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Approximately Correct Label Distribution Learning

ICML 2025 · Label-efficient and robust learning › Recognition and long-tail · approach: Partial and multi-label learning

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Proposes DeltaLDL, the fraction of predictions whose KL divergence to the ground-truth label distribution falls within a threshold, used both as a parameter-free evaluation metric (µ) and as a differentiable learning objective (δ-LDL) for label distribution learning.

Problem

Existing LDL evaluation metrics based on KL divergence are insensitive to subtle distributional changes and have poor discriminability, while average-KLD learning objectives overfit to samples with extreme predictions and can underperform uniform-vector baselines.

Approach

Replace average distance with the percentage of samples whose predictions are approximately correct within a threshold delta; the µ metric integrates this percentage over delta up to a uniform-baseline value, and δ-LDL optimizes a smoothed (ReLU) version of it via adaptive Simpson's rule integration, making it differentiable and parameter-free.

Key results

• On M2B, δ-LDL achieves µ of 58.25% versus 55.36% for the next-best DF-LDL and 53.90% for LRR.
• On fbp5500, δ-LDL reaches µ of 85.99% versus 85.29% for LRR; on SBU 3DFE it reaches 50.73% versus 49.93% for DF-LDL.
• On M2B, δ-LDL's KLD of 0.4882 is below the uniform-vector stochastic baseline of 0.6335, whereas SA-BFGS and LRR fall above it.

Measured effects reported in the paper

Surprising findings

• Average-KLD LDL methods such as SA-BFGS and LRR can perform worse than the expected KLD of uniform-vector predictions on M2B.
• The µ metric and KLD can produce different rankings of LDL methods (e.g., DF-LDL ranks above LDLF under µ but not under KLD on M2B).

Limitations

• δ-LDL does not achieve best performance on all metrics, possibly because it does not fit different shapes of label distributions.
• The µ metric is unstable when the number of test samples is small.

Experimental setup

Datasets: M2B fbp5500 RAF ML SBU 3DFE Natural Scene Music Painting

Benchmarks: M2B fbp5500 SBU 3DFE

Metrics: µ Chebyshev distance Clark distance Canberra distance KLD cosine similarity intersection similarity Spearman's coefficient

Baselines: SA-BFGS LDLLC LDLSF LCLR SCL DPA LRR PT-Bayes AA-kNN DF-LDL LDLF

Builds on: label distribution learning adaptive Simpson's rule Dirichlet distribution assumption LRR DF-LDL

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