EZR: Lightweight Optimization Methods

• EZR is a suite of lightweight, interpretable, and label-efficient methods for optimization and tabular analytics in software engineering.
• It employs techniques like distance-to-heaven scalarization and best/rest partitioning to efficiently navigate high-dimensional search spaces.
• EZR leverages small symbolic models and active learning to achieve near-optimal performance with minimal evaluation budgets.

EZR is a name used in several closely related software-engineering papers to denote lightweight, interpretable, and budget-conscious methods for optimization and tabular analytics. Depending on the source, it refers to a modular framework for “Minimal Data, Maximum Clarity,” an “Efficient Zero-knowledge Ranker” for black-box herding, a “Zoom, Don’t Wander” regional search strategy for budget-constrained SBSE, a baseline correlation-based symbolic learner in a causal-stability study, and a small Python toolkit that implements these ideas with minimal dependencies (Rayegan et al., 10 Sep 2025, Menzies et al., 11 Mar 2026, Ganguly et al., 10 May 2026, Rayegan et al., 17 Feb 2026, Menzies et al., 28 May 2026). Across these works, the recurrent motifs are distance-to-heaven scalarization, best/rest partitioning, compact symbolic models, label efficiency, and explicit resistance to full-state verification, broad global wandering, or opaque black-box explanation.

1. Terminological scope and paper-specific meanings

The term is not fixed to a single expansion or a single algorithm. In “Minimal Data, Maximum Clarity,” EZR is the framework name rather than a spelled-out acronym; in “From Verification to Herding,” it is “Efficient Zero-knowledge Ranker”; in “Zoom, Don’t Wander,” it is the name of a minimal greedy zoom method; in the causality paper it is the baseline correlation-based symbolic learner inherited from the Minimal Data, Maximum Clarity line of work; and in the toolkit paper it names EZR.py, a small Python implementation that unifies Naive Bayes, clustering, trees, local search, simulated annealing, active learning, and complementary Bayes text filtering (Rayegan et al., 10 Sep 2025, Menzies et al., 11 Mar 2026, Ganguly et al., 10 May 2026, Rayegan et al., 17 Feb 2026, Menzies et al., 28 May 2026).

Paper	Meaning of EZR	Defining role
(Rayegan et al., 10 Sep 2025)	Framework name	Active sampling, learning, and explanation for multi-objective optimization
(Menzies et al., 11 Mar 2026)	Efficient Zero-knowledge Ranker	Stochastic learner for herding under Sparsity of Influence
(Ganguly et al., 10 May 2026)	“Zoom, Don’t Wander” method	Greedy regional search with Best and Rest sets
(Rayegan et al., 17 Feb 2026)	Baseline symbolic learner	Correlation-based variance-reduction decision tree
(Menzies et al., 28 May 2026)	EZR.py toolkit	400-line, standard-library implementation of multiple tabular SE methods

This multiplicity is not accidental. The papers share a common substrate—small-sample optimization over tabular SE data with expensive labels—while shifting emphasis from explanation, to herding, to regional search, to causal critique, to code minimalism. A plausible implication is that “EZR” now denotes a methodological lineage rather than one immutable procedure.

2. Shared optimization formalism

A central commonality is scalarization by distance to an ideal point. In the SBSE regional-search paper, the search objective is explicitly handled by distance-to-heaven:

$$\text{D2H}(\mathbf{y}) = \sqrt{\frac{1}{M}\sum_{i=1}^{M} (\hat{y}_i - h_i)^2},$$

with lower values preferred (Ganguly et al., 10 May 2026). The Minimal Data, Maximum Clarity framework and the causal-stability study describe the same basic quantity as the Euclidean distance between normalized objective values and the ideal point where all objectives are optimized, then map it to a win score so that lower d2h corresponds to a higher score (Rayegan et al., 10 Sep 2025, Rayegan et al., 17 Feb 2026).

The “heaven” terminology is also explicit in the toolkit. There, goal columns encode whether higher or lower is desirable, and optimization uses a normalized distance from each goal toward its ideal direction (Menzies et al., 28 May 2026). In the herding paper, the same idea appears as a normalized distance-to-ideal loss used to rank configurations, even though the larger conceptual contrast is between proof-oriented verification and satisficing search (Menzies et al., 11 Mar 2026).

Another recurring structure is the partition of observed rows into a small high-quality subset and a larger complement. In the Minimal Data, Maximum Clarity paper, the top $\sqrt{N}$ configurations by d2h are treated as best, with the remaining $N-\sqrt{N}$ as rest (Rayegan et al., 10 Sep 2025). In the herding paper, the current population is sorted by the same ideal-distance criterion and split into BEST and REST, again with BEST defined as the top $\sqrt{N}$ samples (Menzies et al., 11 Mar 2026). In the Zoom, Don’t Wander paper, Best stores the current best solutions, bounded by $\sqrt{N}$, while Rest stores near-good solutions displaced from Best (Ganguly et al., 10 May 2026). In the toolkit, active learning likewise maintains best and rest as incrementally updated Data objects (Menzies et al., 28 May 2026). This repeated best/rest decomposition is one of the clearest unifying signatures of the EZR line.

The broader search philosophy is deliberately satisficing. The herding paper states the contrast explicitly:

$$\text{Verification: Find } \forall x \in X: \text{Valid}(S(x)),$$

versus

$$\text{Herding: Find } x' \in X \text{ such that } Utility(S(x')) > \tau.$$

The target is therefore “good enough” or near-optimal behavior under constrained budgets, not exhaustive proof over all behaviors (Menzies et al., 11 Mar 2026). The regional-search paper makes a parallel argument from the optimization side: practitioners usually need one good solution rather than an expensive global map or maintained Pareto frontier (Ganguly et al., 10 May 2026).

3. Sampling, search, and ranking mechanisms

The 2025 framework paper casts EZR as an active learner. It begins from a small warm start, uses d2h to define best versus rest, trains a two-class Naive Bayes classifier on that split, and then selects the unlabeled instance with the highest likelihood ratio

$$\frac{Like(x,\mathrm{best})}{Like(x,\mathrm{rest})}.$$

The core algorithm uses a warm start of $n=4$ and stop = 50; experimental budgets are typically about 60 labels for light and medium datasets and 10% of training data plus 10 additional samples for heavy datasets (Rayegan et al., 10 Sep 2025).

The herding paper reinterprets the procedure as a stochastic contrast set learner and discretized sampler. After an initial sample, EZR ranks by normalized distance to the ideal point, splits into BEST and REST, discretizes input attributes into bins, scores ranges by their contrast between BEST and REST, and generates new samples by constraining high-scoring ranges while randomizing the rest. The central scoring rule is

$$Score(r) = \frac{P(r \mid BEST)^2}{P(r \mid REST) + \epsilon}.$$

The paper positions this design relative to TPE and SMAC: it is inspired by the former’s good/bad split but avoids heavier density modeling, and it avoids the repeated random-forest rebuilding associated with the latter by relying on incremental statistics updated with Welford’s algorithm (Menzies et al., 11 Mar 2026).

The SBSE regional-search paper strips the mechanism down even further. EZR there has no surrogate model, no Pareto ranking, and no explicit frontier maintenance. At each iteration it samples 128 candidates from the unlabeled pool in decision space, then evaluates only the first candidate whose normalized Euclidean distance to the centroid of Best is smaller than its distance to the centroid of Rest:

$\sqrt{N}$0

Only that chosen point consumes evaluation budget, so each loop uses exactly one objective evaluation (Ganguly et al., 10 May 2026). This is why the paper calls EZR a “greedy zoom” method.

The toolkit paper exposes the implementation substrate behind these variants. Num, Sym, Data, Cols, and a polymorphic add primitive maintain all summaries incrementally; sub is defined symmetrically as add(..., w=-1); and active acquisition can be driven by a centroid contrast such as distx(row, mids(best)) - distx(row, mids(rest)) (Menzies et al., 28 May 2026). The coding claim is that once these primitives exist, many algorithms reduce to “just a loop” over the same shared data structure.

4. Symbolic explanation and compact modeling

EZR is consistently associated with small symbolic models, especially decision trees. In the Minimal Data, Maximum Clarity framework, the decision tree is trained after active sampling and serves simultaneously as predictor, optimizer surrogate, global feature ranker, and local explainer (Rayegan et al., 10 Sep 2025). The same paper defines a tree-based global importance score in MDI form:

$\sqrt{N}$1

Because the tree is trained on a small, carefully selected sample, the intended result is a shallow, inspectable structure rather than a large opaque model.

Local explanation is cohort-based rather than additive. For a given test instance, EZR routes the instance through the tree and reports the path to a leaf, with the leaf interpreted as a cohort of similar configurations. The paper contrasts this with attribution methods such as LIME, SHAP, and BreakDown: instead of decomposing a prediction into additive feature contributions, EZR describes threshold conditions, cohort membership, and the performance profile of that cohort (Rayegan et al., 10 Sep 2025). The example path in the paper uses threshold conditions such as $\sqrt{N}$2, $\sqrt{N}$3, $\sqrt{N}$4, $\sqrt{N}$5, and $\sqrt{N}$6.

The toolkit paper generalizes the same symbolic minimalism. Classification and regression trees share the same infrastructure, with splits chosen to minimize weighted post-split uncertainty,

$\sqrt{N}$7

and with leaves storing compact summaries of outcomes (Menzies et al., 28 May 2026). Across 120+ MOOT tasks, the paper reports that EZR’s trees typically use fewer than 10 variables even when the data contain hundreds or thousands of features, which it treats as evidence for aggressive sparsity in these domains (Menzies et al., 28 May 2026).

The explanation claims go beyond descriptive ranking. The 2025 framework explicitly argues that EZR’s trees support global, local, and counterfactual reasoning, and maps the approach to Pearl’s Ladder of Causation while characterizing LIME, SHAP, and BreakDown as mostly remaining on the association rung (Rayegan et al., 10 Sep 2025). That claim becomes a point of tension in the later causal-stability paper, where the same tree substrate is reclassified as fundamentally correlational rather than causal.

5. Causality, instability, and interpretive limits

The causality paper treats EZR as the baseline correlation-based symbolic learner and asks whether causality-aware splitting can cure the confusion caused by correlation in software analytics (Rayegan et al., 17 Feb 2026). Its critique is precise: variance reduction, information gain, and Gini impurity identify statistical association, not causal influence. As a result, the same observed association may arise from direct causation, $\sqrt{N}$8, reverse causation, $\sqrt{N}$9, or confounding, $N-\sqrt{N}$0. A variance-reduction tree cannot distinguish among these possibilities (Rayegan et al., 17 Feb 2026).

In that study, EZR’s workflow is to sample and label a small subset, compute d2h, convert it to a win score on a 0–100 scale, train a decision tree, and use the tree to estimate which test row is closest to “heaven” (Rayegan et al., 17 Feb 2026). The split criterion is explicitly variance reduction. At each internal node, EZR selects the attribute that yields the greatest reduction in variance, making child groups more homogeneous in the target value. The paper presents this as useful for interpretability but vulnerable to both interpretive confusion and instability.

Stability is measured with a preregistered bootstrap-ensemble protocol. For human-versus-model comparisons, experts assign ordinal judgments—no impact, mild impact, certain impact—on whether features have direct causal influence on objectives, and these are compared against the feature importance patterns from 20 bootstrap-trained EZR trees (Rayegan et al., 17 Feb 2026). Agreement is summarized by Gini impurity:

$N-\sqrt{N}$1

where lower impurity means higher agreement. For model-versus-model comparisons, the paper examines variance across bootstrap performance distributions, and for performance trade-offs it uses the Kolmogorov–Smirnov statistic

$N-\sqrt{N}$2

together with Cliff’s delta (Rayegan et al., 17 Feb 2026).

The proposed alternative is a causality-aware tree that minimizes normalized conditional entropy,

$N-\sqrt{N}$3

with

$N-\sqrt{N}$4

and supplements that split criterion with confounder filtering based on mutual information and conditional mutual information (Rayegan et al., 17 Feb 2026). The paper notes that minimizing conditional entropy is mathematically related to maximizing information gain, but it still treats EZR’s variance-reduction tree as the relevant correlation baseline. Because the report is preregistered, the excerpt emphasizes intended methodology rather than final numeric outcomes. Its stated position is that EZR is useful but unstable, and that causality-aware splitting may improve stability and robustness without sacrificing optimization performance (Rayegan et al., 17 Feb 2026).

This creates a substantive interpretive boundary around the EZR line. The earlier papers treat small trees as highly actionable and often clearer than attribution-based XAI, whereas the causality paper argues that clarity alone does not license causal interpretation. The juxtaposition suggests that EZR’s symbolic compactness should not be conflated with causal validity.

6. Empirical results, application domains, and software embodiment

The empirical record spans multiple benchmark slices built around MOOT. Reported totals include 60 real-world datasets in the Minimal Data, Maximum Clarity paper, 63 optimization tasks in the herding paper, 114 datasets in the budget-constrained SBSE paper, 120+ or 124 tabular SE tasks in the toolkit paper, and 127 total datasets in the MOOT summary table used for the causal study (Rayegan et al., 10 Sep 2025, Menzies et al., 11 Mar 2026, Ganguly et al., 10 May 2026, Menzies et al., 28 May 2026, Rayegan et al., 17 Feb 2026). Across the papers, the domains include software configuration optimization, cloud performance tuning, software project health, scrum configuration, feature models, software process models, behavioral, financial, and health datasets, reinforcement learning tasks, sales tasks, and software testing tasks (Rayegan et al., 17 Feb 2026, Ganguly et al., 10 May 2026).

The 2025 framework paper reports that EZR reaches at least 90% of best-known performance in 17 of 22 light datasets, 12 of 19 medium datasets, and 15 of 19 heavy datasets. Aggregated over all 60 datasets, the reported counts are 56/60 at least 70% of best-known performance, 51/60 at least 80%, and 44/60 at least 90%, while using about 60 labels on light and medium datasets and 10% of training data plus 10 additional labels on heavy datasets (Rayegan et al., 10 Sep 2025).

The herding paper reports a stronger small-sample saturation claim. Across 63 tasks, EZR achieves 62% optimality with 8 samples, 80% with 16, 90% with 32, 91% with 64, and 92% with 128, identifying a pronounced knee at 32 samples (Menzies et al., 11 Mar 2026). Over 20 runs, the paper states that EZR terminated in minutes whereas SMAC took days. It interprets this as evidence for Sparsity of Influence: a small number of variables, often a “master key” subset $N-\sqrt{N}$5 with $N-\sqrt{N}$6, dominate behavior (Menzies et al., 11 Mar 2026).

The regional-search paper provides the most detailed competitive comparison. At equal budget, EZR wins or ties NSGA-II in 85% of datasets, SPEA2 in 84%, and SMAC in 89%; at a five-times budget disadvantage, EZR-200 still wins or ties NSGA-II-1000 in 79%, SPEA2-1000 in 79%, and SMAC-1000 in 81% of datasets (Ganguly et al., 10 May 2026). The paper further reports that Pareto methods need about 3.3–3.4× more evaluations to reach the regret level attained by EZR at 200 evaluations, while SMAC needs more than 5× due to cold-start overhead. Runtime is described as roughly 2–3 orders of magnitude faster than Pareto methods and global Bayesian search. Even more strikingly, EZR matches or surpasses Pareto methods on frontier metrics extracted from the Best+Rest trajectory: at equal budget, True IGD is 0.04 for EZR versus 0.09 for NSGA-II-200 and 0.07 for SPEA2-200, and HV is 1.03 for EZR versus 0.99 for both NSGA-II and SPEA2 (Ganguly et al., 10 May 2026).

The structural explanation offered in that paper is that Pareto-optimal solutions form a tiny, tight island. Pareto solutions constitute about 0.6% of configurations on median, have lower D2H than non-Pareto solutions in 94% of datasets with significant superiority in 88%, and are tighter in decision space in 85% of datasets (Ganguly et al., 10 May 2026). On that account, methods that wander broadly pay an exploration tax, whereas EZR succeeds by zooming into the compact profitable region.

The toolkit paper translates the line of work into software form. EZR.py is about 400 lines of Python, uses only the standard library, and implements Naive Bayes, k-means, k-means++, classification trees, regression trees, simulated annealing, local search, active learning, and complementary Bayes text-mining relevance filtering (Menzies et al., 28 May 2026). On 120+ tabular SE optimization tasks, the paper states that these small tools perform as well as or better than SHAP, LIME, SMAC3, and FASTREAD-like text filters, while running 500× faster than SMAC3, using orders of magnitude less labeled data, and building trees from fewer than ten variables even when thousands are available (Menzies et al., 28 May 2026). The package is described as open-source and installable via pip install ezr (Menzies et al., 28 May 2026).

Taken together, the EZR literature advances a coherent but contested program: optimization and explanation for tabular software-engineering tasks can often be driven by very small samples, very small symbolic models, and very small codebases. The strongest positive claims concern label efficiency, search speed, sparsity, and interpretability; the strongest caution is that a compact symbolic rule set may still be correlational, unstable under perturbation, or vulnerable to confounding unless causal criteria are introduced explicitly (Rayegan et al., 10 Sep 2025, Ganguly et al., 10 May 2026, Rayegan et al., 17 Feb 2026).