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 </pre><pre class="rust"><code><span class="doccomment">//! Generalized Linear Model module
 //!
 //! &lt;i&gt;This model is likely to undergo changes in the near future.
 //! These changes will improve the learning algorithm.&lt;/i&gt;
 //!
 //! Contains implemention of generalized linear models using
 //! iteratively reweighted least squares.
 //!
 //! The model will automatically add the intercept term to the
 //! input data.
 //!
 //! # Usage
 //!
 //! ```
 //! use rusty_machine::learning::glm::{GenLinearModel, Bernoulli};
 //! use rusty_machine::learning::SupModel;
 //! use rusty_machine::linalg::Matrix;
 //! use rusty_machine::linalg::Vector;
 //!
 //! let inputs = Matrix::new(4,1,vec![1.0,3.0,5.0,7.0]);
 //! let targets = Vector::new(vec![0.,0.,1.,1.]);
 //!
 //! // Construct a GLM with a Bernoulli distribution
 //! // This is equivalent to a logistic regression model.
 //! let mut log_mod = GenLinearModel::new(Bernoulli);
 //!
 //! // Train the model
 //! log_mod.train(&amp;inputs, &amp;targets).unwrap();
 //!
 //! // Now we&#39;ll predict a new point
 //! let new_point = Matrix::new(1,1,vec![10.]);
 //! let output = log_mod.predict(&amp;new_point).unwrap();
 //!
 //! // Hopefully we classified our new point correctly!
 //! assert!(output[0] &gt; 0.5, &quot;Our classifier isn&#39;t very good!&quot;);
 //! ```

 </span><span class="kw">use </span>linalg::Vector;
 <span class="kw">use </span>linalg::{Matrix, BaseMatrix};

 <span class="kw">use </span>learning::{LearningResult, SupModel};
 <span class="kw">use </span>learning::error::{Error, ErrorKind};

 <span class="doccomment">/// The Generalized Linear Model
 ///
 /// The model is generic over a Criterion
 /// which specifies the distribution family and
 /// the link function.
 </span><span class="attribute">#[derive(Debug)]
 </span><span class="kw">pub struct </span>GenLinearModel&lt;C: Criterion&gt; {
     parameters: <span class="prelude-ty">Option</span>&lt;Vector&lt;f64&gt;&gt;,
     criterion: C,
 }

 <span class="kw">impl</span>&lt;C: Criterion&gt; GenLinearModel&lt;C&gt; {
     <span class="doccomment">/// Constructs a new Generalized Linear Model.
     ///
     /// Takes a Criterion which fully specifies the family
     /// and the link function used by the GLM.
     ///
     /// ```
     /// use rusty_machine::learning::glm::GenLinearModel;
     /// use rusty_machine::learning::glm::Bernoulli;
     ///
     /// let glm = GenLinearModel::new(Bernoulli);
     /// ```
     </span><span class="kw">pub fn </span>new(criterion: C) -&gt; GenLinearModel&lt;C&gt; {
         GenLinearModel {
             parameters: <span class="prelude-val">None</span>,
             criterion: criterion,
         }
     }
 }

 <span class="doccomment">/// Supervised model trait for the GLM.
 ///
 /// Predictions are made from the model by computing g^-1(Xb).
 ///
 /// The model is trained using Iteratively Re-weighted Least Squares.
 </span><span class="kw">impl</span>&lt;C: Criterion&gt; SupModel&lt;Matrix&lt;f64&gt;, Vector&lt;f64&gt;&gt; <span class="kw">for </span>GenLinearModel&lt;C&gt; {
     <span class="doccomment">/// Predict output from inputs.
     </span><span class="kw">fn </span>predict(<span class="kw-2">&amp;</span><span class="self">self</span>, inputs: <span class="kw-2">&amp;</span>Matrix&lt;f64&gt;) -&gt; LearningResult&lt;Vector&lt;f64&gt;&gt; {
         <span class="kw">if let </span><span class="prelude-val">Some</span>(<span class="kw-2">ref </span>v) = <span class="self">self</span>.parameters {
             <span class="kw">let </span>ones = Matrix::&lt;f64&gt;::ones(inputs.rows(), <span class="number">1</span>);
             <span class="kw">let </span>full_inputs = ones.hcat(inputs);
             <span class="prelude-val">Ok</span>(<span class="self">self</span>.criterion.apply_link_inv(full_inputs * v))
         } <span class="kw">else </span>{
             <span class="prelude-val">Err</span>(Error::new_untrained())
         }
     }

     <span class="doccomment">/// Train the model using inputs and targets.
     </span><span class="kw">fn </span>train(<span class="kw-2">&amp;mut </span><span class="self">self</span>, inputs: <span class="kw-2">&amp;</span>Matrix&lt;f64&gt;, targets: <span class="kw-2">&amp;</span>Vector&lt;f64&gt;) -&gt; LearningResult&lt;()&gt; {
         <span class="kw">let </span>n = inputs.rows();

         <span class="kw">if </span>n != targets.size() {
             <span class="kw">return </span><span class="prelude-val">Err</span>(Error::new(ErrorKind::InvalidData,
                                   <span class="string">&quot;Training data do not have the same dimensions&quot;</span>));
         }

         <span class="comment">// Construct initial estimate for mu
         </span><span class="kw">let </span><span class="kw-2">mut </span>mu = Vector::new(<span class="self">self</span>.criterion.initialize_mu(targets.data()));
         <span class="kw">let </span><span class="kw-2">mut </span>z = mu.clone();
         <span class="kw">let </span><span class="kw-2">mut </span>beta: Vector&lt;f64&gt; = Vector::new(<span class="macro">vec!</span>[<span class="number">0f64</span>; inputs.cols() + <span class="number">1</span>]);

         <span class="kw">let </span>ones = Matrix::&lt;f64&gt;::ones(inputs.rows(), <span class="number">1</span>);
         <span class="kw">let </span>full_inputs = ones.hcat(inputs);
         <span class="kw">let </span>x_t = full_inputs.transpose();

         <span class="comment">// Iterate to convergence
         </span><span class="kw">for _ in </span><span class="number">0</span>..<span class="number">8 </span>{
             <span class="kw">let </span>w_diag = <span class="self">self</span>.criterion.compute_working_weight(mu.data());
             <span class="kw">let </span>y_bar_data = <span class="self">self</span>.criterion.compute_y_bar(targets.data(), mu.data());

             <span class="kw">let </span>w = Matrix::from_diag(<span class="kw-2">&amp;</span>w_diag);
             <span class="kw">let </span>y_bar = Vector::new(y_bar_data);

             <span class="kw">let </span>x_t_w = <span class="kw-2">&amp;</span>x_t * w;

             <span class="kw">let </span>new_beta = (<span class="kw-2">&amp;</span>x_t_w * <span class="kw-2">&amp;</span>full_inputs)
                 .inverse()
                 .expect(<span class="string">&quot;Could not compute input data inverse.&quot;</span>) *
                            x_t_w * z;
             <span class="kw">let </span>diff = (beta - <span class="kw-2">&amp;</span>new_beta).apply(<span class="kw-2">&amp;</span>|x| x.abs()).sum();
             beta = new_beta;

             <span class="kw">if </span>diff &lt; <span class="number">1e-10 </span>{
                 <span class="kw">break</span>;
             }

             <span class="comment">// Update z and mu
             </span><span class="kw">let </span>fitted = <span class="kw-2">&amp;</span>full_inputs * <span class="kw-2">&amp;</span>beta;
             z = y_bar + <span class="kw-2">&amp;</span>fitted;
             mu = <span class="self">self</span>.criterion.apply_link_inv(fitted);
         }

         <span class="self">self</span>.parameters = <span class="prelude-val">Some</span>(beta);
         <span class="prelude-val">Ok</span>(())
     }
 }

 <span class="doccomment">/// The criterion for the Generalized Linear Model.
 ///
 /// This trait specifies a Link function and requires a model
 /// variance to be specified. The model variance must be defined
 /// to specify the regression family. The other functions need not
 /// be specified but can be used to control optimization.
 </span><span class="kw">pub trait </span>Criterion {
     <span class="doccomment">/// The link function of the GLM Criterion.
     </span><span class="kw">type </span>Link: LinkFunc;

     <span class="doccomment">/// The variance of the regression family.
     </span><span class="kw">fn </span>model_variance(<span class="kw-2">&amp;</span><span class="self">self</span>, mu: f64) -&gt; f64;

     <span class="doccomment">/// Initializes the mean value.
     ///
     /// By default the mean takes the training target values.
     </span><span class="kw">fn </span>initialize_mu(<span class="kw-2">&amp;</span><span class="self">self</span>, y: <span class="kw-2">&amp;</span>[f64]) -&gt; Vec&lt;f64&gt; {
         y.to_vec()
     }

     <span class="doccomment">/// Computes the working weights that make up the diagonal
     /// of the `W` matrix used in the iterative reweighted least squares
     /// algorithm.
     ///
     /// This is equal to:
     ///
     /// 1 / (Var(u) * g&#39;(u) * g&#39;(u))
     </span><span class="kw">fn </span>compute_working_weight(<span class="kw-2">&amp;</span><span class="self">self</span>, mu: <span class="kw-2">&amp;</span>[f64]) -&gt; Vec&lt;f64&gt; {
         <span class="kw">let </span><span class="kw-2">mut </span>working_weights_vec = Vec::with_capacity(mu.len());

         <span class="kw">for </span>m <span class="kw">in </span>mu {
             <span class="kw">let </span>grad = <span class="self">self</span>.link_grad(<span class="kw-2">*</span>m);
             working_weights_vec.push(<span class="number">1f64 </span>/ (<span class="self">self</span>.model_variance(<span class="kw-2">*</span>m) * grad * grad));
         }

         working_weights_vec
     }

     <span class="doccomment">/// Computes the adjustment to the fitted values used during
     /// fitting.
     ///
     /// This is equal to:
     ///
     /// g`(u) * (y - u)
     </span><span class="kw">fn </span>compute_y_bar(<span class="kw-2">&amp;</span><span class="self">self</span>, y: <span class="kw-2">&amp;</span>[f64], mu: <span class="kw-2">&amp;</span>[f64]) -&gt; Vec&lt;f64&gt; {
         <span class="kw">let </span><span class="kw-2">mut </span>y_bar_vec = Vec::with_capacity(mu.len());

         <span class="kw">for </span>(idx, m) <span class="kw">in </span>mu.iter().enumerate() {
             y_bar_vec.push(<span class="self">self</span>.link_grad(<span class="kw-2">*</span>m) * (y[idx] - m));
         }

         y_bar_vec
     }

     <span class="doccomment">/// Applies the link function to a vector.
     </span><span class="kw">fn </span>apply_link_func(<span class="kw-2">&amp;</span><span class="self">self</span>, vec: Vector&lt;f64&gt;) -&gt; Vector&lt;f64&gt; {
         vec.apply(<span class="kw-2">&amp;</span><span class="self">Self</span>::Link::func)
     }

     <span class="doccomment">/// Applies the inverse of the link function to a vector.
     </span><span class="kw">fn </span>apply_link_inv(<span class="kw-2">&amp;</span><span class="self">self</span>, vec: Vector&lt;f64&gt;) -&gt; Vector&lt;f64&gt; {
         vec.apply(<span class="kw-2">&amp;</span><span class="self">Self</span>::Link::func_inv)
     }

     <span class="doccomment">/// Computes the gradient of the link function.
     </span><span class="kw">fn </span>link_grad(<span class="kw-2">&amp;</span><span class="self">self</span>, mu: f64) -&gt; f64 {
         <span class="self">Self</span>::Link::func_grad(mu)
     }
 }

 <span class="doccomment">/// Link functions.
 ///
 /// Used within Generalized Linear Regression models.
 </span><span class="kw">pub trait </span>LinkFunc {
     <span class="doccomment">/// The link function.
     </span><span class="kw">fn </span>func(x: f64) -&gt; f64;

     <span class="doccomment">/// The gradient of the link function.
     </span><span class="kw">fn </span>func_grad(x: f64) -&gt; f64;

     <span class="doccomment">/// The inverse of the link function.
     /// Often called the &#39;mean&#39; function.
     </span><span class="kw">fn </span>func_inv(x: f64) -&gt; f64;
 }

 <span class="doccomment">/// The Logit link function.
 ///
 /// Used primarily as the canonical link in Binomial Regression.
 </span><span class="attribute">#[derive(Clone, Copy, Debug)]
 </span><span class="kw">pub struct </span>Logit;

 <span class="doccomment">/// The Logit link function.
 ///
 /// g(u) = ln(x / (1 - x))
 </span><span class="kw">impl </span>LinkFunc <span class="kw">for </span>Logit {
     <span class="kw">fn </span>func(x: f64) -&gt; f64 {
         (x / (<span class="number">1f64 </span>- x)).ln()
     }

     <span class="kw">fn </span>func_grad(x: f64) -&gt; f64 {
         <span class="number">1f64 </span>/ (x * (<span class="number">1f64 </span>- x))
     }

     <span class="kw">fn </span>func_inv(x: f64) -&gt; f64 {
         <span class="number">1.0 </span>/ (<span class="number">1.0 </span>+ (-x).exp())
     }
 }

 <span class="doccomment">/// The log link function.
 ///
 /// Used primarily as the canonical link in Poisson Regression.
 </span><span class="attribute">#[derive(Clone, Copy, Debug)]
 </span><span class="kw">pub struct </span>Log;

 <span class="doccomment">/// The log link function.
 ///
 /// g(u) = ln(u)
 </span><span class="kw">impl </span>LinkFunc <span class="kw">for </span>Log {
     <span class="kw">fn </span>func(x: f64) -&gt; f64 {
         x.ln()
     }

     <span class="kw">fn </span>func_grad(x: f64) -&gt; f64 {
         <span class="number">1f64 </span>/ x
     }

     <span class="kw">fn </span>func_inv(x: f64) -&gt; f64 {
         x.exp()
     }
 }

 <span class="doccomment">/// The Identity link function.
 ///
 /// Used primarily as the canonical link in Linear Regression.
 </span><span class="attribute">#[derive(Clone, Copy, Debug)]
 </span><span class="kw">pub struct </span>Identity;

 <span class="doccomment">/// The Identity link function.
 ///
 /// g(u) = u
 </span><span class="kw">impl </span>LinkFunc <span class="kw">for </span>Identity {
     <span class="kw">fn </span>func(x: f64) -&gt; f64 {
         x
     }

     <span class="kw">fn </span>func_grad(<span class="kw">_</span>: f64) -&gt; f64 {
         <span class="number">1f64
     </span>}

     <span class="kw">fn </span>func_inv(x: f64) -&gt; f64 {
         x
     }
 }

 <span class="doccomment">/// The Bernoulli regression family.
 ///
 /// This is equivalent to logistic regression.
 </span><span class="attribute">#[derive(Clone, Copy, Debug)]
 </span><span class="kw">pub struct </span>Bernoulli;

 <span class="kw">impl </span>Criterion <span class="kw">for </span>Bernoulli {
     <span class="kw">type </span>Link = Logit;

     <span class="kw">fn </span>model_variance(<span class="kw-2">&amp;</span><span class="self">self</span>, mu: f64) -&gt; f64 {
         <span class="kw">let </span>var = mu * (<span class="number">1f64 </span>- mu);

         <span class="kw">if </span>var.abs() &lt; <span class="number">1e-10 </span>{
             <span class="number">1e-10
         </span>} <span class="kw">else </span>{
             var
         }
     }

     <span class="kw">fn </span>initialize_mu(<span class="kw-2">&amp;</span><span class="self">self</span>, y: <span class="kw-2">&amp;</span>[f64]) -&gt; Vec&lt;f64&gt; {
         <span class="kw">let </span><span class="kw-2">mut </span>mu_data = Vec::with_capacity(y.len());

         <span class="kw">for </span>y_val <span class="kw">in </span>y {
             mu_data.push(<span class="kw">if </span><span class="kw-2">*</span>y_val &lt; <span class="number">1e-10 </span>{
                 <span class="number">1e-10
             </span>} <span class="kw">else if </span><span class="kw-2">*</span>y_val &gt; <span class="number">1f64 </span>- <span class="number">1e-10 </span>{
                 <span class="number">1f64 </span>- <span class="number">1e-10
             </span>} <span class="kw">else </span>{
                 <span class="kw-2">*</span>y_val
             });
         }

         mu_data
     }

     <span class="kw">fn </span>compute_working_weight(<span class="kw-2">&amp;</span><span class="self">self</span>, mu: <span class="kw-2">&amp;</span>[f64]) -&gt; Vec&lt;f64&gt; {
         <span class="kw">let </span><span class="kw-2">mut </span>working_weights_vec = Vec::with_capacity(mu.len());

         <span class="kw">for </span>m <span class="kw">in </span>mu {
             <span class="kw">let </span>var = <span class="self">self</span>.model_variance(<span class="kw-2">*</span>m);

             working_weights_vec.push(<span class="kw">if </span>var.abs() &lt; <span class="number">1e-5 </span>{
                 <span class="number">1e-5
             </span>} <span class="kw">else </span>{
                 var
             });
         }

         working_weights_vec
     }

     <span class="kw">fn </span>compute_y_bar(<span class="kw-2">&amp;</span><span class="self">self</span>, y: <span class="kw-2">&amp;</span>[f64], mu: <span class="kw-2">&amp;</span>[f64]) -&gt; Vec&lt;f64&gt; {
         <span class="kw">let </span><span class="kw-2">mut </span>y_bar_vec = Vec::with_capacity(y.len());

         <span class="kw">for </span>(idx, m) <span class="kw">in </span>mu.iter().enumerate() {
             <span class="kw">let </span>target_diff = y[idx] - m;

             y_bar_vec.push(<span class="kw">if </span>target_diff.abs() &lt; <span class="number">1e-15 </span>{
                 <span class="number">0f64
             </span>} <span class="kw">else </span>{
                 <span class="self">self</span>.link_grad(<span class="kw-2">*</span>m) * target_diff
             });
         }

         y_bar_vec
     }
 }

 <span class="doccomment">/// The Binomial regression family.
 </span><span class="attribute">#[derive(Debug)]
 </span><span class="kw">pub struct </span>Binomial {
     weights: Vec&lt;f64&gt;,
 }

 <span class="kw">impl </span>Criterion <span class="kw">for </span>Binomial {
     <span class="kw">type </span>Link = Logit;

     <span class="kw">fn </span>model_variance(<span class="kw-2">&amp;</span><span class="self">self</span>, mu: f64) -&gt; f64 {
         <span class="kw">let </span>var = mu * (<span class="number">1f64 </span>- mu);

         <span class="kw">if </span>var.abs() &lt; <span class="number">1e-10 </span>{
             <span class="number">1e-10
         </span>} <span class="kw">else </span>{
             var
         }

     }

     <span class="kw">fn </span>initialize_mu(<span class="kw-2">&amp;</span><span class="self">self</span>, y: <span class="kw-2">&amp;</span>[f64]) -&gt; Vec&lt;f64&gt; {
         <span class="kw">let </span><span class="kw-2">mut </span>mu_data = Vec::with_capacity(y.len());

         <span class="kw">for </span>y_val <span class="kw">in </span>y {
             mu_data.push(<span class="kw">if </span><span class="kw-2">*</span>y_val &lt; <span class="number">1e-10 </span>{
                 <span class="number">1e-10
             </span>} <span class="kw">else if </span><span class="kw-2">*</span>y_val &gt; <span class="number">1f64 </span>- <span class="number">1e-10 </span>{
                 <span class="number">1f64 </span>- <span class="number">1e-10
             </span>} <span class="kw">else </span>{
                 <span class="kw-2">*</span>y_val
             });
         }

         mu_data
     }

     <span class="kw">fn </span>compute_working_weight(<span class="kw-2">&amp;</span><span class="self">self</span>, mu: <span class="kw-2">&amp;</span>[f64]) -&gt; Vec&lt;f64&gt; {
         <span class="kw">let </span><span class="kw-2">mut </span>working_weights_vec = Vec::with_capacity(mu.len());

         <span class="kw">for </span>(idx, m) <span class="kw">in </span>mu.iter().enumerate() {
             <span class="kw">let </span>var = <span class="self">self</span>.model_variance(<span class="kw-2">*</span>m) / <span class="self">self</span>.weights[idx];

             working_weights_vec.push(<span class="kw">if </span>var.abs() &lt; <span class="number">1e-5 </span>{
                 <span class="number">1e-5
             </span>} <span class="kw">else </span>{
                 var
             });
         }

         working_weights_vec
     }

     <span class="kw">fn </span>compute_y_bar(<span class="kw-2">&amp;</span><span class="self">self</span>, y: <span class="kw-2">&amp;</span>[f64], mu: <span class="kw-2">&amp;</span>[f64]) -&gt; Vec&lt;f64&gt; {
         <span class="kw">let </span><span class="kw-2">mut </span>y_bar_vec = Vec::with_capacity(y.len());

         <span class="kw">for </span>(idx, m) <span class="kw">in </span>mu.iter().enumerate() {
             <span class="kw">let </span>target_diff = y[idx] - m;

             y_bar_vec.push(<span class="kw">if </span>target_diff.abs() &lt; <span class="number">1e-15 </span>{
                 <span class="number">0f64
             </span>} <span class="kw">else </span>{
                 <span class="self">self</span>.link_grad(<span class="kw-2">*</span>m) * target_diff
             });
         }

         y_bar_vec
     }
 }

 <span class="doccomment">/// The Normal regression family.
 ///
 /// This is equivalent to the Linear Regression model.
 </span><span class="attribute">#[derive(Clone, Copy, Debug)]
 </span><span class="kw">pub struct </span>Normal;

 <span class="kw">impl </span>Criterion <span class="kw">for </span>Normal {
     <span class="kw">type </span>Link = Identity;

     <span class="kw">fn </span>model_variance(<span class="kw-2">&amp;</span><span class="self">self</span>, <span class="kw">_</span>: f64) -&gt; f64 {
         <span class="number">1f64
     </span>}
 }

 <span class="doccomment">/// The Poisson regression family.
 </span><span class="attribute">#[derive(Clone, Copy, Debug)]
 </span><span class="kw">pub struct </span>Poisson;

 <span class="kw">impl </span>Criterion <span class="kw">for </span>Poisson {
     <span class="kw">type </span>Link = Log;

     <span class="kw">fn </span>model_variance(<span class="kw-2">&amp;</span><span class="self">self</span>, mu: f64) -&gt; f64 {
         mu
     }

     <span class="kw">fn </span>initialize_mu(<span class="kw-2">&amp;</span><span class="self">self</span>, y: <span class="kw-2">&amp;</span>[f64]) -&gt; Vec&lt;f64&gt; {
         <span class="kw">let </span><span class="kw-2">mut </span>mu_data = Vec::with_capacity(y.len());

         <span class="kw">for </span>y_val <span class="kw">in </span>y {
             mu_data.push(<span class="kw">if </span><span class="kw-2">*</span>y_val &lt; <span class="number">1e-10 </span>{
                 <span class="number">1e-10
             </span>} <span class="kw">else </span>{
                 <span class="kw-2">*</span>y_val
             });
         }

         mu_data
     }

     <span class="kw">fn </span>compute_working_weight(<span class="kw-2">&amp;</span><span class="self">self</span>, mu: <span class="kw-2">&amp;</span>[f64]) -&gt; Vec&lt;f64&gt; {
         mu.to_vec()
     }
 }
 </code></pre></div>
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