Separatix

separatix profiles labeled feature spaces before supervised model training and returns transparent, confidence-aware guidance about apparent classification or regression complexity.

The intended use case includes learned embeddings, but the package is not restricted to embeddings. It also works on raw feature matrices when you want a coarse diagnostic of whether the observed supervised geometry looks mostly linear, smoothly nonlinear, local or kernel-like, fragmented or discontinuous, bottlenecked, or too unreliable to trust.

separatix does not claim to pick the optimal classifier or regressor. It is a pretraining diagnostic and auditing tool designed to make its reasoning visible.

Installation

pip install separatix

To install the latest development version directly from GitHub:

pip install "git+https://github.com/NiklasMelton/Separatix.git@develop"

Quick start

from separatix import diagnose

recommendation = diagnose(X, y, random_state=0)
print(recommendation)

For a structured audit:

from separatix import diagnose

report = diagnose(X, y, return_report=True, random_state=0)
print(report.recommendation_text)
print(report.decision_path)
print(report.scores)
print(report.to_json())

Experimental protocol: diagnose twice

When a final test set is reserved, run Separatix at the two training sizes that matter:

1. Run it on the selection cohort before choosing and tuning candidate model families against validation data.
2. After validation-based comparison and tuning are complete, combine the training and validation cohorts, rerun Separatix on that enlarged development cohort, and record the second report before fitting the final model.

The first report supports selection-time reasoning. The second records the evidence on the enlarged final development cohort and may inform the final model specification. Compare each report's probe_evaluation.n_samples and effective_train_size_summary (checking status and basis before comparing numeric fields) to explain what rows and fold-fit sizes supported the two runs; these fields are descriptive metadata, not a claim about performance at other training sizes. Neither run should receive test rows or test labels. Make every remaining decision before evaluating the final fitted model once on the untouched test set; that test is the independent assessment of the complete procedure.

See the two-stage experimental protocol for an example and interpretation guidance.

What It Accepts

• Dense NumPy arrays
• SciPy sparse matrices
• pandas DataFrames and Series when pandas is installed
• Binary and multiclass classification targets
• Multilabel binary indicator targets with target_mode="multilabel" or auto-detection for unambiguous 2D indicators
• Continuous single- or multi-target regression with explicit target_mode="regression"
• String or numeric labels treated as categorical class identifiers

Regression is opt-in so numeric class identifiers remain categorical by default. General multioutput classification is not supported.

What It Returns

By default, diagnose(...) returns a plain-text recommendation. With return_report=True, it returns a DiagnosticReport that includes:

• the recommendation label
• plain-text recommendation text
• confidence level
• underlying metric groups
• probe-family evidence, including uncertainty-aware family comparisons
• normalized summary scores
• a visible decision path
• warnings and skipped diagnostics
• sampling and densification events
• preprocessing and runtime metadata

The report is JSON-serializable through report.to_dict() and report.to_json(). Non-finite diagnostic values are represented as JSON null; to_json() never emits non-standard NaN or infinity literals. The default terse form removes large row-level arrays before copying them.

Constructed probe entries also include a compact, versioned probe_recipe for auditing. It records the resolved estimator graph, preprocessing, hyperparameters, training policy, and dynamically detected Python and library versions. Reconstruct the corresponding unfitted estimator through the safe public factory:

from separatix import make_probe_estimator

recipe = report.metrics["probes"]["linear"]["probe_recipe"]
estimator = make_probe_estimator(recipe)

The factory only accepts a fixed allowlist of supported scikit-learn and Separatix probe components; serialized recipes cannot request arbitrary imports. Skipped probes report why a recipe is unavailable instead of implying that an unconstructed estimator can be reproduced. The factory reconstructs the unfitted estimator configuration; it does not replay the diagnostic's row cohort, validation folds, or scoring orchestration. Those details remain separate report evidence.

For multilabel targets, separatix compares probe families across micro F1, macro F1, and sample Jaccard rather than collapsing the evidence into a single weighted score. Optional iterative multilabel stratification can be installed with:

pip install "separatix[multilabel]"

For regression targets, call diagnose(X, y, target_mode="regression"). Regression evidence is compared across variance-weighted R2 and uniform-average R2, with normalized RMSE and target-neighborhood smoothness as supporting diagnostics. Classification-only boundary and fragmentation diagnostics are marked not applicable and do not reduce regression confidence.

All non-dummy probe families learn feature scaling inside each validation training fold. Sparse probes use non-centering scaling. Geometry and topology continue to describe the supplied, unscaled coordinate space, and the report records both choices under preprocessing.

Ordinary probe families are evaluated on one shared row cohort and one shared held-out split plan. When aligned out-of-fold predictions are available, family and dummy comparisons use paired bootstrap intervals; affected comparisons fall back to marginal uncertainty when paired evidence is unavailable. The paired intervals capture covariance between probe errors, but remain diagnostic resampling evidence rather than independent-test confidence intervals.

Reports also expose effective fit-size metadata for these ordinary probes at report.metrics["probe_evaluation"]["effective_train_size_summary"]. Its status is "available" or "unavailable"; when available, basis is "held_out_folds" or "resubstitution". The min, median, mean, and max fields summarize the rows used to fit the ordinary probe instances, and mean_fraction_of_evaluation_cohort is the mean divided by report.metrics["probe_evaluation"]["n_samples"]. That denominator is the shared evaluation cohort after any memory-aware sampling or densification, not necessarily the number of rows originally passed to diagnose. An unavailable summary has basis=None in Python (JSON null) and None for every numeric field (JSON null). This metadata covers ordinary probes only; optional MLP probes are not included. It describes one evaluation run and is not a learning-curve or training-size-sensitivity diagnostic.

Optional feed-forward MLP probes can be installed and enabled explicitly:

pip install "separatix[mlp]"

Set mlp_probes=True and use mlp_device, mlp_trigger_skill_threshold, mlp_min_improvement, and mlp_max_parameters to control them. The skill threshold is only a compute gate: it determines whether MLP probes run and does not participate in a completed override decision. An MLP can override simpler-family guidance only with complete held-out evidence, paired signal above dummy, and a practical paired gain over the strongest simpler probe for the required primary metrics. Failed or infeasible group splits never fall back to in-sample override evidence.

MLP pairwise evidence uses one target-aware paired-bootstrap cache local to the MLP cohort. The ordinary-probe cache cannot be reused literally because MLP probes use their own capped, dense, aligned cohort. The local cache scores the selected best MLP, the dummy baseline, and the metric-specific strongest simpler comparator once, then retains only the comparisons needed for the override. All required simpler comparators are still evaluated and remain available under report.metrics["mlp_probes"]["aligned_comparators"]; pruning the retained pairwise summaries does not weaken the completeness gate. This optimization avoids repeated resampling and scoring, but MLP fitting remains the dominant optional cost and the optimization should not be read as a whole-diagnosis speed guarantee.

The MLP payload's pairwise_comparison_audit records the cache status and resample plan. See the report reference for its exact fields and grouped/class-support behavior.

Optional persistent-topology diagnostics can be installed with:

pip install "separatix[tda]"

For multilabel targets, persistent topology is supporting evidence only. When enabled, it is computed on capped boundary-candidate subsets and a small capped set of high-support label-positive subsets.

For regression targets, optional topology is computed only on capped high-residual and high-local-discontinuity subsets. topology="graph" uses a sparse-compatible mutual-nearest-neighbor component summary; topology="persistent" adds persistent homology when ripser is installed. topology="auto" skips topology under the fast budget and otherwise attempts both summaries. Regression topology is descriptive supporting evidence: it is included in the report but never changes the recommendation label or confidence.

Probe Family Gallery

separatix compares several deliberately small probe families rather than treating one flexible model as a universal answer. The fitted surfaces below illustrate the behavior each probe is intended to detect. The quadratic panel includes both the full expansion and low-rank sketch variants. The final four panels use four independently sampled and calibrated nonlinear tasks, one for each optional conditional MLP subtype. Every named subtype is the selected held-out candidate on its own task and produces a validated MLP override.

The displayed boundaries are illustrative fits. Recommendations use held-out evidence, comparisons against the dummy baseline, uncertainty estimates, and a conservative preference for simpler families. Two-dimensional single-label classification is used here because its boundaries are easy to see. The MLP tasks each add five nuisance coordinates to two visible signal coordinates; their plots show fitted slices at the nuisance-coordinate medians. The compact tasks apply a 400-parameter cap so depth is compared within the compact budget, while the wide tasks compare all four candidates. These deterministic calibrations are architecture exemplars, not claims that one architecture is universally optimal. Multilabel and regression diagnostics use target-appropriate versions of the same probe families and their corresponding metrics.

Regenerate the gallery after installing the example dependencies:

poetry install -E examples -E mlp
poetry run python examples/probe_family_gallery.py

The script checks its coverage against the implemented probe registry and fails if any calibrated task stops selecting its intended MLP subtype or stops clearing the simpler probes. It also requires the selected subtype to lead the next-best eligible MLP by at least 0.01 held-out balanced accuracy.

Recommendation Categories

The same eight machine-readable labels are used for single-label classification, multilabel classification, and explicit regression. Target mode still controls the evidence, confidence rules, and plain-text wording (for example, a shared linear_likely_sufficient label is rendered with regression-specific model suggestions when target_type is regression).

• linear_likely_sufficient
• smooth_nonlinear_recommended
• kernel_or_local_recommended
• high_capacity_or_partitioning_recommended
• feedforward_mlp_recommended
• feature_or_target_bottleneck_likely
• insufficient_data_or_unreliable_geometry
• inconclusive

These categories are intentionally coarse. They describe the apparent geometry and difficulty of the labeled feature space or response surface, not a guaranteed best model choice.

The synthetic recommendation ladder below shows how separatix responds as the designed dataset geometry moves from simple linear structure toward smoother nonlinearity, local or kernel-like structure, fragmented boundaries, and finally weak-signal or random-label bottlenecks. The x-axis is the intended dataset complexity, while the y-axis is the coarse recommendation level reported by separatix.

Decision Pipeline

The recommendation is produced by a fixed, inspectable pipeline:

1. Validate inputs and encode labels.
2. Audit class counts, imbalance, sparsity, and basic dataset conditions.
3. Compute geometry, neighborhood, boundary, fragmentation, and optional topology diagnostics, using a distinct multilabel path for binary indicator targets.
4. Run simple probe models and compare them to a dummy baseline.
5. Build probe-family evidence with uncertainty estimates for linear, smooth_nonlinear, and local_kernel.
6. Apply an uncertainty-aware signal-vs-dummy gate before making any model-family recommendation: balanced accuracy for single-label targets, two of three primary metrics for multilabel targets, or at least one of the two primary R2 summaries for regression. Use paired OOF evidence when available and the documented marginal-uncertainty fallback otherwise.
7. Use conservative escalation: keep the simpler family unless a more complex family has a clear uncertainty-adjusted advantage.
8. Treat fragmentation and optional topology as supporting structural evidence, not as shortcuts around weak probe evidence.
9. Render both a plain-language summary and a structured report, including raw_best_family, recommended_family, and an uncertainty-aware plausible core-family set when a report is requested.

The plausible set is a heuristic competitive frontier over the tested linear, smooth_nonlinear, and local_kernel probes. It is not a formal confidence set and does not claim that retained families perform equally well. Optional MLP and high-capacity structural upgrades remain separate from this core-family comparison.

The full rationale and decision rules are documented in the decision pipeline reference.

Sparse Inputs And Memory Behavior

Sparse matrices are accepted directly. Diagnostics that need dense data use a shared densification policy rather than a separate dense-only code path. When a step would require densification, separatix can fail, skip, or warn and subsample before densifying, depending on configuration. These events are recorded in the report.

max_samples and max_dense_mb are hard limits. Group-aware sampling never splits a group or exceeds the row cap. If no support-preserving sample fits, the affected supervised diagnostic is skipped and reliability is marked insufficient instead of silently dropping classes or labels. The dense-memory budget applies to sparse multilabel targets as well as feature matrices.

When groups are supplied, sampling keeps groups whole and predictive evidence must come from group-disjoint held-out splits. Each evaluated class or label side needs support in both training and test partitions. A single group, an oversized group, or a class confined to too few groups therefore causes the affected supervised evidence to be skipped instead of evaluated on its training rows. Geometry and topology remain descriptive in those cases.

Numeric one-dimensional targets—including non-integral values—remain categorical unless target_mode="regression" is explicit. High-cardinality numeric classification targets produce a warning to make accidental routing visible.

Examples

• Basic breast-cancer report
• Linear hyperplane visualization
• Curvilinear boundary visualization
• High-dimensional linear hyperplane
• High-dimensional curvilinear hyperplane
• Two moons
• Kernel-like circles
• Probe family gallery
• Recommendation complexity ladder
• Multiclass wine data
• OpenML multilabel yeast
• Sparse text-like embeddings

Related Work

This package is not an implementation of a published dataset-complexity procedure, but the project is adjacent to and inspired by prior work on classification complexity and data geometry. In particular, we would like to acknowledge:

• Ho and Basu, "Complexity Measures of Supervised Classification Problems" (PDF)
• Lorena, Garcia, Lehmann, Souto, and Ho, "How Complex Is Your Classification Problem? A Survey on Measuring Classification Complexity" (DOI, PDF)

We do not follow those procedures directly, but they are relevant background for why geometry-aware pretraining diagnostics are useful.

License

The source code is licensed under the GNU Affero General Public License v3.0 or later (AGPLv3-or-later). Commercial licenses are available; please contact the maintainer through GitHub.