful for tabular settings where random forests remain standard. The soft spot is the approximation guarantee itself. The stress-test concern is fair: when outcome shifts are strong or features high-dimensional, the aggregated statistics could select a different split than the true global argmax, and without seeing the explicit error bound and its dependence on heterogeneity strength it is hard to judge how tight the approximation stays in the regimes the method targets. The experiments are described as matching centralized results, but details on the shift severity and dimension would clarify whether the claim generalizes. This is for people working on federated tabular models or privacy-preserving ensembles. A reader who needs a non-heuristic tree method for horizontal partitions would get concrete value from the procedure and the reported results. The work has enough new substance and grounding to deserve a serious referee, mainly to tighten the bounds and check the experiments under heavier heterogeneity.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces FedForest, a federated random forest algorithm for horizontally partitioned data. It claims a splitting procedure that aggregates selected client statistics (local counts or impurity contributions) to closely approximate the centralized optimal split, provides a proof of this approximation, permits splits on client indicator variables for non-parametric personalization, and reports empirical results showing performance parity with centralized RF across heterogeneous benchmarks while remaining communication-efficient.

Significance. If the approximation result holds with error bounds that remain controlled under outcome shift and moderate heterogeneity, the work would fill a notable gap in federated learning for piecewise-constant models. It supplies a principled aggregation rule rather than heuristics, introduces a lightweight personalization mechanism absent from prior federated RF methods, and demonstrates practical viability on tabular data. These elements would be of interest to both the federated-learning and tree-ensemble communities.

major comments (2)

[§4] §4 (Approximation theorem): The proof establishes that the aggregated impurity reduction approximates the centralized argmax but supplies no explicit error bound (e.g., in terms of total-variation distance between client conditional distributions or feature dimension). Without such a bound the claim that the procedure 'closely approximates' the centralized split under complex outcome shifts remains unquantified and load-bearing for the central contribution.
[§5.2] §5.2 (Heterogeneity experiments): The reported benchmarks use moderate covariate and label shifts; no results are shown for high-dimensional feature spaces or extreme per-client outcome heterogeneity where the approximation error could accumulate across trees. This leaves open whether performance parity holds precisely in the regimes the method is intended to address.

minor comments (2)

[§3] Notation for the aggregated client statistics (local counts, impurity contributions) is introduced without a compact table or pseudocode block; a single-line definition would improve readability.
[Abstract] The abstract states 'we prove' without a theorem number or reference to the section containing the formal statement.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address each major comment below and describe the revisions we will incorporate.

read point-by-point responses

Referee: [§4] §4 (Approximation theorem): The proof establishes that the aggregated impurity reduction approximates the centralized argmax but supplies no explicit error bound (e.g., in terms of total-variation distance between client conditional distributions or feature dimension). Without such a bound the claim that the procedure 'closely approximates' the centralized split under complex outcome shifts remains unquantified and load-bearing for the central contribution.

Authors: We appreciate the referee pointing out the need for a quantitative bound. The existing proof in §4 shows that the federated split matches the centralized choice exactly under identical client distributions and provides a qualitative argument for approximation under heterogeneity via convex combination of local statistics. We agree that an explicit error bound would strengthen the central claim. In the revision we will add a corollary deriving a bound on the impurity-reduction difference in terms of total-variation distance between client conditionals and feature dimension. revision: yes
Referee: [§5.2] §5.2 (Heterogeneity experiments): The reported benchmarks use moderate covariate and label shifts; no results are shown for high-dimensional feature spaces or extreme per-client outcome heterogeneity where the approximation error could accumulate across trees. This leaves open whether performance parity holds precisely in the regimes the method is intended to address.

Authors: The current experiments use established heterogeneous tabular benchmarks that already contain non-trivial covariate and label shifts. We concur that additional stress tests under high-dimensional features and extreme per-client outcome heterogeneity would better demonstrate robustness. In the revised manuscript we will include new synthetic experiments with feature dimension up to 100 and controlled extreme outcome shifts to verify that performance parity with centralized RF is preserved. revision: yes

Circularity Check

0 steps flagged

No significant circularity: central claim rests on explicit proof of approximation rather than reduction to fitted inputs or self-citations

full rationale

The paper's derivation chain centers on a mathematical proof that aggregating chosen client statistics (local counts or impurity contributions) yields splits closely approximating the centralized optimum. This is presented as an independent verification step rather than a self-definitional equivalence, a fitted parameter renamed as prediction, or a load-bearing self-citation. No equations or claims reduce by construction to the inputs; the approximation guarantee is argued via proof with stated assumptions on heterogeneity, keeping the result self-contained. Minor self-citations, if present, are not load-bearing for the core splitting procedure.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The method assumes standard horizontal partitioning and that local client statistics (counts or impurity contributions) can be computed and shared without violating privacy. No free parameters or new invented entities are introduced in the abstract.

axioms (2)

domain assumption Data is horizontally partitioned across clients with no vertical features shared.
Stated in the abstract as the setting for FedForest.
domain assumption Clients can compute and transmit local split statistics (e.g., class counts per feature bin) without revealing individual records.
Implicit in the aggregation procedure described.

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discussion (0)

Lean theorems connected to this paper

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unclear
Relation between the paper passage and the cited Recognition theorem.

We prove that our splitting procedure, based on aggregating carefully chosen client statistics, closely approximates the split selected by a centralized algorithm.

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