A hierarchical decomposition for explaining ML performance discrepancies

TL;DR

This paper tackles cross-domain ML performance gaps caused by distribution shifts and introduces HDPD, a nonparametric framework that delivers both aggregate explanations (through $\Lambda_W$, $\Lambda_Z$, $\Lambda_Y$) and detailed, Shapley-based attributions for individual variables. It provides debiased, efficient estimators with asymptotically valid confidence intervals, including a novel binning approach to obtain pathwise-differentiable estimands for $s$-partial outcome shifts. Through simulations and two real-world case studies (hospital readmission and ACS public coverage), the method demonstrates reliable uncertainty quantification and yields actionable insights for targeted interventions, often outperforming existing approaches. The HDPD framework thus offers a principled, model-agnostic way to diagnose and close ML performance gaps across domains by jointly analyzing aggregate shifts and fine-grained variable contributions.

Abstract

Machine learning (ML) algorithms can often differ in performance across domains. Understanding $\textit{why}$ their performance differs is crucial for determining what types of interventions (e.g., algorithmic or operational) are most effective at closing the performance gaps. Existing methods focus on $\textit{aggregate decompositions}$ of the total performance gap into the impact of a shift in the distribution of features $p(X)$ versus the impact of a shift in the conditional distribution of the outcome $p(Y|X)$; however, such coarse explanations offer only a few options for how one can close the performance gap. $\textit{Detailed variable-level decompositions}$ that quantify the importance of each variable to each term in the aggregate decomposition can provide a much deeper understanding and suggest much more targeted interventions. However, existing methods assume knowledge of the full causal graph or make strong parametric assumptions. We introduce a nonparametric hierarchical framework that provides both aggregate and detailed decompositions for explaining why the performance of an ML algorithm differs across domains, without requiring causal knowledge. We derive debiased, computationally-efficient estimators, and statistical inference procedures for asymptotically valid confidence intervals.

Figures (7)

• Figure 1: Hierarchical Decomposition of Performance Differences (HDPD): Aggregate decomposes a drop in model performance between two domains into that due to shifts in the covariate versus outcome distribution. Detailed quantifies the proportion of variation in accuracy changes explained by partial covariate/outcome shifts with respect to a variable or variable subset.
• Figure 2: Decomposition framework for explaining the performance gap from source domain ($D = 0$) to target domain ($D=1$), visualized through directed acyclic graphs. Aggregate decompositions describe the incremental impact of replacing each aggregate variable's distribution at the source with that in the target, indicated by arrows from $D$. Detailed decompositions quantify how well hypothesized partial distribution shifts with respect to variable subsets $Z_s$ explain performance gaps. This work considers partial outcome shifts that fine-tune the risk in the source domain with respect to $Z_{s}$ (as indicated by the additional node $Q=p_0(Y=1|W,Z)$) and partial conditional covariate shifts when $Z_s \rightarrow Z_{-s}$.
• Figure 3: Coverage rates of 90% CIs for aggregate decomposition terms (left) and value of $s$-partial shifts for the conditional covariate (middle) and outcome shifts (right) across dataset sizes $n$.
• Figure 4: Comparison of variable importance reported by proposed method HDPD versus existing methods for conditional covariate (a) and conditional outcome (b) terms.
• Figure 5: Aggregate and detailed decompositions for the performance gaps of (a) a model predicting readmission risk across two patient populations (General$\rightarrow$Heart Failure) and (b) a model predicting insurance coverage across US states (NE$\rightarrow$LA). A subset of VI estimates is shown; see full list in Sec \ref{['sec:data_details']} in the Appendix.

Theorems & Definitions (13)

• Theorem 4.1
• Theorem 4.3
• Theorem 2.2
• Theorem 3.1: Theorem \ref{['thm:aggregate']}
• proof
• Lemma 3.2
• proof
• proof : Proof for Theorem \ref{['thrm:cond_cov_detailed']}
• Lemma 3.4
• proof