Added the following functions for computing statistics on vectors:

mean_sign_agreement(), correlation(), covariance(), r_squared(),
and mean_squared_error()

dlib/statistics/statistics.h

@@ -383,6 +383,137 @@ namespace dlib
         T n;
     };
 
+// ----------------------------------------------------------------------------------------
+
+    template <
+        typename T, 
+        typename alloc
+        >
+    double mean_sign_agreement (
+        const std::vector<T,alloc>& a,
+        const std::vector<T,alloc>& b
+    )
+    {
+        // make sure requires clause is not broken
+        DLIB_ASSERT(a.size() == b.size(),
+                    "\t double mean_sign_agreement(a,b)"
+                    << "\n\t a and b must be the same length."
+                    << "\n\t a.size(): " << a.size()
+                    << "\n\t b.size(): " << b.size()
+        );
+
+        
+        double temp = 0;
+        for (unsigned long i = 0; i < a.size(); ++i)
+        {
+            if (a[i] >= 0 && b[i] >= 0 ||
+                a[i] < 0  && b[i] <  0)
+            {
+                temp += 1;
+            }
+        }
+
+        return temp/a.size();
+    }
+
+// ----------------------------------------------------------------------------------------
+
+    template <
+        typename T, 
+        typename alloc
+        >
+    double correlation (
+        const std::vector<T,alloc>& a,
+        const std::vector<T,alloc>& b
+    )
+    {
+        // make sure requires clause is not broken
+        DLIB_ASSERT(a.size() == b.size() && a.size() > 1,
+                    "\t double correlation(a,b)"
+                    << "\n\t a and b must be the same length and have more than one element."
+                    << "\n\t a.size(): " << a.size()
+                    << "\n\t b.size(): " << b.size()
+        );
+
+        running_scalar_covariance<double> rs;
+        for (unsigned long i = 0; i < a.size(); ++i)
+        {
+            rs.add(a[i], b[i]);
+        }
+        return rs.correlation();
+    }
+
+// ----------------------------------------------------------------------------------------
+
+    template <
+        typename T, 
+        typename alloc
+        >
+    double covariance (
+        const std::vector<T,alloc>& a,
+        const std::vector<T,alloc>& b
+    )
+    {
+        // make sure requires clause is not broken
+        DLIB_ASSERT(a.size() == b.size() && a.size() > 1,
+                    "\t double covariance(a,b)"
+                    << "\n\t a and b must be the same length and have more than one element."
+                    << "\n\t a.size(): " << a.size()
+                    << "\n\t b.size(): " << b.size()
+        );
+
+        running_scalar_covariance<double> rs;
+        for (unsigned long i = 0; i < a.size(); ++i)
+        {
+            rs.add(a[i], b[i]);
+        }
+        return rs.covariance();
+    }
+
+// ----------------------------------------------------------------------------------------
+
+    template <
+        typename T, 
+        typename alloc
+        >
+    double r_squared (
+        const std::vector<T,alloc>& a,
+        const std::vector<T,alloc>& b
+    )
+    {
+        // make sure requires clause is not broken
+        DLIB_ASSERT(a.size() == b.size() && a.size() > 1,
+                    "\t double r_squared(a,b)"
+                    << "\n\t a and b must be the same length and have more than one element."
+                    << "\n\t a.size(): " << a.size()
+                    << "\n\t b.size(): " << b.size()
+        );
+
+        return std::pow(correlation(a,b),2.0);
+    }
+
+// ----------------------------------------------------------------------------------------
+
+    template <
+        typename T, 
+        typename alloc
+        >
+    double mean_squared_error (
+        const std::vector<T,alloc>& a,
+        const std::vector<T,alloc>& b
+    )
+    {
+        // make sure requires clause is not broken
+        DLIB_ASSERT(a.size() == b.size(),
+                    "\t double mean_squared_error(a,b)"
+                    << "\n\t a and b must be the same length."
+                    << "\n\t a.size(): " << a.size()
+                    << "\n\t b.size(): " << b.size()
+        );
+
+        return mean(squared(matrix_cast<double>(vector_to_matrix(a))-matrix_cast<double>(vector_to_matrix(b))));
+    }
+
 // ----------------------------------------------------------------------------------------
 
     template <

dlib/statistics/statistics_abstract.h

@@ -308,6 +308,100 @@ namespace dlib
         !*/
     };
 
+// ----------------------------------------------------------------------------------------
+
+    template <
+        typename T, 
+        typename alloc
+        >
+    double mean_sign_agreement (
+        const std::vector<T,alloc>& a,
+        const std::vector<T,alloc>& b
+    );
+    /*!
+        requires
+            - a.size() == b.size()
+        ensures
+            - returns the number of times a[i] has the same sign as b[i] divided by
+              a.size().  So we return the probability that elements of a and b have
+              the same sign.
+    !*/
+
+// ----------------------------------------------------------------------------------------
+
+    template <
+        typename T, 
+        typename alloc
+        >
+    double correlation (
+        const std::vector<T,alloc>& a,
+        const std::vector<T,alloc>& b
+    );
+    /*!
+        requires
+            - a.size() == b.size()
+            - a.size() > 1
+        ensures
+            - returns the correlation coefficient between all the elements of a and b.
+              (i.e. how correlated is a(i) with b(i))
+    !*/
+
+// ----------------------------------------------------------------------------------------
+
+    template <
+        typename T, 
+        typename alloc
+        >
+    double covariance (
+        const std::vector<T,alloc>& a,
+        const std::vector<T,alloc>& b
+    );
+    /*!
+        requires
+            - a.size() == b.size()
+            - a.size() > 1
+        ensures
+            - returns the covariance between all the elements of a and b.
+              (i.e. how does a(i) vary with b(i))
+    !*/
+
+// ----------------------------------------------------------------------------------------
+
+    template <
+        typename T, 
+        typename alloc
+        >
+    double r_squared (
+        const std::vector<T,alloc>& a,
+        const std::vector<T,alloc>& b
+    );
+    /*!
+        requires
+            - a.size() == b.size()
+            - a.size() > 1
+        ensures
+            - returns the R^2 coefficient of determination between all the elements of a and b.
+              This value is just the square of correlation(a,b).
+    !*/
+
+// ----------------------------------------------------------------------------------------
+
+    template <
+        typename T, 
+        typename alloc
+        >
+    double mean_squared_error (
+        const std::vector<T,alloc>& a,
+        const std::vector<T,alloc>& b
+    );
+    /*!
+        requires
+            - a.size() == b.size()
+        ensures
+            - returns the mean squared error between all the elements of a and b.
+              (i.e. mean(squared(vector_to_matrix(a)-vector_to_matrix(b))))
+    !*/
+
 // ----------------------------------------------------------------------------------------
 
     template <