Multinomial Naive Bayes — Machine Learning/Classical Models

Multinomial Naive Bayes

Machine Learning / Classical Models

A fitted multinomial naive Bayes classifier, evaluated one sample at a time. Each class scores the sample as a weighted count, and the highest score wins:

logp[k] = logprior[k] + Σ_j u[j]·logtheta[k][j]

This is sklearn.naive_bayes.MultinomialNB with class_log_prior_ and feature_log_prob_ pasted in. Both are already logarithms in sklearn and are taken as logarithms here, so nothing is re-derived and the score is a plain dot product plus a constant.

It is the counterpart of Gaussian Naive Bayes, and the choice between them is about the features rather than the classifier: continuous measurements get a Gaussian each, counts or frequencies get this one.

Ports

• u – the sample, a [d,1] column of counts or frequencies, where d is the number of COLUMNS of Feature Log Probabilities. One sample per step; it is checked rather than broadcast.
• idx – [1,1], the winning class, plus Index Base.
• logp – [K,1], every class's log-score in class order. The winner's own score is logp[idx]; feed the whole vector to Softmax for posteriors, or to Confidence Gate or Top K for a decision with a threshold.

Parameters

• Feature Log Probabilities – logtheta, a [K,d] matrix, one class per ROW: sklearn's feature_log_prob_ orientation, so it pastes in without transposing. These are LOGARITHMS of probabilities and are therefore normally negative; a row of them corresponds to one class's feature distribution. Its shape decides both K and d.
• Class Log Priors – [K,1], sklearn's class_log_prior_ – again already logarithms. Adding the same constant to every entry changes no decision, since the scores shift together.
• Index Base – what the first class is numbered, spelled exactly as Argmax Decision, K Means Assign and Gaussian Naive Bayes spell it:
  • Zero-based (PyTorch, numpy) – the first class is 0.
  • One-based (MATLAB) – the first class is 1.
• Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period.

Code export

All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text. Every class's score is unrolled at export time into one multiply-add per feature with the log-probability as a literal, then a comparison chain.

The three HDL targets are genuine synthesizable Q16.16: there is no logarithm, no division and no exponential in the datapath, because the logarithms were taken when the model was fitted.

Simulink bridge

None. Simulink's classifier blocks live in the Statistics and Machine Learning Toolbox, which is not installed on this machine, so there is no predict block here to map onto and a bridge could not be verified even if it were written. Those blocks also take a fitted model OBJECT rather than parameter matrices, which no configuration value can carry. The block therefore has no parity testbench, which is the documented consequence of Support::None. Code export verification still covers it across all ten languages.

Notes

• Stateless and algebraic.
• The score is LINEAR in the input, so this block is Dense Layer(Linear) followed by Argmax Decision in disguise – and it exists as its own block anyway, because a user pasting feature_log_prob_ and class_log_prior_ straight out of sklearn should not have to know that, nor rearrange them into a weight matrix and a bias.
• No state space: the block ends in a comparison, which is not linear.
• Ties go to the LOWEST class index – Argmax Decision's rule, spelled identically in every backend.
• The index is a DISCONTINUOUS function of the input, so the three HDL targets can rank two classes within one Q16.16 quantum (about 1.5×10⁻⁵) the other way round. The logp output is continuous and does not have that property.
• Counts, not measurements. Fed continuous features it will still compute, but the model behind it assumed counts; for continuous features use Gaussian Naive Bayes.