diff --git a/Cargo.toml b/Cargo.toml
index 4779b47..56d0452 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -6,8 +6,7 @@ edition = "2021"
 # See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
 
 [dependencies]
-
-ndarray = {version="*", features=["approx"]}
+ndarray = {version="*", features=["approx-0_5"]}
 thiserror = "*"
 rand = "*"
 bimap = "*"
diff --git a/src/parameter_learning.rs b/src/parameter_learning.rs
index 5270d9e..19c0e4c 100644
--- a/src/parameter_learning.rs
+++ b/src/parameter_learning.rs
@@ -153,3 +153,20 @@ impl ParameterLearning for BayesianApproach {
         return (CIM, M, T);
     }
 }
+
+
+pub struct Cache<P: ParameterLearning> {
+    parameter_learning: P,
+}
+
+impl<P: ParameterLearning> Cache<P> {
+    pub fn fit<T:network::Network>(
+        &mut self,
+        net: &T,
+        dataset: &tools::Dataset,
+        node: usize,
+        parent_set: Option<BTreeSet<usize>>,
+    ) -> (Array3<f64>, Array3<usize>, Array2<f64>) {
+        self.parameter_learning.fit(net, dataset, node, parent_set)
+    }
+}
diff --git a/src/structure_learning.rs b/src/structure_learning.rs
index 8ba91df..b7db7ed 100644
--- a/src/structure_learning.rs
+++ b/src/structure_learning.rs
@@ -1,5 +1,7 @@
 pub mod score_function;
 pub mod score_based_algorithm;
+pub mod constraint_based_algorithm;
+pub mod hypothesis_test;
 use crate::network;
 use crate::tools;
 
diff --git a/src/structure_learning/constraint_based_algorithm.rs b/src/structure_learning/constraint_based_algorithm.rs
new file mode 100644
index 0000000..0d8b655
--- /dev/null
+++ b/src/structure_learning/constraint_based_algorithm.rs
@@ -0,0 +1,5 @@
+
+//pub struct CTPC {
+//
+//}
+
diff --git a/src/structure_learning/hypothesis_test.rs b/src/structure_learning/hypothesis_test.rs
new file mode 100644
index 0000000..fc5c86f
--- /dev/null
+++ b/src/structure_learning/hypothesis_test.rs
@@ -0,0 +1,101 @@
+use ndarray::Array2;
+use ndarray::Array3;
+use ndarray::Axis;
+
+use crate::network;
+use crate::parameter_learning;
+use std::collections::BTreeSet;
+
+pub trait HypothesisTest {
+
+    fn call<T, P>(
+        &self,
+        net: &T,
+        child_node: usize,
+        parent_node: usize,
+        separation_set: &BTreeSet<usize>,
+        cache: parameter_learning::Cache<P>
+    ) -> bool
+    where
+        T: network::Network,
+        P: parameter_learning::ParameterLearning;
+
+}
+
+
+pub struct ChiSquare {
+    pub alpha: f64,
+}
+
+pub struct F {
+
+}
+
+impl ChiSquare {
+    pub fn compare_matrices(
+        &self, i: usize,
+        M1: &Array3<usize>,
+        j: usize,
+        M2: &Array3<usize>
+    ) -> bool {
+        // Bregoli, A., Scutari, M. and Stella, F., 2021.
+        // A constraint-based algorithm for the structural learning of
+        // continuous-time Bayesian networks.
+        // International Journal of Approximate Reasoning, 138, pp.105-122.
+        //
+        // M  = M            M  = M
+        //  1    xx'|s        2    xx'|y,s
+        let M1 = M1.index_axis(Axis(0), i).mapv(|x| x as f64);
+        let M2 = M2.index_axis(Axis(0), j).mapv(|x| x as f64);
+        //                   __________________
+        //                  /    ===
+        //                 /     \       M
+        //                /      /        xx'|s
+        //               /       ===
+        //              /    x'ϵVal /X \
+        //             /            \ i/                  1
+        //K =         /      ------------------       L = -
+        //           /           ===                      K
+        //          /            \       M
+        //         /             /        xx'|y,s
+        //        /              ===
+        //       /           x'ϵVal /X \
+        //   \  /                   \ i/
+        //    \/
+        let K = M1.sum_axis(Axis(1)) / M2.sum_axis(Axis(1));
+        let K = K.mapv(f64::sqrt);
+        // Reshape to column vector.
+        let K = {
+            let n = K.len();
+            K.into_shape((n, 1)).unwrap()
+        };
+        let L = 1.0 / &K;
+        //        =====
+        //         \       K . M  - L . M
+        //          \           2        1
+        //          /      ---------------
+        //         /           M  + M
+        //        =====         2    1
+        //     x'ϵVal /X \
+        //            \ i/
+        let X_2 = (( K * &M2 - L * &M1 ).mapv(|a| a.powi(2)) / (&M2 + &M1)).sum_axis(Axis(1));
+        println!("X_2: {:?}", X_2); 
+        true
+    }
+}
+
+impl HypothesisTest for ChiSquare {
+    fn call<T, P>(
+        &self,
+        net: &T,
+        child_node: usize,
+        parent_node: usize,
+        separation_set: &BTreeSet<usize>,
+        cache: parameter_learning::Cache<P>
+    ) -> bool
+    where
+        T: network::Network,
+        P: parameter_learning::ParameterLearning {
+        todo!()
+    }
+}
diff --git a/tests/structure_learning.rs b/tests/structure_learning.rs
index c91f508..be9c8d5 100644
--- a/tests/structure_learning.rs
+++ b/tests/structure_learning.rs
@@ -7,6 +7,7 @@ use reCTBN::network::Network;
 use reCTBN::params;
 use reCTBN::structure_learning::score_function::*;
 use reCTBN::structure_learning::{score_based_algorithm::*, StructureLearningAlgorithm};
+use reCTBN::structure_learning::hypothesis_test::*;
 use reCTBN::tools::*;
 use std::collections::BTreeSet;
 
@@ -315,3 +316,25 @@ pub fn learn_mixed_discrete_net_3_nodes_hill_climbing_bic_1_parent_constraint()
     let hl = HillClimbing::new(bic, Some(1));
     learn_mixed_discrete_net_3_nodes_1_parent_constraint(hl);
 }
+
+#[test]
+pub fn chi_square_compare_matrices () {
+    let i: usize = 1;
+    let M1 = arr3(&[
+       [[ 1,  2,  3],
+        [ 4,  5,  6]],
+       [[ 22,  12,  90],
+        [3, 20, 40]],
+        [[ 1,  2,  3],
+        [ 4,  5,  6]],
+       [[ 7,  8,  9],
+        [10, 11, 12]]
+    ]);
+    let j: usize = 1;
+    let M2 = arr3(&[[[ 1,  2,  3],     // -- 2 rows  \_
+        [ 4,  5,  6]],
+       [[ 7,  8,  9],
+        [10, 11, 12]]]);
+    let chi_sq = ChiSquare {alpha: 0.5};
+    chi_sq.compare_matrices( i, &M1, j, &M2);
+}