Nonlinear regression

This package is an experiment in using the Zygote automatic differentiation package and the lowrankupdate! function in the LinearAlgebra package to solve the linear least squares problem for a Gauss-Newton update.

The data are represented as a Tables.RowTable, which is a vector of NamedTuples. The model parameters are also a NamedTuple. The model function is given as a function of two arguments - the parameters and a data row.

Example - a Michaelis-Menten fit

In the Michaelis-Menten model for enzyme kinetics,

v = Vm * c / (K + c)

the relationship between the velocity, v, of a reaction and the concentration, c, of the substrate depends on two parameters; Vm, the maximum velocity and K, the Michaelis parameter. The Vm parameter occurs linearly in this expression whereas K is a nonlinear parameter.

julia> using CSV, DataFrames, NLreg

julia> datadir = normpath(joinpath(dirname(pathof(NLreg)), "..", "data"));

julia> PurTrt = first(groupby(CSV.read(joinpath(datadir, "Puromycin.csv")), :state))
12×3 SubDataFrame
│ Row │ conc    │ rate    │ state   │
│     │ Float64 │ Float64 │ String  │
├─────┼─────────┼─────────┼─────────┤
│ 1   │ 0.02    │ 76.0    │ treated │
│ 2   │ 0.02    │ 47.0    │ treated │
│ 3   │ 0.06    │ 97.0    │ treated │
⋮
│ 9   │ 0.56    │ 191.0   │ treated │
│ 10  │ 0.56    │ 201.0   │ treated │
│ 11  │ 1.1     │ 207.0   │ treated │
│ 12  │ 1.1     │ 200.0   │ treated │

julia> pm1 = fit(NLregModel, PurTrt, :rate, (p,d) -> p.Vm * d.conc/(p.K + d.conc),
                  (Vm = 200., K = 0.05))
Nonlinear regression model fit by maximum likelihood

Data schema (response variable is rate)
Tables.Schema:
 :conc   Float64
 :rate   Float64
 :state  String
Number of observations:                  12

Parameter estimates
───────────────────────────────────────
      Estimate   Std.Error  t-statistic
───────────────────────────────────────
Vm  212.684     6.94715        30.6145
K     0.064121  0.00828092      7.74322
───────────────────────────────────────

Sum of squared residuals at convergence: 1195.4488145417758
Achieved convergence criterion:          8.798637504793927e-6