MultinomialNB

src/naive_bayes/mod.rs

@@ -66,5 +66,8 @@ impl<T: RealNumber, M: Matrix<T>, D: NBDistribution<T, M>> BaseNaiveBayes<T, M,
 }
 mod categorical;
 mod gaussian;
+mod multinomial;
+
 pub use categorical::{CategoricalNB, CategoricalNBParameters};
 pub use gaussian::{GaussianNB, GaussianNBParameters};
+pub use multinomial::{MultinomialNB, MultinomialNBParameters};

src/naive_bayes/multinomial.rs

@@ -0,0 +1,278 @@
+use crate::error::Failed;
+use crate::linalg::row_iter;
+use crate::linalg::BaseVector;
+use crate::linalg::Matrix;
+use crate::math::num::RealNumber;
+use crate::math::vector::RealNumberVector;
+use crate::naive_bayes::{BaseNaiveBayes, NBDistribution};
+
+use serde::{Deserialize, Serialize};
+
+/// Naive Bayes classifier for Multinomial features
+#[derive(Serialize, Deserialize, Debug, PartialEq)]
+struct MultinomialNBDistribution<T: RealNumber> {
+    /// class labels known to the classifier
+    class_labels: Vec<T>,
+    class_priors: Vec<T>,
+    feature_prob: Vec<Vec<T>>,
+}
+
+impl<T: RealNumber, M: Matrix<T>> NBDistribution<T, M> for MultinomialNBDistribution<T> {
+    fn prior(&self, class_index: usize) -> T {
+        self.class_priors[class_index]
+    }
+
+    fn log_likelihood(&self, class_index: usize, j: &M::RowVector) -> T {
+        let mut likelihood = T::zero();
+        for feature in 0..j.len() {
+            let value = j.get(feature);
+            likelihood += value * self.feature_prob[class_index][feature].ln();
+        }
+        likelihood
+    }
+
+    fn classes(&self) -> &Vec<T> {
+        &self.class_labels
+    }
+}
+
+/// `MultinomialNB` parameters. Use `Default::default()` for default values.
+#[derive(Serialize, Deserialize, Debug)]
+pub struct MultinomialNBParameters<T: RealNumber> {
+    /// Additive (Laplace/Lidstone) smoothing parameter (0 for no smoothing).
+    pub alpha: T,
+    /// Prior probabilities of the classes. If specified the priors are not adjusted according to the data
+    pub priors: Option<Vec<T>>,
+}
+
+impl<T: RealNumber> MultinomialNBParameters<T> {
+    /// Create MultinomialNBParameters with specific paramaters.
+    pub fn new(alpha: T, priors: Option<Vec<T>>) -> Self {
+        Self { alpha, priors }
+    }
+}
+
+impl<T: RealNumber> Default for MultinomialNBParameters<T> {
+    fn default() -> Self {
+        Self {
+            alpha: T::one(),
+            priors: None,
+        }
+    }
+}
+
+impl<T: RealNumber> MultinomialNBDistribution<T> {
+    /// Fits the distribution to a NxM matrix where N is number of samples and M is number of features.
+    /// * `x` - training data.
+    /// * `y` - vector with target values (classes) of length N.
+    /// * `priors` - Optional vector with prior probabilities of the classes. If not defined,
+    /// priors are adjusted according to the data.
+    /// * `alpha` - Additive (Laplace/Lidstone) smoothing parameter.
+    pub fn fit<M: Matrix<T>>(
+        x: &M,
+        y: &M::RowVector,
+        alpha: T,
+        priors: Option<Vec<T>>,
+    ) -> Result<Self, Failed> {
+        let (n_samples, n_features) = x.shape();
+        let y_samples = y.len();
+        if y_samples != n_samples {
+            return Err(Failed::fit(&format!(
+                "Size of x should equal size of y; |x|=[{}], |y|=[{}]",
+                n_samples, y_samples
+            )));
+        }
+
+        if n_samples == 0 {
+            return Err(Failed::fit(&format!(
+                "Size of x and y should greater than 0; |x|=[{}]",
+                n_samples
+            )));
+        }
+        if alpha < T::zero() {
+            return Err(Failed::fit(&format!(
+                "Alpha should be greater than 0; |alpha|=[{}]",
+                alpha
+            )));
+        }
+
+        let y = y.to_vec();
+
+        let (class_labels, indices) = <Vec<T> as RealNumberVector<T>>::unique_with_indices(&y);
+        let mut class_count = vec![T::zero(); class_labels.len()];
+
+        for class_index in indices.iter() {
+            class_count[*class_index] += T::one();
+        }
+
+        let class_priors = if let Some(class_priors) = priors {
+            if class_priors.len() != class_labels.len() {
+                return Err(Failed::fit(
+                    "Size of priors provided does not match the number of classes of the data.",
+                ));
+            }
+            class_priors
+        } else {
+            class_count
+                .iter()
+                .map(|&c| c / T::from(n_samples).unwrap())
+                .collect()
+        };
+
+        let mut feature_in_class_counter = vec![vec![T::zero(); n_features]; class_labels.len()];
+
+        for (row, class_index) in row_iter(x).zip(indices) {
+            for idx in 0..n_features {
+                feature_in_class_counter[class_index][idx] += row[idx];
+            }
+        }
+
+        let feature_prob = feature_in_class_counter
+            .iter()
+            .map(|feature_count| {
+                let n_c = feature_count.sum();
+                feature_count
+                    .iter()
+                    .map(|&count| (count + alpha) / (n_c + alpha * T::from(n_features).unwrap()))
+                    .collect()
+            })
+            .collect();
+
+        Ok(Self {
+            class_labels,
+            class_priors,
+            feature_prob,
+        })
+    }
+}
+
+/// MultinomialNB implements the categorical naive Bayes algorithm for categorically distributed data.
+#[derive(Serialize, Deserialize, Debug, PartialEq)]
+pub struct MultinomialNB<T: RealNumber, M: Matrix<T>> {
+    inner: BaseNaiveBayes<T, M, MultinomialNBDistribution<T>>,
+}
+
+impl<T: RealNumber, M: Matrix<T>> MultinomialNB<T, M> {
+    /// Fits MultinomialNB with given data
+    /// * `x` - training data of size NxM where N is the number of samples and M is the number of
+    /// features.
+    /// * `y` - vector with target values (classes) of length N.
+    /// * `parameters` - additional parameters like class priors, alpha for smoothing and
+    /// binarizing threshold.
+    pub fn fit(
+        x: &M,
+        y: &M::RowVector,
+        parameters: MultinomialNBParameters<T>,
+    ) -> Result<Self, Failed> {
+        let distribution =
+            MultinomialNBDistribution::fit(x, y, parameters.alpha, parameters.priors)?;
+        let inner = BaseNaiveBayes::fit(distribution)?;
+        Ok(Self { inner })
+    }
+
+    /// Estimates the class labels for the provided data.
+    /// * `x` - data of shape NxM where N is number of data points to estimate and M is number of features.
+    /// Returns a vector of size N with class estimates.
+    pub fn predict(&self, x: &M) -> Result<M::RowVector, Failed> {
+        self.inner.predict(x)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::linalg::naive::dense_matrix::DenseMatrix;
+
+    #[test]
+    fn run_multinomial_naive_bayes() {
+        // Tests that MultinomialNB when alpha=1.0 gives the same values as
+        // those given for the toy example in Manning, Raghavan, and
+        // Schuetze's "Introduction to Information Retrieval" book:
+        // https://nlp.stanford.edu/IR-book/html/htmledition/naive-bayes-text-classification-1.html
+
+        // Training data points are:
+        // Chinese Beijing Chinese (class: China)
+        // Chinese Chinese Shanghai (class: China)
+        // Chinese Macao (class: China)
+        // Tokyo Japan Chinese (class: Japan)
+        let x = DenseMatrix::<f64>::from_2d_array(&[
+            &[1., 2., 0., 0., 0., 0.],
+            &[0., 2., 0., 0., 1., 0.],
+            &[0., 1., 0., 1., 0., 0.],
+            &[0., 1., 1., 0., 0., 1.],
+        ]);
+        let y = vec![0., 0., 0., 1.];
+        let mnb = MultinomialNB::fit(&x, &y, Default::default()).unwrap();
+
+        assert_eq!(mnb.inner.distribution.class_priors, &[0.75, 0.25]);
+        assert_eq!(
+            mnb.inner.distribution.feature_prob,
+            &[
+                &[1. / 7., 3. / 7., 1. / 14., 1. / 7., 1. / 7., 1. / 14.],
+                &[1. / 9., 2. / 9.0, 2. / 9.0, 1. / 9.0, 1. / 9.0, 2. / 9.0]
+            ]
+        );
+
+        // Testing data point is:
+        //  Chinese Chinese Chinese Tokyo Japan
+        let x_test = DenseMatrix::<f64>::from_2d_array(&[&[0., 3., 1., 0., 0., 1.]]);
+        let y_hat = mnb.predict(&x_test).unwrap();
+
+        assert_eq!(y_hat, &[0.]);
+    }
+
+    #[test]
+    fn multinomial_nb_scikit_parity() {
+        let x = DenseMatrix::<f64>::from_2d_array(&[
+            &[2., 4., 0., 0., 2., 1., 2., 4., 2., 0.],
+            &[3., 4., 0., 2., 1., 0., 1., 4., 0., 3.],
+            &[1., 4., 2., 4., 1., 0., 1., 2., 3., 2.],
+            &[0., 3., 3., 4., 1., 0., 3., 1., 1., 1.],
+            &[0., 2., 1., 4., 3., 4., 1., 2., 3., 1.],
+            &[3., 2., 4., 1., 3., 0., 2., 4., 0., 2.],
+            &[3., 1., 3., 0., 2., 0., 4., 4., 3., 4.],
+            &[2., 2., 2., 0., 1., 1., 2., 1., 0., 1.],
+            &[3., 3., 2., 2., 0., 2., 3., 2., 2., 3.],
+            &[4., 3., 4., 4., 4., 2., 2., 0., 1., 4.],
+            &[3., 4., 2., 2., 1., 4., 4., 4., 1., 3.],
+            &[3., 0., 1., 4., 4., 0., 0., 3., 2., 4.],
+            &[2., 0., 3., 3., 1., 2., 0., 2., 4., 1.],
+            &[2., 4., 0., 4., 2., 4., 1., 3., 1., 4.],
+            &[0., 2., 2., 3., 4., 0., 4., 4., 4., 4.],
+        ]);
+        let y = vec![2., 2., 0., 0., 0., 2., 1., 1., 0., 1., 0., 0., 2., 0., 2.];
+        let nb = MultinomialNB::fit(&x, &y, Default::default()).unwrap();
+
+        let y_hat = nb.predict(&x).unwrap();
+
+        assert!(nb
+            .inner
+            .distribution
+            .class_priors
+            .approximate_eq(&vec!(0.46, 0.2, 0.33), 1e-2));
+        assert!(nb.inner.distribution.feature_prob[1].approximate_eq(
+            &vec!(0.07, 0.12, 0.07, 0.15, 0.07, 0.09, 0.08, 0.10, 0.08, 0.11),
+            1e-1
+        ));
+        assert!(y_hat.approximate_eq(
+            &vec!(2.0, 2.0, 0.0, 0.0, 0.0, 2.0, 2.0, 1.0, 0.0, 1.0, 0.0, 2.0, 0.0, 0.0, 2.0),
+            1e-5
+        ));
+    }
+    #[test]
+    fn serde() {
+        let x = DenseMatrix::<f64>::from_2d_array(&[
+            &[1., 1., 0., 0., 0., 0.],
+            &[0., 1., 0., 0., 1., 0.],
+            &[0., 1., 0., 1., 0., 0.],
+            &[0., 1., 1., 0., 0., 1.],
+        ]);
+        let y = vec![0., 0., 0., 1.];
+
+        let mnb = MultinomialNB::fit(&x, &y, Default::default()).unwrap();
+        let deserialized_mnb: MultinomialNB<f64, DenseMatrix<f64>> =
+            serde_json::from_str(&serde_json::to_string(&mnb).unwrap()).unwrap();
+
+        assert_eq!(mnb, deserialized_mnb);
+    }
+}