Multinomial logistic regression (#159)

* Generalized argmin param across dimensions

* Wrote multinomial loss and gradient

* Finished multi fitted model

* Implement dot and norm on ArgminParams

* Add test for multinomial loss and grad

* Add multi logistic regression tests

* Add docs

algorithms/linfa-logistic/Cargo.toml

@@ -16,6 +16,7 @@ categories = ["algorithms", "mathematics", "science"]
 [dependencies]
 ndarray = { version = "0.15", features = ["approx", "blas"] }
 ndarray-linalg = "0.14"
+ndarray-stats = "0.5.0"
 num-traits = "0.2"
 argmin = { version = "0.4.6", features = ["ndarrayl"] }
 serde = "1.0"

algorithms/linfa-logistic/src/argmin_param.rs

@@ -1,4 +1,4 @@
-//! This module defines newtypes for ndarray's Array1.
+//! This module defines newtypes for ndarray's Array.
 //!
 //! This is necessary to be able to abstract over floats (f32 and f64) so that
 //! the logistic regression code can be abstract in the float type it works
@@ -8,51 +8,60 @@
 
 use crate::float::Float;
 use argmin::prelude::*;
-use ndarray::Array1;
+use ndarray::{Array, ArrayBase, Data, Dimension, Zip};
 use serde::{Deserialize, Serialize};
 
+pub fn elem_dot<F: linfa::Float, A1: Data<Elem = F>, A2: Data<Elem = F>, D: Dimension>(
+    a: &ArrayBase<A1, D>,
+    b: &ArrayBase<A2, D>,
+) -> F {
+    Zip::from(a)
+        .and(b)
+        .fold(F::zero(), |acc, &a, &b| acc + a * b)
+}
+
 #[derive(Serialize, Clone, Deserialize, Debug, Default)]
-pub struct ArgminParam<F>(pub Array1<F>);
+pub struct ArgminParam<F, D: Dimension>(pub Array<F, D>);
 
-impl<F> ArgminParam<F> {
+impl<F, D: Dimension> ArgminParam<F, D> {
     #[inline]
-    pub fn as_array(&self) -> &Array1<F> {
+    pub fn as_array(&self) -> &Array<F, D> {
         &self.0
     }
 }
 
-impl<F: Float> ArgminSub<ArgminParam<F>, ArgminParam<F>> for ArgminParam<F> {
-    fn sub(&self, other: &ArgminParam<F>) -> ArgminParam<F> {
+impl<F: Float, D: Dimension> ArgminSub<ArgminParam<F, D>, ArgminParam<F, D>> for ArgminParam<F, D> {
+    fn sub(&self, other: &ArgminParam<F, D>) -> ArgminParam<F, D> {
         ArgminParam(&self.0 - &other.0)
     }
 }
 
-impl<F: Float> ArgminAdd<ArgminParam<F>, ArgminParam<F>> for ArgminParam<F> {
-    fn add(&self, other: &ArgminParam<F>) -> ArgminParam<F> {
+impl<F: Float, D: Dimension> ArgminAdd<ArgminParam<F, D>, ArgminParam<F, D>> for ArgminParam<F, D> {
+    fn add(&self, other: &ArgminParam<F, D>) -> ArgminParam<F, D> {
         ArgminParam(&self.0 + &other.0)
     }
 }
 
-impl<F: Float> ArgminDot<ArgminParam<F>, F> for ArgminParam<F> {
-    fn dot(&self, other: &ArgminParam<F>) -> F {
-        self.0.dot(&other.0)
+impl<F: Float, D: Dimension> ArgminDot<ArgminParam<F, D>, F> for ArgminParam<F, D> {
+    fn dot(&self, other: &ArgminParam<F, D>) -> F {
+        elem_dot(&self.0, &other.0)
     }
 }
 
-impl<F: Float> ArgminNorm<F> for ArgminParam<F> {
+impl<F: Float, D: Dimension> ArgminNorm<F> for ArgminParam<F, D> {
     fn norm(&self) -> F {
-        self.0.dot(&self.0)
+        num_traits::Float::sqrt(elem_dot(&self.0, &self.0))
     }
 }
 
-impl<F: Float> ArgminMul<F, ArgminParam<F>> for ArgminParam<F> {
-    fn mul(&self, other: &F) -> ArgminParam<F> {
+impl<F: Float, D: Dimension> ArgminMul<F, ArgminParam<F, D>> for ArgminParam<F, D> {
+    fn mul(&self, other: &F) -> ArgminParam<F, D> {
         ArgminParam(&self.0 * *other)
     }
 }
 
-impl<F: Float> ArgminMul<ArgminParam<F>, ArgminParam<F>> for ArgminParam<F> {
-    fn mul(&self, other: &ArgminParam<F>) -> ArgminParam<F> {
+impl<F: Float, D: Dimension> ArgminMul<ArgminParam<F, D>, ArgminParam<F, D>> for ArgminParam<F, D> {
+    fn mul(&self, other: &ArgminParam<F, D>) -> ArgminParam<F, D> {
         ArgminParam(&self.0 * &other.0)
     }
 }

algorithms/linfa-logistic/src/float.rs

@@ -1,6 +1,6 @@
 use crate::argmin_param::ArgminParam;
 use argmin::prelude::{ArgminFloat, ArgminMul};
-use ndarray::NdFloat;
+use ndarray::{Dimension, Ix1, Ix2, NdFloat};
 use ndarray_linalg::Lapack;
 use num_traits::FromPrimitive;
 
@@ -13,21 +13,22 @@ pub trait Float:
     + Default
     + Clone
     + FromPrimitive
-    + ArgminMul<ArgminParam<Self>, ArgminParam<Self>>
+    + ArgminMul<ArgminParam<Self, Ix1>, ArgminParam<Self, Ix1>>
+    + ArgminMul<ArgminParam<Self, Ix2>, ArgminParam<Self, Ix2>>
     + linfa::Float
 {
     const POSITIVE_LABEL: Self;
     const NEGATIVE_LABEL: Self;
 }
 
-impl ArgminMul<ArgminParam<Self>, ArgminParam<Self>> for f64 {
-    fn mul(&self, other: &ArgminParam<Self>) -> ArgminParam<Self> {
+impl<D: Dimension> ArgminMul<ArgminParam<Self, D>, ArgminParam<Self, D>> for f64 {
+    fn mul(&self, other: &ArgminParam<Self, D>) -> ArgminParam<Self, D> {
         ArgminParam(&other.0 * *self)
     }
 }
 
-impl ArgminMul<ArgminParam<Self>, ArgminParam<Self>> for f32 {
-    fn mul(&self, other: &ArgminParam<Self>) -> ArgminParam<Self> {
+impl<D: Dimension> ArgminMul<ArgminParam<Self, D>, ArgminParam<Self, D>> for f32 {
+    fn mul(&self, other: &ArgminParam<Self, D>) -> ArgminParam<Self, D> {
         ArgminParam(&other.0 * *self)
     }
 }