0104 — Generalized linear models are written natively: Accord is LGPL-2.1, ML.NET stops at logistic

Status: accepted · Date: 2026-09-11

Context

#338 proposed a project for "Advanced GLMs, time series and econometric summaries" and put its own Phase 1 first: inventory what Math.NET, ML.NET and Deedle actually cover, and identify the genuine holes as opposed to the ones that are only a matter of ergonomics.

One third of that issue closed before this reading began. Decision 0096 shipped the OLS summary table as Lodestar.Stats.Regression and drew the boundary in its own Consequences:

This package is OLS and its table; anything with a link function or a time index falls on that issue's side of the line.

This decision takes the link function. The time index is decision 0105.

The instruction is #427's protocol and decision 0074: read the incumbent's exported surface through a MetadataLoadContext, not its README; check the first-party incumbent and the dominant third-party one; and check our own repository before declaring a gap.

The reading

Read on 2026-09-11. Each package was installed into a throwaway project outside this repository, its dependency closure resolved with dotnet publish, and the target assembly loaded through a PathAssemblyResolver over that closure plus the running runtime's reference assemblies. A bare lib/*.dll cannot be read — the missing-dependency failure 0074 hit on Mosaik.Core.

Member counts below exclude property and event accessors, which are one member counted twice. On that basis MathNet.Numerics 5.0.0 reads 336 exported types and Accord.Statistics 3.8.0 reads 561 — reproducing 0096's type counts exactly. The member totals do not reproduce 0096's, because 0096 did not state its basis; the counts below are comparable with each other and with nothing else. That this cannot be settled is #619.

Only declarations were read. No method body of any assembly was opened, which is what decision 0003 constrains.

Accord.Statistics 3.8.0 — the whole thing, and it is LGPL-2.1

561 exported types, 5 620 members. It ships a complete generalized linear model:

Accord.Statistics.Models.Regression.GeneralizedLinearRegression
Accord.Statistics.Models.Regression.LogisticRegression
Accord.Statistics.Models.Regression.MultinomialLogisticRegression
Accord.Statistics.Models.Regression.ProportionalHazards
Accord.Statistics.Models.Regression.Fitting.IterativeReweightedLeastSquares
  ComputeStandardErrors, GetInformationMatrix, Gradient, HasConverged
Accord.Statistics.Links.ILinkFunction
  Absolute, Cauchit, Identity, Inverse, InverseSquared, Logit,
  Log, LogLog, Probit, Sin, Threshold            (ten implementations)
Accord.Statistics.Analysis.LogisticRegressionAnalysis
  Coefficients, StandardErrors, WaldTests, Confidences, OddsRatios,
  Deviance, LogLikelihood, ChiSquare, LikelihoodRatioTests,
  InformationMatrix, GetConfidenceInterval, GetPredictionInterval
Accord.Statistics.Analysis.MultinomialLogisticRegressionAnalysis
Accord.Statistics.Analysis.StepwiseLogisticRegressionAnalysis

That is the table statsmodels prints, plus Cox regression and stepwise selection. It is also LGPL-2.1, last released 2017-10-19, accord-net/framework archived with its last push 2020-11-18.

Microsoft.ML 5.0.0 — inference exists, and it is logistic only

The first-party incumbent, MIT, dotnet/machinelearning at 9 358 stars and pushed 2026-09-10. Microsoft.ML.StandardTrainers reads 77 exported types, 220 members. Searching the assembly rather than the namespace found what a README would have hidden — there is coefficient inference:

Microsoft.ML.Trainers.CoefficientStatistics
  Estimate, StandardError, ZScore, PValue, Index
Microsoft.ML.Trainers.LinearModelParameterStatistics
  GetWeightsCoefficientStatistics, GetBiasStatistics, GetBiasStatisticsForValue
Microsoft.ML.Trainers.ModelStatisticsBase
  Deviance, NullDeviance, ParametersCount, TrainingExampleCount

Four things bound it, and together they are the gap.

It is binary logistic only. LbfgsPoissonRegressionTrainer produces PoissonRegressionModelParameters, which declares no public member of its own — a Poisson fit comes back with no standard error, no p-value and no deviance.

The table is incomplete even for logistic: no confidence interval on a coefficient, no odds ratio, no dispersion, no AIC or BIC, no likelihood-ratio test.

The standard errors are not in this package. ComputeLogisticRegressionStandardDeviation declares ComputeStandardDeviation and no public constructor; the only concrete implementation is ComputeLRTrainingStdThroughMkl, in Microsoft.ML.Mkl.Components 5.0.0, which carries a native Intel MKL redistributable. Asking ML.NET for a standard error means taking that dependency.

And there is no link function as a concept anywhere in the assembly — no ILinkFunction, no family, no way to say "Gamma with a log link".

cs-glm 1.0.1 — the capability is there and the package does not install

The only NuGet hit for generalized linear model besides Accord. Its nuspec describes "Generalized Linear Model in .NET", and it is not empty: the GlmSharp.dll it bundles reads 21 exported types and 112 members, with a real stack —

GlmSharp.Glm
  DistributionFamily, GetLinkFunction, Solve, Predict, Statistics, MaxIters, Tol
GlmSharp.GlmDistributionFamily
  Bernouli, Binomial, Categorical, Exponential, Gamma,
  InverseGaussian, Multinomial, Normal, Poisson
GlmSharp.GlmIrls, GlmIrlsQrNewton, GlmIrlsSvdNewton

— and it installs nothing. Its assemblies sit at lib/net461/Release/ and lib/net461/Debug/; a subfolder of a target-framework folder is not a lib asset path, so dotnet add package followed by dotnet publish copied zero assemblies into the closure. The file above had to be lifted out of the package cache by hand to be read at all. It is net461 only, 1 star, frozen 2018-05-04, and it misspells Bernouli in a public enum.

This is the one entry the protocol changed the verdict on. Dismissed on its date it would have looked like an ordinary stale package; read, it is a package that cannot be consumed as published.

MathNet.Numerics 5.0.0 — distributions, not a fitter

336 exported types, 5 707 members, re-read for this question after 0096 read it for linear regression. Distributions.Poisson, Distributions.Logistic and Distributions.ConwayMaxwellPoisson are probability distributions. Across 5 707 members there is no link function, no iteratively reweighted least squares and no generalized linear fit of any kind.

The searches that returned nothing

query, nuget.org, 2026-09-11	packages
negative binomial	0
econometrics	0

Recorded rather than omitted, which is what decision 0099 established an empty search is for.

Our own repository

Per #427's last clause, checked before the gap was declared:

src/Lodestar.Metrics/PoissonDeviance.cs, GammaDeviance.cs, TweedieDeviance.cs
src/Lodestar.Decomposition/NmfBetaLoss.cs

All four are evaluation, not fitting. The three deviances are scikit-learn's mean_*_deviance metrics, which score a GLM's predictions once something else has produced them; NmfBetaLoss is the beta-loss family for non-negative matrix factorisation. Nothing here fits a model, and a reader who greps for Poisson should not conclude the domain is half-built.

Decision

A generalized linear model with its inference table is written natively, as #616.

The gap is not that nobody did it. Three .NET packages did, and each is disqualified for a different reason that has nothing to do with quality: Accord's licence, ML.NET's scope, and cs-glm's packaging. What does not exist is a maintained, permissively licensed, framework-free GLM table — the same sentence 0096 reached for OLS, for the same two of the same three reasons.

The first lot is the IRLS solver over the Householder QR Lodestar.Decomposition already publishes, two families with their canonical links — binomial/logit and Poisson/log — and the summary table that makes it inference: coefficients, standard errors, Wald z, p-values, intervals, deviance, null deviance, dispersion, log-likelihood and AIC.

Explicitly not in the first lot: negative binomial, Gamma and inverse Gaussian families; multinomial and ordinal responses; offsets and exposure; mixed effects; regularised fits. Each is its own lot, and #616 names them so that the first one is not quietly widened.

The package is not named here. Core tier, zero external dependencies, net10.0;netstandard2.0 (decision 0076); two-level naming, so Lodestar.Stats.Glm is available and Lodestar.Stats and Lodestar.Stats.Regression are taken. Whether it earns a package at all is the question 0096 answered on audience, and it is answered the same way — with a measurement — when #616's spec is written, not before.

What the licences decide, and what they do not

Accord.Statistics is refused on its licence, not on its capability and not on its age. LGPL-2.1 is copyleft and decision 0003 admits permissive references only; a core package taking it would also have failed 0076 immediately, whatever the licence said. Being archived is a reason to prefer a maintained implementation, not the reason it is refused — 0099's framing, kept.

Two licences could not be read from package metadata, which is the trap decision 0075 named and 0099 paid again. cs-glm publishes a bare GitHub URL rather than an SPDX expression; cschen1205/cs-glm reports MIT. Deedle 8.1.0 publishes no licence field at all and fslaborg/Deedle reports BSD-2-Clause — recorded here because 0105 relies on it.

And what a licence does not decide: Accord.Statistics stays admissible in bench/, which ships nothing. That is 0096's precedent and #616 carries it as an acceptance criterion.

Consequences

• #616 is opened with this reading as its evidence, on milestone 0.7.0, with a spec owed before any code.
• docs/migration/statsmodels.md stops saying "⚠️ gap — write or work around" for GLMs and says what was read instead, naming ML.NET's logistic table and its four bounds.
• The oracle is statsmodels 0.15.0, already in tools/requirements.lock.txt since #566, so this lot costs no lock churn and raises no Python-floor question — unlike #566 itself, which pulled pandas, patsy and formulaic in.
• A bench/README.md section is owed by the lot that ships code, not by this decision. It will measure against Accord.Statistics, for the reason above.
• The member counts here are not comparable with 0096's, because neither states a basis that the other shares. #619 is where that stops being true for the sixth reading.
• #338 is discharged by this decision and 0105 together, and closes: it asked for a reconnaissance, a decision per subject and a roadmap, and all three now exist. Its three subjects leave as #616, #617 and #621.
• Mixed and hierarchical models were not read. Neither this decision nor 0105 covers them, no capability search was run for them, and #621 exists so that closing #338 does not turn an unexamined subject into a settled one. Its verdict is allowed to be "not written".