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 </pre><pre class="rust"><code><span class="doccomment">//! Gaussian Mixture Models
 //!
 //! Provides implementation of GMMs using the EM algorithm.
 //!
 //! # Usage
 //!
 //! ```
 //! use rusty_machine::linalg::Matrix;
 //! use rusty_machine::learning::gmm::{CovOption, GaussianMixtureModel};
 //! use rusty_machine::learning::UnSupModel;
 //!
 //! let inputs = Matrix::new(4, 2, vec![1.0, 2.0, -3.0, -3.0, 0.1, 1.5, -5.0, -2.5]);
 //! let test_inputs = Matrix::new(3, 2, vec![1.0, 2.0, 3.0, 2.9, -4.4, -2.5]);
 //!
 //! // Create gmm with k(=2) classes.
 //! let mut model = GaussianMixtureModel::new(2);
 //! model.set_max_iters(10);
 //! model.cov_option = CovOption::Diagonal;
 //!
 //! // Where inputs is a Matrix with features in columns.
 //! model.train(&amp;inputs).unwrap();
 //!
 //! // Print the means and covariances of the GMM
 //! println!(&quot;{:?}&quot;, model.means());
 //! println!(&quot;{:?}&quot;, model.covariances());
 //!
 //! // Where test_inputs is a Matrix with features in columns.
 //! let post_probs = model.predict(&amp;test_inputs).unwrap();
 //!
 //! // Probabilities that each point comes from each Gaussian.
 //! println!(&quot;{:?}&quot;, post_probs.data());
 //! ```
 </span><span class="kw">use </span>linalg::{Matrix, MatrixSlice, Vector, BaseMatrix, BaseMatrixMut, Axes};
 <span class="kw">use </span>rulinalg::utils;
 <span class="kw">use </span>rulinalg::matrix::decomposition::{PartialPivLu};

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

 <span class="doccomment">/// Covariance options for GMMs.
 ///
 /// - Full : The full covariance structure.
 /// - Regularized : Adds a regularization constant to the covariance diagonal.
 /// - Diagonal : Only the diagonal covariance structure.
 </span><span class="attribute">#[derive(Clone, Copy, Debug)]
 </span><span class="kw">pub enum </span>CovOption {
     <span class="doccomment">/// The full covariance structure.
     </span>Full,
     <span class="doccomment">/// Adds a regularization constant to the covariance diagonal.
     </span>Regularized(f64),
     <span class="doccomment">/// Only the diagonal covariance structure.
     </span>Diagonal,
 }


 <span class="doccomment">/// A Gaussian Mixture Model
 </span><span class="attribute">#[derive(Debug)]
 </span><span class="kw">pub struct </span>GaussianMixtureModel {
     comp_count: usize,
     mix_weights: Vector&lt;f64&gt;,
     model_means: <span class="prelude-ty">Option</span>&lt;Matrix&lt;f64&gt;&gt;,
     model_covars: <span class="prelude-ty">Option</span>&lt;Vec&lt;Matrix&lt;f64&gt;&gt;&gt;,
     log_lik: f64,
     max_iters: usize,
     <span class="doccomment">/// The covariance options for the GMM.
     </span><span class="kw">pub </span>cov_option: CovOption,
 }

 <span class="kw">impl </span>UnSupModel&lt;Matrix&lt;f64&gt;, Matrix&lt;f64&gt;&gt; <span class="kw">for </span>GaussianMixtureModel {
     <span class="doccomment">/// Train the model using inputs.
     </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;) -&gt; LearningResult&lt;()&gt; {
         <span class="kw">let </span>reg_value = <span class="kw">if </span>inputs.rows() &gt; <span class="number">1 </span>{
             <span class="number">1f64 </span>/ (inputs.rows() - <span class="number">1</span>) <span class="kw">as </span>f64
         } <span class="kw">else </span>{
             <span class="kw">return </span><span class="prelude-val">Err</span>(Error::new(ErrorKind::InvalidData, <span class="string">&quot;Only one row of data provided.&quot;</span>));
         };

         <span class="comment">// Initialization:
         </span><span class="kw">let </span>k = <span class="self">self</span>.comp_count;

         <span class="self">self</span>.model_covars = {
             <span class="kw">let </span>cov_mat = <span class="self">self</span>.initialize_covariances(inputs, reg_value)<span class="question-mark">?</span>;
             <span class="prelude-val">Some</span>(<span class="macro">vec!</span>[cov_mat; k])
         };

         <span class="kw">let </span>random_rows: Vec&lt;usize&gt; =
             rand_utils::reservoir_sample(<span class="kw-2">&amp;</span>(<span class="number">0</span>..inputs.rows()).collect::&lt;Vec&lt;usize&gt;&gt;(), k);
         <span class="self">self</span>.model_means = <span class="prelude-val">Some</span>(inputs.select_rows(<span class="kw-2">&amp;</span>random_rows));

         <span class="kw">for _ in </span><span class="number">0</span>..<span class="self">self</span>.max_iters {
             <span class="kw">let </span>log_lik_0 = <span class="self">self</span>.log_lik;

             <span class="kw">let </span>(weights, log_lik_1) = <span class="self">self</span>.membership_weights(inputs)<span class="question-mark">?</span>;

             <span class="kw">if </span>(log_lik_1 - log_lik_0).abs() &lt; <span class="number">1e-15 </span>{
                 <span class="kw">break</span>;
             }

             <span class="self">self</span>.log_lik = log_lik_1;

             <span class="self">self</span>.update_params(inputs, weights);
         }

         <span class="prelude-val">Ok</span>(())
     }

     <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;Matrix&lt;f64&gt;&gt; {
         <span class="kw">if let </span>(<span class="kw-2">&amp;</span><span class="prelude-val">Some</span>(<span class="kw">_</span>), <span class="kw-2">&amp;</span><span class="prelude-val">Some</span>(<span class="kw">_</span>)) = (<span class="kw-2">&amp;</span><span class="self">self</span>.model_means, <span class="kw-2">&amp;</span><span class="self">self</span>.model_covars) {
             <span class="prelude-val">Ok</span>(<span class="self">self</span>.membership_weights(inputs)<span class="question-mark">?</span>.<span class="number">0</span>)
         } <span class="kw">else </span>{
             <span class="prelude-val">Err</span>(Error::new_untrained())
         }

     }
 }

 <span class="kw">impl </span>GaussianMixtureModel {
     <span class="doccomment">/// Constructs a new Gaussian Mixture Model
     ///
     /// Defaults to 100 maximum iterations and
     /// full covariance structure.
     ///
     /// # Examples
     /// ```
     /// use rusty_machine::learning::gmm::GaussianMixtureModel;
     ///
     /// let gmm = GaussianMixtureModel::new(3);
     /// ```
     </span><span class="kw">pub fn </span>new(k: usize) -&gt; GaussianMixtureModel {
         GaussianMixtureModel {
             comp_count: k,
             mix_weights: Vector::ones(k) / (k <span class="kw">as </span>f64),
             model_means: <span class="prelude-val">None</span>,
             model_covars: <span class="prelude-val">None</span>,
             log_lik: <span class="number">0f64</span>,
             max_iters: <span class="number">100</span>,
             cov_option: CovOption::Full,
         }
     }

     <span class="doccomment">/// Constructs a new GMM with the specified prior mixture weights.
     ///
     /// The mixture weights must have the same length as the number of components.
     /// Each element of the mixture weights must be non-negative.
     ///
     /// # Examples
     ///
     /// ```
     /// use rusty_machine::learning::gmm::GaussianMixtureModel;
     /// use rusty_machine::linalg::Vector;
     ///
     /// let mix_weights = Vector::new(vec![0.25, 0.25, 0.5]);
     ///
     /// let gmm = GaussianMixtureModel::with_weights(3, mix_weights).unwrap();
     /// ```
     ///
     /// # Failures
     ///
     /// Fails if either of the following conditions are met:
     ///
     /// - Mixture weights do not have length k.
     /// - Mixture weights have a negative entry.
     </span><span class="kw">pub fn </span>with_weights(k: usize, mixture_weights: Vector&lt;f64&gt;) -&gt; LearningResult&lt;GaussianMixtureModel&gt; {
         <span class="kw">if </span>mixture_weights.size() != k {
             <span class="prelude-val">Err</span>(Error::new(ErrorKind::InvalidParameters, <span class="string">&quot;Mixture weights must have length k.&quot;</span>))
         } <span class="kw">else if </span>mixture_weights.data().iter().any(|<span class="kw-2">&amp;</span>x| x &lt; <span class="number">0f64</span>) {
             <span class="prelude-val">Err</span>(Error::new(ErrorKind::InvalidParameters, <span class="string">&quot;Mixture weights must have only non-negative entries.&quot;</span>))
         } <span class="kw">else </span>{
             <span class="kw">let </span>sum = mixture_weights.sum();
             <span class="kw">let </span>normalized_weights = mixture_weights / sum;

             <span class="prelude-val">Ok</span>(GaussianMixtureModel {
                 comp_count: k,
                 mix_weights: normalized_weights,
                 model_means: <span class="prelude-val">None</span>,
                 model_covars: <span class="prelude-val">None</span>,
                 log_lik: <span class="number">0f64</span>,
                 max_iters: <span class="number">100</span>,
                 cov_option: CovOption::Full,
             })
         }
     }

     <span class="doccomment">/// The model means
     ///
     /// Returns an Option&lt;&amp;Matrix&lt;f64&gt;&gt; containing
     /// the model means. Each row represents
     /// the mean of one of the Gaussians.
     </span><span class="kw">pub fn </span>means(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; <span class="prelude-ty">Option</span>&lt;<span class="kw-2">&amp;</span>Matrix&lt;f64&gt;&gt; {
         <span class="self">self</span>.model_means.as_ref()
     }

     <span class="doccomment">/// The model covariances
     ///
     /// Returns an Option&lt;&amp;Vec&lt;Matrix&lt;f64&gt;&gt;&gt; containing
     /// the model covariances. Each Matrix in the vector
     /// is the covariance of one of the Gaussians.
     </span><span class="kw">pub fn </span>covariances(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; <span class="prelude-ty">Option</span>&lt;<span class="kw-2">&amp;</span>Vec&lt;Matrix&lt;f64&gt;&gt;&gt; {
         <span class="self">self</span>.model_covars.as_ref()
     }

     <span class="doccomment">/// The model mixture weights
     ///
     /// Returns a reference to the model mixture weights.
     /// These are the weighted contributions of each underlying
     /// Gaussian to the model distribution.
     </span><span class="kw">pub fn </span>mixture_weights(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; <span class="kw-2">&amp;</span>Vector&lt;f64&gt; {
         <span class="kw-2">&amp;</span><span class="self">self</span>.mix_weights
     }

     <span class="doccomment">/// Sets the max number of iterations for the EM algorithm.
     ///
     /// # Examples
     ///
     /// ```
     /// use rusty_machine::learning::gmm::GaussianMixtureModel;
     ///
     /// let mut gmm = GaussianMixtureModel::new(2);
     /// gmm.set_max_iters(5);
     /// ```
     </span><span class="kw">pub fn </span>set_max_iters(<span class="kw-2">&amp;mut </span><span class="self">self</span>, iters: usize) {
         <span class="self">self</span>.max_iters = iters;
     }

     <span class="kw">fn </span>initialize_covariances(<span class="kw-2">&amp;</span><span class="self">self</span>, inputs: <span class="kw-2">&amp;</span>Matrix&lt;f64&gt;, reg_value: f64) -&gt; LearningResult&lt;Matrix&lt;f64&gt;&gt; {
         <span class="kw">match </span><span class="self">self</span>.cov_option {
             CovOption::Diagonal =&gt; {
                 <span class="kw">let </span>variance = inputs.variance(Axes::Row)<span class="question-mark">?</span>;
                 <span class="prelude-val">Ok</span>(Matrix::from_diag(variance.data()) * reg_value.sqrt())
             }

             CovOption::Full | CovOption::Regularized(<span class="kw">_</span>) =&gt; {
                 <span class="kw">let </span>means = inputs.mean(Axes::Row);
                 <span class="kw">let </span><span class="kw-2">mut </span>cov_mat = Matrix::zeros(inputs.cols(), inputs.cols());
                 <span class="kw">for </span>(j, <span class="kw-2">mut </span>row) <span class="kw">in </span>cov_mat.row_iter_mut().enumerate() {
                     <span class="kw">for </span>(k, elem) <span class="kw">in </span>row.iter_mut().enumerate() {
                         <span class="kw-2">*</span>elem = inputs.row_iter().map(|r| {
                             (r[j] - means[j]) * (r[k] - means[k])
                         }).sum::&lt;f64&gt;();
                     }
                 }
                 cov_mat <span class="kw-2">*</span>= reg_value;
                 <span class="kw">if let </span>CovOption::Regularized(eps) = <span class="self">self</span>.cov_option {
                     cov_mat += Matrix::&lt;f64&gt;::identity(cov_mat.cols()) * eps;
                 }
                 <span class="prelude-val">Ok</span>(cov_mat)
             }
         }
     }

     <span class="kw">fn </span>membership_weights(<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;(Matrix&lt;f64&gt;, f64)&gt; {
         <span class="kw">let </span>n = inputs.rows();

         <span class="kw">let </span><span class="kw-2">mut </span>member_weights_data = Vec::with_capacity(n * <span class="self">self</span>.comp_count);

         <span class="comment">// We compute the determinants and inverses now
         </span><span class="kw">let </span><span class="kw-2">mut </span>cov_sqrt_dets = Vec::with_capacity(<span class="self">self</span>.comp_count);
         <span class="kw">let </span><span class="kw-2">mut </span>cov_invs = Vec::with_capacity(<span class="self">self</span>.comp_count);

         <span class="kw">if let </span><span class="prelude-val">Some</span>(<span class="kw-2">ref </span>covars) = <span class="self">self</span>.model_covars {
             <span class="kw">for </span>cov <span class="kw">in </span>covars {
                 <span class="kw">let </span>lup = PartialPivLu::decompose(cov.clone()).expect(<span class="string">&quot;Covariance could not be lup decomposed&quot;</span>);
                 <span class="kw">let </span>covar_det = lup.det();
                 <span class="comment">// TODO: We can probably remove this inverse for a more stable solve elsewhere.
                 </span><span class="kw">let </span>covar_inv = lup.inverse().map_err(Error::from)<span class="question-mark">?</span>;

                 cov_sqrt_dets.push(covar_det.sqrt());
                 cov_invs.push(covar_inv);
             }
         }

         <span class="kw">let </span><span class="kw-2">mut </span>log_lik = <span class="number">0f64</span>;

         <span class="comment">// Now we compute the membership weights
         </span><span class="kw">if let </span><span class="prelude-val">Some</span>(<span class="kw-2">ref </span>means) = <span class="self">self</span>.model_means {
             <span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..n {
                 <span class="kw">let </span><span class="kw-2">mut </span>pdfs = Vec::with_capacity(<span class="self">self</span>.comp_count);
                 <span class="kw">let </span>x_i = MatrixSlice::from_matrix(inputs, [i, <span class="number">0</span>], <span class="number">1</span>, inputs.cols());

                 <span class="kw">for </span>j <span class="kw">in </span><span class="number">0</span>..<span class="self">self</span>.comp_count {
                     <span class="kw">let </span>mu_j = MatrixSlice::from_matrix(means, [j, <span class="number">0</span>], <span class="number">1</span>, means.cols());
                     <span class="kw">let </span>diff = x_i - mu_j;

                     <span class="kw">let </span>pdf = (<span class="kw-2">&amp;</span>diff * <span class="kw-2">&amp;</span>cov_invs[j] * diff.transpose() * -<span class="number">0.5</span>).into_vec()[<span class="number">0</span>]
                         .exp() / cov_sqrt_dets[j];
                     pdfs.push(pdf);
                 }

                 <span class="kw">let </span>weighted_pdf_sum = utils::dot(<span class="kw-2">&amp;</span>pdfs, <span class="self">self</span>.mix_weights.data());

                 <span class="kw">for </span>(idx, pdf) <span class="kw">in </span>pdfs.iter().enumerate() {
                     member_weights_data.push(<span class="self">self</span>.mix_weights[idx] * pdf / (weighted_pdf_sum));
                 }

                 log_lik += weighted_pdf_sum.ln();
             }
         }

         <span class="prelude-val">Ok</span>((Matrix::new(n, <span class="self">self</span>.comp_count, member_weights_data), log_lik))
     }

     <span class="kw">fn </span>update_params(<span class="kw-2">&amp;mut </span><span class="self">self</span>, inputs: <span class="kw-2">&amp;</span>Matrix&lt;f64&gt;, membership_weights: Matrix&lt;f64&gt;) {
         <span class="kw">let </span>n = membership_weights.rows();
         <span class="kw">let </span>d = inputs.cols();

         <span class="kw">let </span>sum_weights = membership_weights.sum_rows();

         <span class="self">self</span>.mix_weights = <span class="kw-2">&amp;</span>sum_weights / (n <span class="kw">as </span>f64);

         <span class="kw">let </span><span class="kw-2">mut </span>new_means = membership_weights.transpose() * inputs;

         <span class="kw">for </span>(<span class="kw-2">mut </span>mean, w) <span class="kw">in </span>new_means.row_iter_mut().zip(sum_weights.data().iter()) {
             <span class="kw-2">*</span>mean /= <span class="kw-2">*</span>w;
         }

         <span class="kw">let </span><span class="kw-2">mut </span>new_covs = Vec::with_capacity(<span class="self">self</span>.comp_count);

         <span class="kw">for </span>k <span class="kw">in </span><span class="number">0</span>..<span class="self">self</span>.comp_count {
             <span class="kw">let </span><span class="kw-2">mut </span>cov_mat = Matrix::zeros(d, d);
             <span class="kw">let </span>new_means_k = MatrixSlice::from_matrix(<span class="kw-2">&amp;</span>new_means, [k, <span class="number">0</span>], <span class="number">1</span>, d);

             <span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..n {
                 <span class="kw">let </span>inputs_i = MatrixSlice::from_matrix(inputs, [i, <span class="number">0</span>], <span class="number">1</span>, d);
                 <span class="kw">let </span>diff = inputs_i - new_means_k;
                 cov_mat += <span class="self">self</span>.compute_cov(diff, membership_weights[[i, k]]);
             }

             <span class="kw">if let </span>CovOption::Regularized(eps) = <span class="self">self</span>.cov_option {
                 cov_mat += Matrix::&lt;f64&gt;::identity(cov_mat.cols()) * eps;
             }

             new_covs.push(cov_mat / sum_weights[k]);

         }

         <span class="self">self</span>.model_means = <span class="prelude-val">Some</span>(new_means);
         <span class="self">self</span>.model_covars = <span class="prelude-val">Some</span>(new_covs);
     }

     <span class="kw">fn </span>compute_cov(<span class="kw-2">&amp;</span><span class="self">self</span>, diff: Matrix&lt;f64&gt;, weight: f64) -&gt; Matrix&lt;f64&gt; {
         <span class="kw">match </span><span class="self">self</span>.cov_option {
             CovOption::Full | CovOption::Regularized(<span class="kw">_</span>) =&gt; (diff.transpose() * diff) * weight,
             CovOption::Diagonal =&gt; Matrix::from_diag(<span class="kw-2">&amp;</span>diff.elemul(<span class="kw-2">&amp;</span>diff).into_vec()) * weight,
         }
     }
 }

 <span class="attribute">#[cfg(test)]
 </span><span class="kw">mod </span>tests {
     <span class="kw">use </span><span class="kw">super</span>::GaussianMixtureModel;
     <span class="kw">use </span>linalg::Vector;

     <span class="attribute">#[test]
     </span><span class="kw">fn </span>test_means_none() {
         <span class="kw">let </span>model = GaussianMixtureModel::new(<span class="number">5</span>);

         <span class="macro">assert_eq!</span>(model.means(), <span class="prelude-val">None</span>);
     }

     <span class="attribute">#[test]
     </span><span class="kw">fn </span>test_covars_none() {
         <span class="kw">let </span>model = GaussianMixtureModel::new(<span class="number">5</span>);

         <span class="macro">assert_eq!</span>(model.covariances(), <span class="prelude-val">None</span>);
     }

     <span class="attribute">#[test]
     </span><span class="kw">fn </span>test_negative_mixtures() {
         <span class="kw">let </span>mix_weights = Vector::new(<span class="macro">vec!</span>[-<span class="number">0.25</span>, <span class="number">0.75</span>, <span class="number">0.5</span>]);
         <span class="kw">let </span>gmm_res = GaussianMixtureModel::with_weights(<span class="number">3</span>, mix_weights);
         <span class="macro">assert!</span>(gmm_res.is_err());
     }

     <span class="attribute">#[test]
     </span><span class="kw">fn </span>test_wrong_length_mixtures() {
         <span class="kw">let </span>mix_weights = Vector::new(<span class="macro">vec!</span>[<span class="number">0.1</span>, <span class="number">0.25</span>, <span class="number">0.75</span>, <span class="number">0.5</span>]);
         <span class="kw">let </span>gmm_res = GaussianMixtureModel::with_weights(<span class="number">3</span>, mix_weights);
         <span class="macro">assert!</span>(gmm_res.is_err());
     }
 }
 </code></pre></div>
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