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FedIncome: Federated Learning for Income Estimation in Digital Lending Under Data Sovereignty Constraints

Sultan Amed, Tanmay Sen, Sayantan Banerjee

arXiv:2609.27654v1stat.MLcs.LGq-fin.ST

TL;DR

Lenders often lack verified income, while data-sharing constraints limit pooling records that could help smaller institutions estimate it. FedIncome uses federated learning to train a shared income model without pooling raw records, and its best model approaches pooled performance while improving on local-only training. The paper also evaluates how replacing reported income affects simulated lending decisions under location-aware DTI rules.

  • Problem

    Verified income is often unavailable, and privacy, governance, or commercial constraints can prevent lenders from pooling records for income estimation.

    Source: §1 · p. 2

  • Method

    FedIncome trains residual multilayer perceptrons across clients, compares five aggregation procedures, and applies estimates to state- and income-specific DTI thresholds.

    Source: §1 · p. 3

  • Results

    FedNova achieves out-of-time R2 of 0.608 versus 0.619 for pooled centralised training, while federation improves out-of-time performance over local-only training across all sample-size groups.

    Source: §7 · p. 26

  • Takeaways & Limitations

    FedIncome supports collaborative learning under data-locality constraints, with relatively small aggregate loss versus pooled training and larger gains versus local-only estimation.

    Source: §7 · p. 26

    The 50 state-level clients are simulated from one LendingClub platform, so the analysis does not capture cross-lender differences in underwriting, measurement, missingness, features, or data quality.

    Source: Limitations and Further Research · p. 25

Abstract

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Verified income is often unavailable in digital loan applications, forcing lenders to rely on reported income and potentially leading to over-lending, overly conservative offers, or rejection of creditworthy applicants. Cross-institutional data-sharing constraints make this problem especially difficult for smaller lenders with limited training data. We introduce FedIncome, a federated learning framework for income estimation that enables institutions to train a shared model without pooling raw borrower records. Using more than one million LendingClub loans partitioned into $50$ state-level clients, we simulate a heterogeneous lending consortium. The best federated model achieves out-of-time $R^2=0.608$, compared with $0.619$ for a pooled centralised benchmark. Small-sample clients obtain an average out-of-time $R^2$ improvement of $3.8$ percentage points relative to the pooled centralised benchmark, while the fitted client-level relationship places the empirical crossover at approximately $4,790$ training observations in this setting. When pooling is infeasible and the relevant alternative is local-only training, federation improves out-of-time performance across all sample-size groups, with the largest gains for data-scarce clients. We also combine federated income estimates with state- and income-specific debt-to-income thresholds. In a retrospective decision analysis, replacing reported income with the federated estimate increases simulated approval rates with only modest changes in observed default rates. FedIncome supports collaborative learning under data-locality constraints with little aggregate loss relative to pooled training and larger gains relative to local-only estimation.

1 Introduction

Income estimates shape affordability decisions, but scarce verified records and restrictions on pooling make reliable models difficult for smaller lenders. FedIncome studies federated income regression against pooled and local-only alternatives, then examines its effects in location-aware DTI decisions.

1 Introduction

  • Income errors can move applicants across approval boundaries: overestimation may yield unaffordable loans, while underestimation may restrict offers or reject creditworthy applicants.DTI compares monthly debt obligations with gross monthly income and informs approval and loan size.Source: §1 · p. 2
  • Pooling may be infeasible for privacy, governance, or commercial reasons, making local-only model development the relevant alternative under stricter data-sovereignty constraints.Federated learning trains a shared model while borrower-level records remain with participating institutions, though model updates may still reveal information without additional safeguards.Source: §1 · pp. 2–3
  • FedIncome compares five federated aggregation procedures for income estimation and links estimates to state- and income-specific DTI thresholds to study lending outcomes.The framework uses residual multilayer perceptrons; the analysis compares approval and default outcomes when reported income is replaced by a federated estimate.Source: §1 · pp. 3–4
  • The study partitions LendingClub records into 50 state-level clients, creating sample-size and regional-income variation while holding feature definitions and data collection fixed.The clients are simulated institutions, so the design does not capture every form of heterogeneity in a real consortium.Source: §1 · p. 3
  • For clients with fewer than 1,807 training observations, federation improves out-of-time R2 by 3.8 percentage points versus pooled centralised training; the fitted crossover is about 4,790 observations.The crossover is specific to this LendingClub experiment, not a general participation rule; versus local-only training, federation improves out-of-time R2 across all sample-size groups, with largest gains for data-scarce clients.Source: §1 · p. 3
  • 0.608 out-of-time R2 for FedNova versus 0.619 for the pooled centralised benchmark; FedNova’s MAPE is 31.8% versus 35.6%.The MAPE difference is concentrated among low- and middle-income borrowers, so the relative model ranking depends on the loss measure and response range.Source: §1 · p. 3

2 Related Work

Prior income-estimation work and federated finance studies leave gaps around continuous income regression across data-constrained institutions and the downstream consequences of prediction differences. FedIncome connects federated prediction, client-level comparisons, and threshold-based lending decisions.

Income Estimation in Consumer Credit

  • Existing income-estimation work relies on single-institution data or proprietary alternative data, leaving settings with distributed records that cannot be pooled less directly addressed.This distinction matters because institutions with the smallest historical portfolios may have the greatest need for additional information.Source: §2 · p. 4

Research Gaps and Contribution

  • Federated financial applications largely address classification, while continuous income regression is less studied despite income’s skew, client heterogeneity, and role in affordability calculations.The review identifies a gap in evaluating federated regression under a common architecture, client-participation scheme, and temporal validation design.Source: §2 · pp. 4–5

Federated Learning in Financial Services

  • The review distinguishes federation’s comparison with pooled training from its comparison with local-only training: these address data-boundary costs and collaboration’s value when pooling is infeasible, respectively.The paper retains both benchmarks in its empirical analysis.Source: §2 · pp. 4–5

Data Sharing, Privacy, and Institutional Heterogeneity

  • Federation avoids routine transfer of raw borrower records, but updates can reveal information; it is a data-local training architecture, not by itself a formal privacy guarantee.Formal privacy mechanisms such as differential privacy or secure computation involve additional statistical or computational costs.Source: §2 · p. 5

Research Gaps and Contribution

  • FedIncome evaluates how federation’s gains vary with client sample size and adds a local-only counterfactual for data-sovereignty settings where pooling is ruled out.Its client-level risk decomposition allows federated and pooled estimator rankings to change with client size.Source: §2 · p. 5
  • The paper connects federated income predictions to state- and income-specific DTI thresholds and examines resulting approval and default outcomes.Its methodological analysis distinguishes prediction discrepancy from decision discrepancy and relates income-estimation error to disagreement between DTI-based rules.Source: §2 · p. 5

3 Methodology

This section describes FedIncome’s approach to estimating income across heterogeneous clients while keeping borrower records local, including federated optimization, aggregation, and risk-controlled threshold calibration. It also presents a deployment analysis comparing DTI-based approvals using reported and federated income, measuring changes relative to reported income.

3.1 Problem Formulation and Assumptions

  • The framework minimizes a sample-size-weighted income-prediction objective, while federation approximates collaborative training without moving borrower records; its assumptions cover verified labels, common features, and non-strategic client participation.The baseline protects raw-data locality but does not itself guarantee confidentiality of model updates; stronger privacy mechanisms can be added.Source: §3.1 · p. 7

3.2 Federated Learning; 3.2.1 Training Procedure

  • FedIncome simulates 50 state-level clients with training samples from 743 to 68,743 observations and differing income distributions, as controlled proxies for heterogeneous institutions.In each communication round, the server selects clients, broadcasts global parameters, receives local updates, and aggregates them while records remain local.Source: §3.2 · p. 7, §3.2.1 · pp. 7–8

3.2.2 Aggregation Strategies

  • The five compared aggregators are FedAvg, FedProx, SCAFFOLD, FedAdam, and FedNova, which address weighted averaging, local drift, update-direction differences, adaptive server optimization, and unequal local computation.FedProx adds a proximal penalty, while SCAFFOLD uses client and server control variates to correct systematic differences between local and global update directions.Source: §3.2.2 · p. 8

3.2.3 A Client-Level Federation–Centralisation Crossover

  • Under the stylized risk decomposition, federation can have a sample-size-dependent advantage for small clients and persistent client-specific costs, with a sign change near Ck/Bk rather than a universal cutoff.The quantities governing that crossover depend on client distributions, consortium representation, architecture, participation, and optimization configuration.Source: §3.2.3 · p. 9

3.3 Location-Aware Debt-to-Income Calibration; 3.3.1 Income Stratification

  • The decision rule translates estimated income into affordability through DTI and allows thresholds to vary jointly by state and income stratum, estimated from verified-income borrowers.For deployment-tier borrowers, the policy stratum is assigned using reported income and held fixed when the income measure in the DTI denominator is replaced.Source: §3.3 · pp. 9–10, §3.3.1 · p. 10

3.3.2 Threshold Optimization

  • For each state-stratum cell, the policy selects the most permissive DTI threshold whose approved population stays within the state-level default-risk ceiling, balancing approval access against observed risk.The ceiling is set to the state’s overall observed default rate among verified borrowers and held fixed across income strata.Source: §3.3.2 · pp. 10–11

3.3.3 Estimation Algorithm

  • Threshold estimation searches candidate DTI percentiles and chooses the highest-approval option meeting the empirical risk ceiling, with median imputation for cells under 30 observations and a conservative fallback if none qualifies.The same verified sample for construction and evaluation makes this an empirical policy-selection rule, not a finite-sample population-risk guarantee; independent calibration is proposed for formal control.Source: §3.3.3 · pp. 11–12
  • Section 5.4.3 uses Algorithm 1, while Theorem 3.1 describes a separate risk-controlled extension.If the state-level ceiling is estimated rather than fixed, its sampling uncertainty must enter the confidence bound; the theorem excludes cells using small-cell imputation or fallback.Source: §3.3.3 · p. 13

3.3.4 Application to Deployment-Tier Borrowers

  • The deployment analysis replaces reported income with FedNova predictions while keeping the income stratum and policy threshold fixed based on reported income.Reported income is an operational reference, not verified ground truth; the analysis does not establish that either income measure equals latent true income.Source: §3.3.4 · p. 13
  • Approval decisions can differ when reported and predicted incomes diverge, especially for applicants close to the applicable DTI threshold.Proposition 3.3 identifies income discrepancy and distance from the policy boundary as the two sources of decision sensitivity.Source: §3.3.4 · p. 13

4 Experimental Setup

The experiments use LendingClub records to train and evaluate income models, with verified-income records supplying training labels and other verification groups used for DTI decision analysis. They compare predictive metrics across time and implement federated and centralised pipelines with different preprocessing information constraints.

4.1 Data Description

  • Verified-income records provide training labels, while source-verified and not-verified records are reserved for comparing reported income with FedIncome estimates in DTI decision analysis.LendingClub records are partitioned into state-level clients; source-verified records have a verified source but an unconfirmed amount, while not-verified income is self-reported.Source: §4.1 · p. 14

4.2 Performance Metrics

  • R2 measures explained variation and RMSE measures error on the original income scale, with larger deviations receiving relatively greater weight.Source: §4.2 · p. 14
  • MAPE expresses error relative to observed income, while MBE captures prediction direction; all four metrics are computed in-time and out-of-time.MAPE is interpreted jointly with R2 and RMSE because smaller denominators receive greater weight; positive MBE indicates overprediction and negative MBE underprediction.Source: §4.2 · p. 15

4.3 Implementation Details

  • A residual multilayer perceptron is evaluated with five aggregation procedures in a common simulation framework, using layer normalization for clients with substantially different sample sizes.The model has hidden dimension 256, three residual blocks, and dropout rate 0.3; federated training uses 10 communication rounds, 10 local epochs, and 30% client participation per round.Source: §4.3 · p. 15
  • Centralised preprocessing uses pooled training statistics, whereas federated preprocessing uses client-specific statistics, so the comparison tests complete pipelines under different information constraints.Each pipeline imputes missing values with training-set medians and standardizes numerical features; no borrower observations are pooled for federated preprocessing.Source: §4.3 · p. 15

5 Experimental Results and Analysis

The analysis selects a Residual MLP for federation, compares FedNova with pooled training, and examines client-size differences and DTI-based lending decisions. Results vary by metric and client group; retrospective approval changes are descriptive, not causal.

5.2 Federated versus Centralized Performance

  • FedNova attains OOT R2 = 0.608 versus 0.619 for the pooled centralized benchmark, a relative R2 gap of approximately 1.8%.Its OOT RMSE is $32,869 versus $32,394 centrally, an increase of approximately $475.Source: Table 4 · p. 17, §5.2.1 · p. 17

5.2.1 Aggregate Performance Gap

  • FedNova records OOT MAPE of 31.83% versus 35.59% centrally, with its advantage concentrated in low- and middle-income terciles.MAPE is lower by 7.5 and 4.7 percentage points in the low- and middle-income terciles, respectively, while centralization performs better by 1.2 points in the high-income tercile.Source: §5.2.1 · pp. 17–18, Table 5 · p. 18

5.2.2 Aggregation Strategy Comparison

  • FedNova and FedAvg perform best among the federated procedures, while SCAFFOLD performs substantially worse under this configuration.Over 10 communication rounds, FedNova and FedAvg improve smoothly toward similar final values; the empirical ranking is specific to this experimental design.Source: §5.2.2 · p. 18, §5.2.3 · p. 18

5.3.1 Stratified Analysis by Sample Size

  • Low-sample clients (mean training size n = 936) gain 3.8 percentage points in OOT R2 with FedNova, while high-sample clients slightly favor centralization.Low-sample client win rates are 70.6% in-time and 76.5% out-of-time; FedNova has lower average MAPE across all three sample-size categories.Source: §5.3.1 · pp. 18–19, Table 6 · p. 20

5.3.2 Empirical Calibration of the Crossover

  • The fitted federation–centralization relationship crosses near 4,790 training observations in this experiment; federation also beats local-only training across observed size groups, especially for smaller clients.The crossover depends on the sample, partition, architecture, preprocessing, participation, communication budget, and aggregation method; it is not a general participation rule.Source: §5.3.2 · pp. 20–21, Figure 6 · p. 21, §5.3.3 · p. 21

5.4.1 Optimal Threshold Heterogeneity

  • Estimated DTI thresholds range from 11.2% to 46.7% across state–income cells, and mean thresholds rise from 22.7% in the low-income stratum to 28.9% in the high-income stratum.Substantial within-stratum dispersion indicates that the relation between DTI and observed default differs across states.Source: Table 7 · p. 21, §5.4.1 · pp. 21–22

5.4.2 DTI Distribution Shifts

  • Replacing reported income with FedNova predictions shifts DTI distributions in the source-verified and not-verified groups, while observed default generally increases with DTI under both inputs.For those deployment groups, the shifts cannot distinguish reporting error from model error, and default-profile differences do not establish recovery of true income or correction of misreporting.Source: Figure 7 · p. 22, §5.4.2 · p. 22, §5.4.3 · p. 22

5.4.4 Approval and Default Trade-offs

  • Predicted income raises simulated approvals by 4.6 percentage points in the source-verified group and 7.8 points in the not-verified group, with observed defaults among approved loans rising 0.29 and 0.31 points, respectively.These retrospective comparisons do not observe counterfactual repayment behavior under alternative loan terms, and no independent income benchmark establishes whether decisions move closer to latent true income.Source: §5.4.4 · pp. 22–23, Table 8 · p. 23

6 Discussion

FedIncome approaches pooled income-regression performance overall, but its relative value varies by client size and by whether pooling is feasible. The discussion connects income predictions to DTI-based decisions while emphasizing that the empirical findings are bounded by the study’s data, training setup, and retrospective design.

Methodological Contributions

  • FedNova achieves out-of-time R2 of 0.608 versus 0.619 for the pooled centralized benchmark, with lower MAPE particularly in low- and middle-income portions of the distribution.Because preprocessing information differs between the pipelines, this comparison describes complete training regimes rather than aggregation alone.Source: Methodological Contributions · p. 24
  • Low-sample clients gain an average 3.8 percentage points in out-of-time R2 over the pooled centralized benchmark, while high-sample clients show a small average centralized advantage.The fitted client-level relationship places the empirical crossover at approximately 4,800 training observations in this experiment, not as a universal participation threshold.Source: Methodological Contributions · p. 24
  • Against local-only training, FedNova improves out-of-time performance across all observed sample-size groups, with the largest gains among data-scarce clients.The pooled benchmark measures the cost of respecting data boundaries; the local-only comparison measures collaboration’s value when pooling is unavailable.Source: Methodological Contributions · p. 24
  • Income predictions matter for approval only when they change an applicant’s position relative to a DTI threshold; discrepancies farther from the boundary need not change decisions.Smaller discrepancies can matter near the threshold.Source: Methodological Contributions · p. 24
  • FedNova and FedAvg perform best in this experiment, but the ranking is specific to partial participation, a finite communication budget, nonlinear models, and a strongly skewed response.The result is not a general ordering of federated algorithms or a contradiction of theoretical guarantees.Source: Methodological Contributions · p. 24

Practical Implications

  • Replacing reported income with FedNova predictions raises simulated approval rates by 4.6 percentage points for source-verified and 7.8 for not-verified applicants, while observed default rates rise by 0.29 and 0.31 percentage points, respectively.These retrospective comparisons do not estimate causal deployment effects or observe repayment behavior under changed approvals or loan terms.Source: Practical Implications · p. 25

Limitations and Further Research

  • Raw-data locality alone gives no formal privacy guarantee, preprocessing differs between centralized and federated pipelines, and the DTI analysis is retrospective rather than causal.The study also treats verified income as its target despite possible measurement error, lacks true income in deployment groups, and studies income prediction as a standalone task.Source: Limitations and Further Research · pp. 25–26
  • The federation simulates one LendingClub platform partitioned across states, holding feature definitions and data collection fixed while omitting cross-lender differences in policies, measurement, missingness, features, and data quality.The direction of these omitted differences’ effect is unknown; validation on genuinely multi-institutional data is an identified next step.Source: Limitations and Further Research · p. 25

7 Conclusion

The paper proposes FedIncome for continuous income regression when borrower records cannot be freely pooled. In state-partitioned LendingClub data, FedNova performs close to pooled training overall and improves on local-only training across sample-size groups; retrospective DTI analyses show approval-rate changes alongside small observed default-rate changes.

7 Conclusion

  • FedIncome lets participating clients retain borrower records locally while contributing to a shared continuous income-regression model.The evaluation uses more than one million LendingClub loans partitioned across 50 state-level clients.Source: §7 · p. 26
  • FedNova achieves out-of-time R2 of 0.608 compared with 0.619 for the pooled centralized benchmark, while federation improves performance over local-only training across sample-size groups.Gains are largest among data-scarce clients.Source: §7 · p. 26
  • Replacing reported income with FedNova predictions raises simulated approval rates by 4.6 percentage points in the source-verified group and 7.8 in the not-verified group, with observed default rates rising by 0.29 and 0.31 percentage points, respectively.These are retrospective results, not causal policy effects.Source: §7 · p. 26
  • Federated income estimation supports collaborative learning under data-locality constraints with relatively small aggregate loss versus pooled training and larger gains versus local-only estimation.The findings underscore evaluating federated systems at the client level and tracing prediction differences through downstream decision rules.Source: §7 · p. 26

A Related Work Synthesis

The synthesis situates FedIncome among income-estimation research and industry approaches, and records its federated design and principal performance comparison.

A Related Work Synthesis

  • The synthesis reviews predictive approaches, data sources, and application settings relevant to income estimation.Its table is titled as a synthesis of income-estimation research and related industry approaches.Source: A Related Work Synthesis · p. 30, Table 9 · p. 30
  • The table’s stated columns are study, objective, method, data, and main finding.The supplied entries identify Aruhan et al. (2020) as automating income verification in loan origination with a machine-learning pipeline using applicant and income-document information.Source: A Related Work Synthesis · p. 31
  • FedIncome is summarized as federated income estimation without borrower-record pooling, using more than one million LendingClub loans across 50 state-level clients and a residual MLP with five aggregation procedures.FedNova’s out-of-time R2 is 0.608 versus 0.619 for the pooled centralized benchmark; gains are largest for data-scarce clients and positive versus local-only training across sample-size groups.Source: A Related Work Synthesis · p. 31
  • The synthesis notes that data-local federated training does not itself provide a formal privacy guarantee.Borrower-level records are not pooled during model training.Source: A Related Work Synthesis · p. 31

B.1 Centralized Benchmark Models

The centralized benchmark selects a Residual MLP after comparing six model families, then uses that architecture for federated experiments. The appendix describes its residual-block design and contrasts pooled training with local-only training when pooling is unavailable.

B.1 Centralized Benchmark Models

  • The Residual MLP has the strongest out-of-time R2 among six pooled-data model families and is selected as the federated base model.The candidates include linear, tree-based, FT-Transformer, and Residual MLP models.Source: §B.1 · p. 31

B.2 Residual MLP Architecture

  • The federated Residual MLP maps features through an input projection, three residual blocks, and a linear output layer that predicts scalar income.Each block applies Linear, LayerNorm, ReLU, and Dropout before an additive skip connection.Source: Figure 9 · p. 31, §B.2 · p. 32
  • Layer normalization avoids dependence on batch-level moments, while additive skip connections support residual transformations and optimization in deeper networks.The specified model uses hidden dimension 256 and dropout probability 0.3.Source: §B.2 · p. 32
  • Training uses Adam, learning rate 0.001, weight decay 10^-4, batch size 16, mean squared error, and 10 local epochs per client before aggregation.The same architecture is used across aggregation procedures so predictive differences reflect training rules rather than model specification.Source: §B.2 · p. 32

C.1 Motivation

  • When pooling is unavailable, the relevant alternative to federation is local-only training on each institution’s own observations.The pooled comparison measures decentralized training against a combined-data benchmark; the local comparison measures collaborative learning’s value under no-pooling constraints.Source: §C.1 · p. 32

C.2 Experimental Protocol

The local-only counterfactual and FedNova comparator use the same model architecture and client-specific preprocessing. Both are evaluated on the same observations within each state, with states grouped by training-sample size.

C.2 Experimental Protocol

  • Each of the 50 state-level clients trains an independent Residual MLP using only its own observations for the local-only counterfactual.Source: §C.2 · p. 32
  • The local-only and FedNova models are compared on identical in-time and out-of-time observations within each state.Source: §C.2 · p. 32
  • States are grouped as Low (n ≤1,807; 17 states), Mid (1,807 < n ≤5,948; 16 states), and High (n > 5,948; 17 states).Source: §C.2 · p. 32

C.3 Aggregate Federation Gain

FedNova improves out-of-time R2 over local-only training in every client sample-size category, with larger average gains among smaller clients. Its out-of-time R2 advantage over local-only models also holds for most clients in each category.

C.3 Aggregate Federation Gain

  • 0.152, 0.068, and 0.027 are FedNova’s out-of-time R2 gains over local-only training for low-, mid-, and high-sample clients, respectively.The gains decline as client sample size increases.Source: §C.3 · p. 33, Table 10 · p. 33
  • The local-only comparison measures cross-client collaboration’s value, unlike the federated–centralised comparison, where both procedures use consortium-wide information.Source: §C.3 · p. 33
  • 94.1%, 100%, and 82.4% of low-, mid-, and high-sample states, respectively, have higher out-of-time R2 with FedNova than with local-only training.Source: §C.3 · p. 33

C.4 Three-Way Comparison

The three-way comparison shows that FedNova outperforms local-only estimation across sample-size groups, while its comparison with pooled centralised training varies by group. FedNova also has the lowest average MAPE in every group.

C.4 Three-Way Comparison

  • For low-sample clients, average out-of-time R2 is 0.581 with FedNova, 0.543 with pooled centralised training, and 0.429 with local-only estimation.For mid-sample clients, FedNova and centralised training both reach 0.618, versus 0.550 locally; for high-sample clients, centralised training leads while FedNova remains above local-only.Source: §C.4 · p. 33, Table 11 · p. 33
  • FedNova records the lowest average MAPE in all three sample-size categories.The local-only model has the highest MAPE in the low- and high-sample groups and remains above FedNova in the middle group.Source: §C.4 · p. 33
  • The experiment does not identify which optimization or preprocessing component accounts for FedNova’s group-specific advantages over the pooled model.Source: §C.4 · p. 33

C.5 State-Level Heterogeneity

State-level gains vary: FedNova has lower out-of-time R2 than local training in four clients, including three large-sample states and one low-sample exception. Overall, it improves on local-only training in 46 of 50 clients.

C.5 State-Level Heterogeneity

  • FedNova has lower out-of-time R2 than local training in four of 50 states: Hawaii, California, New York, and Texas.The figure plots state-level gains against sample size, with dotted lines marking sample-size terciles.Source: §C.5 · p. 33, Figure 10 · p. 34
  • California, New York, and Texas are high-sample clients with more than 25,000 training observations and federation gains between −0.043 and −0.015.Source: §C.5 · p. 33
  • Hawaii is a low-sample exception with about 1,600 observations and a federation gain of approximately −0.079; the analysis does not identify why.Across all states, FedNova improves out-of-time R2 for 46 of 50 clients, motivating client-specific validation and potentially personalization or local calibration where distributions differ substantially.Source: §C.5 · p. 34

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