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Bernoulli Naive Bayes Classifier

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Problem statement

For this exercise, implement a Bernoulli naive Bayes classifier directly, without a machine-learning library. The training matrix train has binary feature values and one integer class label in labels per row. All classes 0..numClasses-1 occur in training.

Fit the following fixed model. Let count[c] be the number of training rows labeled c, and ones[c][j] the number of those rows whose feature j is 1.

Class prior: prior[c] = count[c] / n.
Add-one conditional smoothing: p[c][j] = (ones[c][j] + 1) / (count[c] + 2).
For a query x, its natural-log score for class c is ln(prior[c]) + sum_j(x[j]*ln(p[c][j]) + (1-x[j])*ln(1-p[c][j])).

For each row of queries, find the maximum class score and return the smallest class label whose score differs from that maximum by at most 10^-10. This numerical tie rule is part of the exercise contract. Return labels in query order; an empty query matrix returns an empty array. Do not smooth the class prior or transform the already-binary features.

Function

bernoulliClassify(train: int[][], labels: int[], numClasses: int, queries: int[][]) → int[]

Examples

Example 1

train = [[0],[1]]labels = [0,1]numClasses = 2queries = [[0],[1]]return = [0,1]

Each class has one example; smoothed likelihood favors the class matching the query.

Example 2

train = [[0,1],[1,0],[0,1],[1,0]]labels = [0,1,0,1]numClasses = 2queries = [[0,1],[1,0],[1,1],[0,0]]return = [0,1,0,0]

The first two queries favor their matching class. The last two have equal scores and choose label0.

Example 3

train = [[1],[1],[1],[0]]labels = [0,0,0,1]numClasses = 2queries = [[0],[1]]return = [1,0]

The empirical prior favors class0, but a zero query still favors class1: 1/6 is larger than 3/20.

Constraints

2 <= numClasses <= 10 and numClasses <= train.length <= 500.
labels.length = train.length; every class is represented.
Every training row and query row has the same feature count d, where 1 <= d <= 50.
Every matrix entry is 0 or 1, and 0 <= labels[i] < numClasses.
0 <= queries.length <= 200.
For every query, each class has exactly the maximum mathematical log score or trails that maximum by at least 10^-8.