Count Regression — Maximum Likelihood
Model counts with a log link: μ̂ = exp(w·x + b). Fit by minimizing negative log-likelihood. Switch datasets and models; watch the loss curve.
Counts and Mean Curve
MLE
μ̂ = exp(w·x + b) Observed counts ±1 std dev x guide
xyμ̂per-point NLL
Total NLL = 0.00000
Controls
Counts
Poisson
0.300
2.000
lr = 0.01000
μ̂ = exp(0.300 · x + 2.000)
b:
2.000
w:
0.300
NLL:
0.00000
Iter:
0