PaperlayerView exact revision on arXiv

Source-linked AI summary

LUCID: Local Understanding of Covariate Importance with Conditional Density Estimation

Yixiao Wang, Srikar Katta, Jon Donnelly, Emanuele Borgonovo, Cynthia Rudin

arXiv:2610.35740v1cs.LGstat.ML

TL;DR

Local variable-importance scores can hide observation-level heterogeneity, while perturbation methods may neglect feature dependence or rely on restricted approximations. LUCID uses full conditional distributions for plausible replacements; the paper reports stable performance and practical utility across simulated and real-world examples.

  • Problem

    Global importance scores can obscure when and for which observations a feature matters, while local perturbation schemes may not capture feature dependence.

    Source: §1 · p. 1

  • Method

    LUCID measures local importance by replacing features with plausible draws from their conditional distribution given the remaining covariates.

    Source: §3.2 · p. 3

  • Results

    LUCID captures heterogeneous local importance under complex covariate dependence, with reported high accuracy, robustness, and computational scalability.

    Source: §1 · p. 2

  • Takeaways & Limitations

    On the Bike Sharing data, temperature importance varies over the day, and its conditional replacement distribution shifts across seasons.

    Source: §5.2 · p. 9

    The decomposition assumes the model's predictions have finite variance across perturbations; for asymmetric Bregman divergences, the divergence direction matters.

    Source: §3.3 · pp. 3, 5

Abstract

from arXiv · show

Computing local-level variable importance (VI) is critical for understanding machine learning models. Local permutation-based VI metrics offer a simple yet powerful approach, measuring how much a model's output changes when perturbing its inputs. However, existing perturbation strategies often ignore feature dependence or account for it only through restricted approximations. Perturbing a feature without fully respecting this dependence can generate unrealistic counterfactuals, thereby evaluating the model in regions unsupported by the observed data distribution. We address this gap by introducing a new model-agnostic local VI metric and estimator, Local Understanding of Covariate Importance with conditional Density estimation (LUCID). LUCID perturbs features of interest using plausible values drawn from the full conditional distribution given the remaining observed features. We establish theoretical connections between LUCID and existing VI measures, and provide an estimator with convergence guarantees and uncertainty quantification. Finally, we demonstrate LUCID's stable performance and practical utility across simulated and real-world examples.

1 Introduction

Population-level variable-importance scores can hide how feature importance varies across observations. LUCID addresses this and the challenge of dependence-aware perturbation by using full conditional feature distributions.

1 Introduction

  • Population averages can obscure when and for which observations a feature matters, motivating local variable importance.Distinct local importance patterns can share the same population average.Source: §1 · p. 1
  • Marginal replacements can break feature dependence and produce implausible counterfactuals, while restricted conditional schemes may bias local scores.Errors across observations can cancel when averaged, and flexible conditional estimation is needed to capture observation-specific structure.Source: §1 · p. 2
  • LUCID measures observation-level feature importance by replacing a feature with plausible draws from its conditional density given the remaining observed features.The framework also decomposes importance, supports feature groups, and provides estimation guarantees and Bayesian uncertainty quantification.Source: §1 · p. 2

2 Related Work

Prior permutation-based importance methods include marginal and conditional approaches at global and local levels. LUCID defines observation-level importance using the full conditional feature distribution.

2 Related Work

  • Permutation-based VI measures feature relevance through changes in model behavior after perturbation, with methods developed at global and local levels.The literature includes both marginal and conditional approaches.Source: §2 · p. 2
  • LUCID uses the full conditional feature distribution so replacements preserve dependence between the feature of interest and remaining covariates.Other explanation methods, including SHAP and LIME, target different estimands.Source: §2 · p. 3

3 Our Method: LUCID

LUCID measures the change in a fixed model's prediction under conditionally plausible feature replacements, with the remaining covariates held fixed. Its decomposition distinguishes output variability from the observed prediction's displacement and extends to feature groups.

3.1 Notation and Background

  • Permutation feature importance uses marginal replacements, conditional permutation importance uses conditional replacements, and LOCO evaluates loss from a reduced model.LOCO typically uses a model refitted without the feature of interest.Source: §3.1 · p. 3

3.2 LUCID Definition

  • For an observation, LUCID is the expected prediction discrepancy when the feature is replaced by a draw from its conditional distribution, holding other covariates fixed.Averaging LUCID over the population recovers conditional permutation feature importance.Source: §3.2 · p. 3

3.3 Understanding LUCID

  • Under squared loss, LUCID decomposes into dispersion across plausible replacements and displacement of the observed prediction from their mean.Dispersion and displacement capture distinct local mechanisms; their population averages contribute equally, but their local contributions can differ.Source: §3.3 · p. 4
  • Under squared loss, local LOCO captures displacement, while LUCID additionally captures conditional output dispersion, which can change local feature rankings.The global factor-of-two relationship between CPFI and LOCO does not generally hold locally; the decomposition also extends to Bregman divergences.Source: §3.3 · pp. 4–5

3.4 LUCID for Feature Groups

  • Group LUCID jointly varies a feature group conditional on the remaining covariates, and generally need not equal the sum of individual LUCID scores.Individual scores can be small when group members carry overlapping information.Source: §3.4 · p. 5

4 Estimating LUCID

LUCID estimation combines conditional replacement draws with evaluations of a fixed predictive model. Its stability result transfers conditional-density estimation rates to LUCID, and DR-BART provides posterior estimates and uncertainty quantification.

4.1 Conditional-Sampling Estimation

  • A plug-in Monte Carlo estimator applies to any conditional density estimator by drawing conditional replacements and evaluating the fixed model.The procedure requires conditionally plausible draws and model evaluations.Source: §4 · p. 5, §4.1 · p. 5

4.2 Stability and Convergence

  • Under a bounded-loss condition, conditional-density estimation error passes to LUCID without a loss in convergence rate.For squared loss, bounded model outputs are sufficient.Source: §4.2 · pp. 5–6

4.3 Implementing LUCID with DRBART

  • DR-BART estimates conditional distributions; posterior draws induce LUCID draws for point estimates and uncertainty quantification.Under the stated conditions, the induced LUCID posterior contracts at the conditional-density rate in L2(PZ,X).Source: §4.3 · p. 6
  • Fitted DR-BART conditional samplers can be reused across observations, and empirical runtime and memory scaling is reported on higher-dimensional benchmark datasets.The reported datasets include examples with more than 105 observations and more than 50 features.Source: §4.3 · p. 6

5 Experiments

The experiments compare LUCID estimation with analytical results in synthetic settings and examine individual and group importance on bike-sharing data. Across these settings, LUCID captures local heterogeneity, while DR-BART estimates are consistently accurate across varied synthetic dependence structures.

5.1 Synthetic Experiments

  • DR-BART is the most consistently accurate conditional estimator across five synthetic DGPs, with the best average MSE rank and qualitative conclusions confirmed over 50 seeds.The DGPs cover discontinuity, correlation, heteroskedasticity, interaction structure, and extreme tails.Source: §5.1 · pp. 6–7, Table 2 · p. 7
  • LUCID captures the discontinuity in which X1 matters only for observations with X3 > 0, while LIME, SHAP, conditional SHAP, and local LOCO assign it nonzero importance when inactive.Global importance gives X1 and X2 identical scores, masking that only one matters at any given observation.Source: §5.1 · p. 7, Figure 3 · p. 7
  • With correlated features, conditional LUCID reflects X1’s redundancy as ρ increases, unlike marginal permutation importance, which remains 2.The analytical-average LUCID is 2(1 − ρ^2).Source: §5.1 · p. 8
  • As independent irrelevant features are added across five DGPs, ARF’s LUCID estimation MSE rises sharply, while DR-BART remains far more stable.The added features do not change X1’s true conditional distribution or analytical LUCID.Source: Figure 5 · p. 8, §5.1 · pp. 8–9
  • For heteroskedastic data, globally permuted residuals miss the changing conditional variance; only CDE-based approaches capture the changing spread, with DR-BART closest to the analytical CDE.The analytical local importance is x2^1 + x2^2, whereas residual methods yield x2^1 + 1.Source: §5.1 · p. 8, Figure 4 · p. 8
  • Across five DGPs, DR-BART posterior intervals for active X1 observations generally achieve coverage close to nominal 90% and 95% levels, with DGP 1 somewhat conservative and DGP 3 slightly below nominal at 95%.Interval widths increase with the credible level; inactive observations are excluded because their LUCIDs are zero and recovered exactly.Source: §5.1 · p. 9, Table 3 · p. 9

5.2 Real-Dataset Experiments

  • On bike-sharing data, hour importance varies over the day and between working and non-working days; working-day importance peaks during morning and evening commutes.Hour is only weakly predictable from remaining features, so the observed heterogeneity mainly reflects changes in model sensitivity to hour.Source: §5.2 · p. 9, Figure 6 · p. 10
  • For the weather group, joint LUCID exceeds the sum of individual LUCIDs during the day, especially in evening rush hours; the temperature–season pair shows a similar gap, unlike the other pairs.The smaller gaps for temperature–humidity and humidity–season may reflect the remaining feature constraining joint replacements.Source: §5.2 · pp. 9–10, Figure 7 · p. 10

6 Conclusion

LUCID measures local variable importance using conditionally plausible feature replacements, with an interpretable decomposition and theoretical guarantees. The appendix relates this measure to existing global and local importance measures and extends its analysis beyond squared loss.

6 Conclusion

  • LUCID measures how a fixed model responds to conditionally plausible feature changes and offers an interpretable decomposition, convergence guarantees, and Bayesian uncertainty quantification.Its estimation framework accommodates modern conditional-density estimators and feature groups.Source: §6 · p. 10

A Related Work

  • Existing perturbation-based methods use marginal draws or restricted conditional approximations, while LUCID defines local importance using the full conditional feature distribution.Residual-based methods can be biased when residual distributions vary with covariates; tree-based approaches may miss local variation or leave too few observations.Source: A Related Work · p. 13

C.1 Setup and Global–Local Identity

  • The global average of local LUCID equals global conditional permutation importance when the expected loss is finite.The identity is established using the true conditional replacement distribution.Source: §C.1 · p. 16

C.2 Squared-Loss Decomposition and the Relationship with LOCO

  • Under squared loss, LUCID decomposes into displacement from the conditional-mean reduced predictor and variation among conditionally plausible outputs.A reduced model obtained by finite-sample refitting need not equal this conditional-mean projection.Source: §C.2 · p. 16

C.3 Bregman Decomposition and Global Identities

  • For strictly convex Bregman divergences, LUCID is zero exactly when the model output is unchanged almost surely under conditional replacements.The global factor-of-two identity need not hold for asymmetric divergences.Source: §C.3 · p. 18
  • The Bregman analysis extends to feature groups by drawing replacements jointly conditional on the remaining covariates.Reversing the comparison leads to a dual-coordinate formulation, whose details are outside the paper's scope.Source: §C.3 · pp. 18–19

C.4 Stability Under Conditional-Distribution Error

The section examines how conditional-density error affects LUCID and develops contraction, moment, and convergence guarantees for DR-BART and posterior averaging. It also addresses the separate Monte Carlo error from finite posterior draws and conditional replacements, along with the computational and memory trade-offs of direct conditional sampling and batching.

C.4 Stability Under Conditional-Distribution Error

  • LUCID’s local importance error inherits the conditional-density estimator’s rate, while its root mean squared error bounds population-average importance error; finite evaluation sampling adds a separate error.Hellinger distance satisfies the distance-control condition, and its squared value is bounded by 2.Source: §C.4 · pp. 19–20

C.5 Posterior Contraction and Posterior Moment Control

  • Posterior contraction transfers to LUCID importance, but matching the rate for posterior averages additionally requires quantitative posterior-tail and second-moment control.Convergence of posterior tail probability to zero alone is insufficient to guarantee the same rate for a posterior mean.Source: §C.5 · pp. 20, 21, 27

C.6 DR-BART Specialization

  • Under the stated DR-BART regularity and prior conditions, the density posterior contracts at the corollary’s rate, and LUCID’s posterior satisfies the stated contraction and moment bounds if Equation (C.21) holds.The conditions impose smoothness, sparsity, quantile restrictions, and specified prior and approximation requirements.Source: §C.6 · p. 28

C.7 Convergence Rate of Posterior Averaging

  • The posterior mean conditional density serves as a conceptual replacement distribution, and under the stated posterior bounds, its induced LUCID achieves the corresponding convergence rate.The replacement distribution need not be fitted or evaluated explicitly.Source: §C.7 · p. 29
  • Finite posterior draws and conditional replacements add Monte Carlo error beyond the convergence rate of the exact posterior mean, requiring separate control.The convergence results establish the rate for the exact posterior mean; they do not cover this additional sampling error.Source: §C.7 · p. 30

D.1 Implementation Details

  • For continuous features, DR-BART’s latent-variable representation enables direct draws from each fitted conditional distribution without grid discretization or numerical CDF inversion.The approach also avoids constructing and storing a density-evaluation matrix for sampling.Source: §D.1 · p. 31
  • For binary and categorical features, classification BART estimates conditional category probabilities, which define Bernoulli or categorical replacement distributions.Each posterior draw specifies a complete conditional distribution for LUCID estimation and posterior summarization.Source: §D.1 · p. 32
  • Posterior-predictive sampling estimates the posterior mean, while separate LUCID estimates for each posterior draw yield credible intervals that can also reflect finite-M variability.The intervals primarily describe uncertainty induced by the conditional density estimator when within-draw Monte Carlo error is negligible.Source: §D.1 · p. 32
  • For feature groups, sequential conditional factors use previously sampled group members to represent within-group dependence; posterior draws of the factors support group-level uncertainty summaries.The factor models are fit using remaining covariates and preceding group members as predictors.Source: §D.1 · pp. 32–33

D.2 Additional Implementation Details for Direct Conditional Sampling and Batched LUCID Computation

  • Batching samples across observations and evaluates predictions across replacements, trading vectorized efficiency for memory; streaming can reduce sampling workspace to O(Abatchp) instead of O(AbatchMp).The current implementation materializes all M replacements per evaluation batch to enable vectorized tree evaluation and reduce per-call overhead.Source: §D.2 · pp. 33, 35
  • For one feature and fixed posterior draw, generating M replacements for N observations takes O(NM(p+τf)) time and O(AbatchMp) storage, excluding fitted-model storage and predictive-model evaluation.The storage bound is per job, and τf is the cost of evaluating the conditional mean and standard deviation at one conditioning–latent pair.Source: §D.2 · pp. 33–35

D.3 Experimental Setup

The experiments combine real-world tabular datasets with synthetic data-generating processes. Real-data evaluation includes cross-fitted XGBoost models, while the synthetic analyses use fixed prediction functions.

D.3 Experimental Setup

  • The primary real-data case study uses the 2011 hourly UCI Bike Sharing subset, containing 8,645 observations.Source: §D.3 · p. 35
  • Four additional OpenXAI datasets—Heart, German Credit, HELOC, and Give Me Some Credit—extend evaluation to higher-dimensional tabular data.Source: §D.3 · p. 35
  • Real-data experiments use five-fold cross-fitting: each XGBoost model is trained on four folds, held fixed on the held-out fold, and shared across methods.Source: §D.3 · pp. 36–37

E Additional DGP Results

E.1 Synthetic Data-Generating Processes

Five synthetic DGPs isolate aspects of local conditional variable importance, with analytical LUCID and global conditional permutation feature importance reported for relevant features. The calculations illustrate how importance behaves across independent, correlated, heteroskedastic, discontinuous, and extreme-tail settings.

E.1 Synthetic Data-Generating Processes

  • Table 5 reports five synthetic DGPs alongside analytical LUCID for relevant features and global conditional permutation feature importance (CPFI) under squared loss.Source: §E.1 · p. 38, Table 5 · p. 38

E.2 Analytical LUCID Calculations

  • In DGP 1, independent features make conditional replacements equal their marginals; perturbing X1 matters only when X3 > 0, while X3 flips across zero with probability 1/2.Source: §E.2 · p. 39
  • In DGP 2, only perturbations of X1 affect prediction because g(x) = x1.Source: §E.2 · p. 39
  • In DGP 3, X1’s conditional variance depends on local X2, but I2(x) = 0 because the prediction does not directly depend on X2.Source: §E.2 · p. 40
  • In DGP 4, X2 and X3 determine X1’s conditional distribution but not prediction once x1 is fixed; CPFI1 = 2 and CPFI2 = CPFI3 = 0.Source: §E.2 · p. 40
  • In DGP 5, the indicator-changing probability is 0.02 when H(x2) = 0 and 0.98 when H(x2) = 1.Source: §E.2 · p. 41

E.3 Stress Test Across Random Seeds

Across repeated seeds, DR-BART remains competitive across varied dependence structures, while local importance estimates can fail when replacement schemes ignore context or miss interactions. LUCID and local LOCO can also produce different feature rankings because they capture different aspects of local importance.

E.3 Stress Test Across Random Seeds

  • DR-BART achieved the best mean rank, 1.80, across 250 paired DGP–seed settings, and its performance persisted across repeated realizations.It was followed by ARF (2.84) and cs-PFI (3.29).Source: §E.3 · p. 42, Table 7 · p. 42

E.5 DGP 2: Correlated Features

  • At ρ = 0.9, conditional permutation methods captured correlation-induced restrictions on replacements, whereas marginal permutation missed the corresponding local importance pattern.The reported comparison is for the correlated-features DGP.Source: §E.5 · pp. 42–43

E.6 DGP 3: Heteroskedastic Conditional Dependence

  • Even with the correct conditional mean, a common replacement variance causes local error because it cannot represent the context-dependent conditional variance.The local error persists with arbitrarily many Monte Carlo replacements, despite exact recovery of global-average importance.Source: §E.6 · p. 43

E.7 DGP 4: Interacted Discontinuity

  • DR-BART estimates were closest to analytical LUCID in the XOR-interaction DGP; ARF’s MSE was approximately 3× higher than DR-BART’s.cs-PFI resembled marginal permutation, consistent with its transformation-tree partition failing to recover the pure interaction.Source: §E.7 · p. 44

E.8 DGP 5: Extreme Tail

  • Analytical local LOCO and LUCID rankings differed for 67.4% of cases, while estimated rankings differed for 69.6% of evaluated instances.LUCID includes prediction variability under conditional replacement, which local LOCO omits; the analytical disagreement is intrinsic to the measures, not fixable by improving LOCO estimation alone.Source: §E.8 · p. 45

E.9 Complete Conditional Replacement Distributions

DR-BART most consistently tracks the analytical conditional replacement distributions across the five simulated dependence structures. The pointwise results complement aggregate comparisons by showing where estimation errors occur across the covariate space.

E.9 Complete Conditional Replacement Distributions

  • Across five conditional structures, DR-BART most consistently tracked changes in the true conditional distributions’ location, scale, and shape.Other methods could perform well when their structural assumptions matched a DGP, but their performance was less uniform.Source: §E.9 · p. 45
  • Under correlated features, DR-BART followed the changing conditional location and restricted spread; marginal permutation missed the restriction by retaining the marginal distribution.Several other conditional methods captured the trend but had larger location or scale errors at extreme conditioning points.Source: §E.9 · p. 45, Figure 10 · p. 46
  • Under heteroskedastic dependence, DR-BART reproduced the near-degenerate median-quantile distribution and wider tail distributions more closely than residual-permutation or subgroup methods.The figure compares estimated replacement distributions at five empirical quantiles of X2.Source: §E.9 · p. 45, Figure 11 · p. 46
  • With X3 = 1, DR-BART captured the abrupt location shift in the interacted-discontinuity DGP; cs-PFI and marginal permutation missed the regime-specific location.The conditional variance remained approximately constant across the shift.Source: Figure 9 · p. 46, §E.9 · p. 47

E.10 Complete Pointwise Results

  • The pointwise LUCID figures show estimation errors across evaluation observations, complementing aggregate MSE comparisons with their locations in covariate space.MSE values for SHAP, conditional SHAP, and LIME are not directly comparable estimation errors because those methods target different estimands.Source: §E.10 · p. 47

E.11 Additional Posterior Credible Interval Results

Across five DGPs, empirical coverage generally rose with nominal credible-interval levels, with interval widths increasing accordingly. DGP 3 showed mild undercoverage at the 95% level, and the figures compare pointwise intervals with analytical LUCID values.

E.11 Additional Posterior Credible Interval Results

  • Across five DGPs, empirical coverage generally increased with nominal level, while average credible-interval width increased accordingly.The reported levels were 50%, 80%, 90%, and 95%.Source: §E.11 · p. 47, Table 8 · p. 48
  • At the 95% nominal level, DGP 3 showed mild undercoverage, with extreme heteroskedastic observations remaining challenging in finite samples.The figures show pointwise intervals for X1 across the five DGPs.Source: §E.11 · p. 47, Figure 21 · p. 54
  • The interval plots compare posterior means and credible intervals with analytical LUCID, distinguishing covered from missed values.Observations are ordered by observed X1, and 1,000 points are randomly selected for each figure.Source: §E.11 · p. 47, Figure 19 · p. 53, Figure 20 · p. 54

E.12 Additional Results on the cs-PFI Simulation

The cs-PFI simulation shows that conditional-sampler performance varies with dependence structure, while DR-BART has the best overall mean rank across 16 settings. Additional Bike Sharing results illustrate context-varying importance and replacement distributions, and feature predictability helps interpret individual LUCID.

E.12 Additional Results on the cs-PFI Simulation

  • DR-BART achieved the best overall mean rank of 2.31 across 16 settings, followed by cs-PFI at 2.81.Its relative performance varied substantially with conditional-distribution structure.Source: §E.12 · p. 57, Table 10 · p. 57
  • In the nonlinear setting, cs-PFI performed best in all four configurations, while DR-BART ranked second in three; DR-BART’s error fell as sample size increased.For p = 10, its MSE fell from 41.87 at n = 300 to 3.86 at n = 3000; for p = 90, it fell from 101.58 to 3.97.Source: §E.12 · p. 58
  • No conditional sampler dominated across dependence structures: subgroup permutation excelled with simple tree-partition structure, while direct density estimation was more competitive for smooth or distributed dependence.LUCID is agnostic to the conditional density estimator, so these results describe sampler trade-offs rather than a framework restriction.Source: §E.12 · p. 58

F.1 Complete Individual LUCID Results

  • On Bike Sharing data, temperature, humidity, and season showed context-varying importance and replacement distributions, while hour and working-day distributions were comparatively stable.The figure contrasts DR-BART conditional replacement distributions across covariate contexts with marginal permutation distributions.Source: §F.1 · p. 59, Figure 23 · p. 59

F.2 Feature Dependence and the Interpretation of Individual LUCID

  • High feature predictability can restrict conditional replacement variation, so a small LUCID may reflect limited replacement variation or limited model sensitivity.Low predictability alone does not imply large LUCID; the model’s response to replacement also matters.Source: §F.2 · p. 60
  • Temperature was particularly predictable from remaining features, while hour and working day had very low predictability; pairwise correlation is a weaker diagnostic than predictability.The reported patterns help distinguish replacement restrictions from model response when interpreting LUCID.Source: §F.2 · p. 60

F.3 Predictability Diagnostics for Feature Groups

Group-predictability diagnostics help assess candidate feature groups, while the squared-loss decomposition shows that local importance can arise through different mechanisms. Conditional replacement methods generally preserve feature support and context-dependent shifts better than marginal permutation, though CMR can generate off-support values.

F.3 Predictability Diagnostics for Feature Groups

  • Outside predictability measures how well covariates outside a group explain its features; within-group predictability measures the additional predictive value of other group members.High outside predictability suggests limited information beyond remaining covariates, while high within-group predictability makes joint perturbation particularly informative relative to separate perturbations.Source: §F.3 · p. 61
  • For season–temperature, outside predictability is 0.198 and within-group predictability is 0.450, supporting this pair as a candidate for complementary group analysis.The humidity–season pair has outside predictability of 0.298 and within-group predictability of 0.054, making it less naturally motivated by shared conditional information.Source: §F.3 · p. 62
  • Group predictability metrics are diagnostics, not a unique grouping rule; substantive knowledge and the scientific question remain important when choosing groups.Group LUCID complements individual importance because group importance is not fully reflected by summing member-level LUCIDs and varies across covariate context.Source: §F.3 · p. 62

F.4 Dispersion–Displacement Decomposition

  • 51.3% of mean LUCID comes from dispersion and 48.7% from displacement, but this near-even average masks observation-level heterogeneity.Figure 25 decomposes each observation’s hour LUCID into dispersion V and displacement D.Source: §F.4 · p. 62, Figure 25 · p. 63
  • Hour LUCID can be displacement-driven at late night or working-day commute peaks, but dispersion contributes more around midday and at similar non-working-day hours.Thus, a large local importance for the same feature can arise through different mechanisms.Source: §F.4 · pp. 62–63

F.5 Conditional Replacement Distributions Across Methods

  • DR-BART, ARF, cs-PFI, and GCMR generally preserve feature support and structure, whereas CMR can generate off-support values and marginal permutation misses context-dependent shifts.The differences are most visible for temperature and humidity, whose replacement distributions vary across seasons or hour periods.Source: §F.5 · pp. 63–64, Figure 27 · p. 65, Figure 28 · p. 66

F.6 Runtime and Memory Scaling on OpenXAI Datasets

DR-BART-based LUCID is computationally demanding because it fits a flexible conditional density model separately for each feature, yet it ran on all four benchmark datasets. Feature-specific jobs are independent, so parallel execution can reduce wall-clock time relative to serial totals.

F.6 Runtime and Memory Scaling on OpenXAI Datasets

  • DR-BART is substantially more computationally demanding than simpler replacement schemes because it fits a flexible conditional density model separately for each feature.Feature-specific jobs are independent and can run concurrently, so actual wall-clock time can be substantially lower than serial totals.Source: §F.6 · p. 69
  • On GMSC with 102,209 observations, DR-BART ran; each feature-specific task averaged approximately 9,015 seconds and used up to approximately 41.9 GiB, while ten serial jobs took approximately 1,503 minutes per fold.The serial runtime assumes feature computations are not parallelized; the reported memory is the maximum peak among feature-specific jobs.Source: Table 14 · p. 70, Table 15 · p. 70, §F.6 · p. 70

Related papers

Loading 2610.35740v1…