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Exposing Blind Spots in Deep Imbalanced Regression Evaluation
Noah C. Puetz, Jens U. Brandt, Marc Hilbert, Elena Raponi, Thomas Bäck, Thomas Bartz-Beielstein
TL;DR
Imbalanced targets make reliable prediction across the full range challenging, while DIR evaluation has sought broader data, more decisive metrics, and better assessment of tail stability. This paper evaluates DIR on multimodal virtual-sensing tasks, adopts balanced metrics including bMASE, and reevaluates methods across random seeds. It finds tail degradation and instability, uneven transfer of DIR methods, and no single method that solves MUVIS-DIR.
Problem
Rare target regimes may be consequential, yet imbalanced training distributions leave standard models less reliable across the full target range.
Source: §1 · p. 2Method
The study evaluates DIR on multimodal virtual-sensing tasks, uses balanced metrics including bMASE, and analyzes performance stability as a function of local target support.
Source: §3.1 · p. 3, §3.2 · p. 5, §6 · p. 9Results
Standard models show tail degradation masked by global MAE; DIR methods improve balanced performance but transfer unevenly, and tail regions are least stable across seeds.
Source: §6 · p. 9Takeaways & Limitations
DIR evaluation requires broader data domains, balanced scalar metrics, and explicit attention to tail reliability; no single method solves MUVIS-DIR.
Source: §6 · p. 9The benchmark focuses on virtual sensing rather than the full space of time-series regression, including forecasting and sequence-to-sequence settings.
Source: §5 · p. 9
Abstract
from arXiv · showhide
Deep Imbalanced Regression (DIR) addresses a common failure mode of regression models: target distributions are highly non-uniform, causing models to perform best in densely populated target regions even when reliable performance is required across the full target range. Despite rapid methodological progress, DIR evaluation remains constrained by three blind spots: it is dominated by image-based benchmarks, its standard many-/medium-/few-shot protocol is diagnostic but not decision-complete, and tail-region stability across random seeds has not been systematically evaluated. We revisit DIR evaluation along these three axes. First, we broaden the data domain by evaluating DIR on a multimodal virtual sensing benchmark (\textsc{MuViS}) with nine time-series extrinsic regression tasks across six physical domains, where rare target values often correspond to operationally meaningful regimes. Second, we adopt balanced MAE (\emph{bMAE}) and introduce balanced Mean Absolute Scaled Error (\emph{bMASE}), a scale-normalized metric for decision-complete comparison across methods and datasets. Third, through a repeated reevaluation of six representative DIR methods across multiple random seeds, we show that the tail regions targeted by DIR exhibit particularly high sensitivity to seed-level variability. Our results show that standard virtual-sensing models exhibit substantial tail degradation hidden by global MAE, that existing DIR methods can improve balanced performance but transfer unevenly to multimodal time-series data, and that tail-region instability remains a largely hidden failure mode under current DIR evaluation practice. Together, these findings and our publicly available code provide a reproducible basis for future DIR research toward regression systems that capture rare target regimes as reliably as common ones.
1 Introduction
Imbalanced targets make reliable prediction across the full range difficult because standard models perform best in dense regions and degrade in rare, often consequential ones. The paper revisits DIR evaluation through broader data domains, balanced scalar metrics, and repeated seed-level evaluation.
1 Introduction
- Rare, practically consequential target values are often underrepresented, while standard deep models perform best in dense regions and degrade in sparse ones.This creates a mismatch between the training distribution and the need for reliable performance across the full target range.Source: §1 · p. 2
- DIR evaluation has three blind spots: limited non-image data, shot-region scores without a principled scalar ranking, and limited attention to experimental stability.The many-/medium-/few-shot partitions are difficult to interpret consistently across continuous datasets, and tail variability may be especially high under sparse supervision.Source: §1 · p. 2
- The paper broadens the data domain with MUVIS, adopts bMAE and introduces scale-invariant bMASE, and evaluates seed-level variability in underrepresented regions.These three directions align with the data, metric, and stability blind spots, respectively.Source: §1 · p. 2
2 Related Work
DIR methods extend imbalance-aware learning to continuous targets, but the empirical evidence remains concentrated in image benchmarks. Existing time-series evaluations use distinct datasets, limiting direct comparisons across methods.
2 Related Work
- DIR extends imbalance-aware learning beyond categorical classification, where removing class boundaries makes direct transfer of reweighting and resampling strategies non-trivial.Yang et al. [2] introduced DIR and found that classification strategies transferred poorly to continuous targets.Source: §2 · p. 2
- Figure 2 presents task-specific target imbalance across the nine MUVIS-DIR tasks and reports sequence length, feature channels, sample size, skewness, and kurtosis.Source: Figure 2 · p. 3
- DIR methods span algorithm-level, representation-learning, and architectural approaches, with orthogonal methods distinguished from those requiring specialized architectures or training.The listed families include loss or weighting changes, latent-space reshaping, and predictor modifications.Source: §2 · p. 3
- Fourteen of fifteen surveyed DIR method papers evaluate at least one image benchmark, while only three evaluate time-series data, each on a different dataset.None of those three releases a public training pipeline for its time-series task, and two use limited or integer-valued targets.Source: §2 · p. 3
3 Extending the Evaluation Framework of DIR
The evaluation framework broadens DIR to multimodal time-series virtual sensing and replaces shot-region-only reporting with balanced scalar metrics. It also treats stability in underrepresented regions as an evaluation criterion.
3 Extending the Evaluation Framework of DIR
- The framework extends DIR along three axes: multimodal time-series regression, balanced scalar metrics for cross-dataset comparison, and empirical analysis of stability in underrepresented regions.Source: §3 · p. 3
3.1 Benchmark Extension: MUVIS-DIR
- MUVIS-DIR uses nine continuous regression tasks across six physical domains, with multimodal time-series inputs and a single sensor-like target.Virtual sensing infers hard-to-measure physical quantities from available sensor measurements; rare target regions can represent safety-critical, clinically relevant, or physically extreme regimes.Source: §3.1 · pp. 3–4
- MUVIS-DIR frames training targets as non-uniformly distributed even though evaluation seeks generalization to a more balanced target distribution.This mismatch is described as an implicit target-distribution shift that weakens the standard empirical-risk-minimization assumption.Source: §3.1 · p. 4
3.2 Metric Extension: Balanced Scalar Evaluation
- Many-/medium-/few-shot reporting uses arbitrary thresholds for continuous targets and gives no scalar criterion for resolving gains in rare regions against losses in dense ones.The synthetic example shows that model rankings vary with the selected shot region; averaging the three scores adds another arbitrary rule.Source: §3.2 · p. 4, Figure 3 · p. 4
- Balanced MAE macro-averages per-bin MAE so each target bin receives equal weight regardless of its sample count, while retaining original target units.Equal-width binning approximates uniform weighting over the continuous target range.Source: §3.2 · p. 5
- bMASE scales balanced error by the error of a trivial constant predictor, enabling comparisons across datasets with different physical quantities and scales.A bMASE below 1 improves on the constant predictor, and values closer to 0 indicate stronger performance; the geometric mean aggregates normalized ratios invariant to reference choice.Source: §3.2 · p. 5
- The framework uses L1-based balanced metrics because squared-error metrics are especially unstable in bins with very small sample counts.Per-bin MSE depends on fourth-order error moments, whereas MAE depends on second-order moments through the variance of absolute error.Source: §3.2 · p. 5
4 Experiments
The experiments test virtual-sensor imbalance, balanced evaluation of DIR methods, and seed stability. They find substantial tail errors, uneven method transfer, and persistent instability in sparse regions.
4.1 Imbalance Bias in Standard Virtual Sensors
- 4.42×: on PM10, bMAE exposes error that global MAE masks, with extreme upper-tail performance approaching a naive median predictor in a critical air-quality regime.Across the representative tasks, per-bin MAE rises in sparse regions except on BATTERY SOC, whose target support is less imbalanced.Source: Figure 4 · p. 6, §4.1 · p. 6
- Many-/median-/few-shot reporting can leave bins undefined and underweight severe errors when a nominal few-shot region contains its own dense subregions.On PM2.5, most samples in the few-shot range of approximately y = 300 to y = 1000 cluster near its lower end.Source: §4.1 · p. 6
4.2 DIR Methods under Balanced Evaluation
- 0.1732 GMean bMASE: UVote beats VANILLA’s 0.2163, is best on four datasets, and four of six methods improve VANILLA, while RnC degrades performance.LDS is the strongest evaluated orthogonal method, with 0.1997 GMean bMASE, and its largest single improvement is on PM10, from 0.6869 to 0.4765.Source: Table 2 · p. 7, §4.2 · p. 7
- Focal-L1 improves high-heart-rate PPGDALIA regions and UVote reduces MONTEREY tail error, while LDS trades dense-region performance for better PM10 tail performance.Figure 5 compares per-bin MAE above and signed difference to VANILLA below.Source: Figure 5 · p. 7, §4.2 · p. 7
4.3 Tail Instability Across Seeds
- −0.57 to −0.95: VANILLA’s bin-count/per-bin-MAE-variability Spearman correlations show that lower local support tracks greater instability, a trend retained by the best DIR methods.On MONTEREY, UVote improves bMASE but retains a similar density-dependent variance trend; sparse bins show greater seed-level dispersion.Source: Figure 6 · p. 8, §4.3 · p. 8, Figure 7 · p. 8
- Tail accuracy and tail stability should be evaluated jointly; reporting only average variance or a single seed is insufficient for underrepresented regions.The authors identify stability as an evaluation concern, not a new optimization remedy.Source: §4.3 · p. 8
4.4 Discussion
- MUVIS-DIR adds multimodal time-series tasks with physically meaningful tail regimes and public code, extending the benchmark landscape as an open challenge.The discussion frames it as a benchmark for evaluating future DIR methods, not a solved application.Source: §4.4 · p. 8
- bMASE supplies a scalar basis for ranking methods across datasets, physical units, and imbalance regimes while retaining dataset-level detail.The discussion presents this as addressing ambiguity in many-/medium-/few-shot reporting.Source: §4.4 · p. 9
5 Limitations and Future Work
The study’s scope is bounded by its virtual-sensing benchmark, selective method comparison, discretized balanced metrics, and diagnostic-only stability analysis.
5 Limitations and Future Work
- MUVIS-DIR isolates multimodal sensor-based sequence-to-value regression, so it does not cover forecasting or sequence-to-sequence settings where imbalance can vary across the prediction horizon.The authors identify those settings as future work.Source: §5 · p. 9
- The six-method comparison is selective and is evidence of uneven transfer to multimodal time series, not a definitive ranking of all DIR methods.The authors call for testing newer methods and combinations of orthogonal interventions.Source: §5 · p. 9
- bMAE and bMASE depend on target-range discretization, although the shared data-driven bins agree closely with a continuous kernel-based alternative.Balanced evaluation still requires choosing a local target resolution.Source: §5 · p. 9
- The stability analysis diagnoses higher seed-level variability in low-density regions but does not propose a method to stabilize tail performance.The authors point to reducing variability across initialization, data order, and optimization trajectories as future work.Source: §5 · p. 9
6 Conclusion
The conclusion identifies three gaps in DIR evaluation and addresses them with a virtual-sensing benchmark, a balanced cross-dataset metric, and an analysis of seed stability. Experiments find tail degradation and instability, while DIR methods transfer unevenly to multimodal time series.
6 Conclusion
- MUVIS-DIR adds multimodal virtual-sensing time-series regression tasks with practically meaningful tails, while bMASE enables scale-normalized comparison across methods and datasets.The paper also analyzes performance stability as a function of local target support.Source: §6 · p. 9
- Standard models can show tail degradation hidden by global MAE; DIR methods can improve balanced performance but transfer unevenly, and tails are least stable across seeds.The authors do not claim that any single method solves MUVIS-DIR.Source: §6 · p. 9
A Appendix
- The appendix outlines supplementary analyses, reproduction instructions, and publicly accessible code for the experiments.It assigns data-, metric-, and stability-blind-spot analyses to Appendices C, D, and E, respectively.Source: A Appendix · p. 13
B Mathematical Notations
- The notation section defines symbols for multimodal inputs, continuous targets, prediction errors, balanced metrics, target bins, and seed-level instability.It includes the reference predictor used to scale bMASE and the per-bin standard deviation across seeds.Source: B Mathematical Notations · p. 14
C Data Blind Spot Appendix
- The data-blind-spot appendix surveys DIR methods and their evaluation domains, then characterizes MUVIS statistically and explains why uniform target-range performance matters operationally.It presents the benchmark as a response to the narrow empirical evidence behind current DIR claims.Source: C Data Blind Spot Appendix · pp. 14–15
C.1 DIR Methods and Dataset Landscape
The landscape appendix makes the concentration of DIR evaluations in image benchmarks visible and catalogs methods alongside their evaluation datasets and architectures.
C.1 DIR Methods and Dataset Landscape
- 18 of the 19 surveyed methods use AgeDB-DIR or IMDB-WIKI-DIR as a primary evaluation, and only a small subset goes beyond facial-image regression.Source: §C.1 · p. 15
- The overview table organizes DIR methods by type, venue, datasets, models, orthogonality to backbones, and public repository availability.It distinguishes algorithm-level, representation-learning, and architectural methods.Source: Table 4 · p. 15
- The listed evaluation landscape includes text-regression and tabular datasets alongside image benchmarks, as illustrated by Im-Context’s dataset list.Source: §C.1 · p. 16
C.2 MUVIS Dataset Overview
MUVIS spans a wide range of target imbalance and effective support, and its tails correspond to operationally consequential regimes. The appendix also examines balanced metrics’ distribution invariance and the discrete-versus-continuous estimation choice.
C.2 MUVIS Dataset Overview
- IR ranges from 2.0 on Battery SoC to 41.2 on Monterey, while Seff ranges from 0.92 down to 0.25 across the nine tasks.This spans near-uniform through extremely peaked target distributions.Source: §C.2 · p. 17
C.2.1 Domain motivation for tail-region reliability
- Across tasks, tails mark operationally critical regimes—including near-limit vehicle handling and process faults—so frequency-weighted MAE and R2 down-weight regimes applications care about.Source: §C.2.1 · pp. 17–18
D Metric Blind Spot Appendix
- The metric appendix investigates how standard and balanced metrics respond to test-distribution changes, and whether bMAE’s numerator can be estimated discretely or continuously.Source: D Metric Blind Spot Appendix · p. 18
D.1 Distribution invariance of standard and balanced metrics
- bMAE and bMASE are robust to test-distribution sensitivity, supporting a scalar model ranking that is consistent across test-set compositions.The paper frames this as its goal for DIR evaluation.Source: §D.1 · p. 18
D.1.1 Experimental setup
- Four deterministic error profiles are evaluated across Gaussian, Laplace, and Weibull test distributions, with metric stability assessed by variation and ranking consistency.The profiles represent tail collapse, uniformly mediocre and strong predictors, and a tail specialist.Source: §D.1.1 · pp. 18–19
D.1.2 Results
Across test-distribution shifts, balanced metrics remain stable while standard metrics can drift; the paper also validates a discrete bMAE estimator against a continuous alternative and adopts it for its simplicity and matching rankings.
D.1.2 Results
- SERA’s per-model CV reaches 0.515 on Weibull and 0.452 on Gaussian because its threshold-wise squared-error sums vary with test-set counts above each threshold.The authors specify this concern for DIR’s uniform-performance objective, not as a blanket rejection of SERA or other standard metrics.Source: §D.1.2 · pp. 19–20
D.2 Theoretical grounding and continuous estimation of bMAE
- The discrete bMAE estimator approximates conditional absolute error integrated uniformly over the target range, using each bin’s per-sample MAE at its midpoint.The uniform measure gives every target-range point equal contribution, independent of empirical test-set density.Source: §D.2 · p. 20
- For Ntest ≥2000, discrete and continuous estimators agree within 1–5% on bMAE and within 0.01 on bMASE across three distribution families.At Ntest = 10,000, |∆bMASE| < 0.004; the discrete estimates produce the same model rankings in all settings considered.Source: §D.2 · pp. 20, 22
D.1.2 Results
- Balanced bMAE and bMASE maintain per-model CV ≤0.005 across distributions and one ranking across α, with τ(0↔0.95)=+1.00.Standard metrics and SERA drift with α for at least one model; the balanced metrics remain flat.Source: §D.1.2 · p. 19, Figure 9 · p. 20, Table 6 · p. 22
D.2 Theoretical grounding and continuous estimation of bMAE
- The authors adopt the discrete estimator because it is simpler, transparent in its assumptions, and matches the continuous estimator’s model rankings in the tested settings.The continuous alternative uses Nadaraya–Watson kernel regression and a uniform grid; results are stable from G≈100 onward.Source: §D.2 · pp. 20, 22
- L1-based balanced metrics are preferred because rare bins make squared-error estimates especially sensitive to heavy-tailed errors and outliers.The paper motivates bMASE as an L1-based balanced metric.Source: §D.2 · p. 22
E Stability Blind Spot Appendix
The appendix characterizes label noise across MUVIS tasks because noise and target imbalance interact, complicating interpretation of DIR results. Severe imbalance can coincide with noisy tails, so reweighting rare samples may amplify unreliable gradients.
Noise method
- The normalized noise ratio uses each sample’s k=20 nearest neighbours in PCA-reduced feature space; r≈0 indicates a clean local mapping, while r>1 signals multi-valued or strongly heteroscedastic regimes.Per-target-bin medians and IQRs summarize the ratios.Source: E Stability Blind Spot Appendix · p. 23
Noise results
- PM10 upper-tail noise exceeds r >3.5, while Monterey rises from r ≈0.05 centrally to r > 1 in both tails; battery SoC remains below r<0.02 throughout.Chem. Conc. has a milder U-shaped profile below r = 1; Hart Rate and Tire Temp. are more uniform.Source: E Stability Blind Spot Appendix · p. 24
- On severely imbalanced tasks, tail up-weighting must contend with amplified gradient noise alongside data scarcity; on near-uniform battery SoC, tail error is characterized as purely a capacity problem.The noise profiles complement imbalance ratio and effective support by characterizing how much residual tail error may be eliminated.Source: E Stability Blind Spot Appendix · p. 24
F Implementation and Reproducibility
The appendix documents a shared, reproducible implementation protocol for the nine MUVIS-DIR datasets, with fixed dataset-specific backbones and configurations selected before the ten-seed evaluation.
F.1 Data, Splits, and Preprocessing
- The experiments use the nine MUVIS-DIR datasets with inherited train/test files and no additional upstream preprocessing or target transformations; targets remain in physical units.Inputs are standardized channel-wise using training-subset statistics only.Source: §F.1 · pp. 24–25
F.2 Backbone and Training Protocol
- All methods use dataset-specific ResNet1D architecture parameters fixed from the original MUVIS optimization, with a shared training protocol unless method-specific schedules are stated.The shared protocol uses L1 loss, Adam, 120 epochs, and restores the checkpoint with the lowest validation MAE.Source: §F.2 · p. 25
F.3 DIR Method Configurations
- LDS, SQInv, and Focal-L1 alter loss weighting, ConR and RnC add contrastive objectives, and UVote uses uncertainty-aware expert heads.Method-specific configurations and hyperparameters are summarized in the appendix tables.Source: §F.3 · p. 25, Table 8 · p. 26, Table 9 · p. 26
F.4 Hyperparameter Selection
- Configurations are selected separately for each dataset–method pair using validation bMAE at seed 42, then fixed for the final evaluation across all ten seeds.Method-specific sweeps are run for Focal-L1, ConR, and RnC.Source: §F.4 · p. 25
F.5 Seeds and Statistical Reporting
- The final runs use ten seeds, and tables report their mean with confidence intervals computed from seed-wise results.Each seed controls the split, initialization, shuffling, dropout, and data-loading worker randomness.Source: §F.5 · p. 26
- Results are statistically reproducible rather than guaranteed bitwise identical across hardware and software stacks because some GPU operations may remain implementation-dependent.Deterministic backend options are set where available, but strict bitwise determinism is not enforced.Source: §F.5 · p. 26
G.1 Re-evaluation of MUVIS Models
The appendix re-evaluates original MUVIS models under balanced metrics and complements aggregate results with per-bin error plots across the nine datasets. The plots expose regional error profiles and compare each dataset’s best DIR method with the vanilla baseline.
G.1 Re-evaluation of MUVIS Models
- Six original MUVIS baselines are re-evaluated under bMAE and bMASE across ten seeds using the original protocol, but with MSE rather than L1 training loss.The authors note that differences from the main-text ResNet1D results therefore reflect the change in training loss.Source: §G.1 · p. 27, Table 11 · p. 27, Table 12 · p. 28
G.2 Performance comparison
- Per-bin MAE plots cover all nine datasets and show where methods improve, match, or degrade relative to vanilla across the target range.The appendix notes that similar aggregate bMAE or bMASE improvements can arise from different regional error profiles.Source: §G.2 · p. 27, Figure 13 · p. 29, Figure 14 · p. 30
- Figure 16 compares each dataset’s best-performing DIR method directly with vanilla, using signed differences to show whether gains cluster in sparse regions or spread across the target range.The supplied figure description specifies the upper row as per-bin MAE and the lower row as signed differences to baseline.Source: §G.2 · p. 28, Figure 16 · p. 32