Improving Regression Performance with Distributional Losses (1806.04613v1)

Abstract: There is growing evidence that converting targets to soft targets in supervised learning can provide considerable gains in performance. Much of this work has considered classification, converting hard zero-one values to soft labels---such as by adding label noise, incorporating label ambiguity or using distillation. In parallel, there is some evidence from a regression setting in reinforcement learning that learning distributions can improve performance. In this work, we investigate the reasons for this improvement, in a regression setting. We introduce a novel distributional regression loss, and similarly find it significantly improves prediction accuracy. We investigate several common hypotheses, around reducing overfitting and improved representations. We instead find evidence for an alternative hypothesis: this loss is easier to optimize, with better behaved gradients, resulting in improved generalization. We provide theoretical support for this alternative hypothesis, by characterizing the norm of the gradients of this loss.

• The paper introduces Histogram Loss (HL), which employs KL-divergence between predicted and target distributions to improve gradient stability.
• Empirical results show that the HL-Gaussian variant significantly enhances regression accuracy across multiple datasets compared to ℓ2 loss.
• The theoretical analysis reveals that HL achieves a smaller local Lipschitz constant, leading to more efficient and stable optimization.

Improving Regression Performance with Distributional Losses

This paper explores the impact of distributional losses in regression tasks, focusing on improving prediction accuracy through the introduction of a novel Histogram Loss (HL). While traditional regression often relies on minimizing squared-error loss, this research investigates the advantages of adopting a distributional approach to loss formulation, specifically through the KL-divergence to a histogram density.

Key Contributions

• Histogram Loss (HL): The authors propose the HL, which incorporates a target distribution rather than estimating the mean directly. This loss function generalizes the use of soft targets by utilizing the KL-divergence between a predicted histogram distribution and a target distribution, improving gradient behavior and optimization stability.
• Performance Improvements: HL-Gaussian, a variant of HL using a Gaussian target distribution, demonstrates superior prediction accuracy in various datasets, emphasizing its utility in enhancing generalization without overfitting.
• Optimization Benefits: Through theoretical analysis, the paper characterizes the norm of the gradients associated with the HL, showing a more stable gradient behavior leading to better training efficiency. This is attributed to a smaller local Lipschitz constant compared to traditional $\ell_2$ losses.

Empirical Evaluation

The empirical studies conducted reveal:

1. Robustness and Flexibility: The HL framework provides robustness across different parameter settings, such as the number of bins and variance, without significantly impacting performance negatively.
2. Comparison With $\ell_2$: Across datasets including CT Position and Song Year, the HL demonstrated superior or comparable accuracy to $\ell_2$, specifically improving cases where target distributions are beneficial.
3. Impact of Representation: Experiments suggest that HL-Gaussian does not necessarily improve internal network representations, indicating that its benefits are derived from improved optimization dynamics rather than better representation learning.

Theoretical Implications

This work extends the understanding of how loss functions impact the ease of optimization beyond conventional choices. By focusing on the distributional properties of the target outputs, HL offers a compelling argument for rethinking regression loss formulations. The investigation into the optimization properties not only advances the methodology in regression but provides foundational insights useful for broader applications, including those in reinforcement learning.

Practical Implications

The proposed HL could be particularly useful in scenarios requiring robust model performance despite noisy or ambiguous data. The stability in training it offers aligns well with modern machine learning practices that prioritize faster convergence and generalization, reducing the trial-and-error typically involved in hyperparameter tuning.

Future Directions

Potential future work includes:

• Adaptive Histogram Loss: Developing methods to dynamically adjust the loss based on model feedback or data characteristics could further enhance its adaptability and performance.
• Cross-Domain Applications: Given its theoretical grounding, exploring HL’s utility in other domains where uncertainty and variance are critical can further validate its versatility.

In conclusion, the paper presents significant insights into regression performance through distributional losses. The development and analysis of Histogram Loss offer a new perspective on training neural networks for regression tasks, advocating for a balanced integration of statistics and machine learning principles.