lasso.rb in rumale-linear_model-0.25.0

- old
+ new
@@ -1,111 +1,157 @@
 # frozen_string_literal: true
 
+require 'rumale/base/estimator'
 require 'rumale/base/regressor'
 require 'rumale/validation'
-require 'rumale/linear_model/base_sgd'
 
+require_relative 'base_estimator'
+
 module Rumale
   module LinearModel
-    # Lasso is a class that implements Lasso Regression
-    # with stochastic gradient descent (SGD) optimization.
+    # Lasso is a class that implements Lasso Regression with coordinate descent optimization.
     #
     # @example
     #   require 'rumale/linear_model/lasso'
     #
-    #   estimator =
-    #     Rumale::LinearModel::Lasso.new(reg_param: 0.1, max_iter: 1000, batch_size: 20, random_seed: 1)
+    #   estimator = Rumale::LinearModel::Lasso.new(reg_param: 0.1)
     #   estimator.fit(training_samples, traininig_values)
     #   results = estimator.predict(testing_samples)
     #
     # *Reference*
-    # - Shalev-Shwartz, S., and Singer, Y., "Pegasos: Primal Estimated sub-GrAdient SOlver for SVM," Proc. ICML'07, pp. 807--814, 2007.
-    # - Tsuruoka, Y., Tsujii, J., and Ananiadou, S., "Stochastic Gradient Descent Training for L1-regularized Log-linear Models with Cumulative Penalty," Proc. ACL'09, pp. 477--485, 2009.
-    # - Bottou, L., "Large-Scale Machine Learning with Stochastic Gradient Descent," Proc. COMPSTAT'10, pp. 177--186, 2010.
-    class Lasso < BaseSGD
-      include ::Rumale::Base::Regressor
+    # - Friedman, J., Hastie, T., and Tibshirani, R., "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, 33 (1), pp. 1--22, 2010.
+    # - Simon, N., Friedman, J., and Hastie, T., "A Blockwise Descent Algorithm for Group-penalized Multiresponse and Multinomial Regression," arXiv preprint arXiv:1311.6529, 2013.
+    class Lasso < Rumale::LinearModel::BaseEstimator
+      include Rumale::Base::Regressor
 
-      # Return the weight vector.
-      # @return [Numo::DFloat] (shape: [n_outputs, n_features])
-      attr_reader :weight_vec
+      # Return the number of iterations performed in coordinate descent optimization.
+      # @return [Integer]
+      attr_reader :n_iter
 
-      # Return the bias term (a.k.a. intercept).
-      # @return [Numo::DFloat] (shape: [n_outputs])
-      attr_reader :bias_term
-
-      # Return the random generator for random sampling.
-      # @return [Random]
-      attr_reader :rng
-
       # Create a new Lasso regressor.
       #
-      # @param learning_rate [Float] The initial value of learning rate.
-      #   The learning rate decreases as the iteration proceeds according to the equation: learning_rate / (1 + decay * t).
-      # @param decay [Float] The smoothing parameter for decreasing learning rate as the iteration proceeds.
-      #   If nil is given, the decay sets to 'reg_param * learning_rate'.
-      # @param momentum [Float] The momentum factor.
       # @param reg_param [Float] The regularization parameter.
       # @param fit_bias [Boolean] The flag indicating whether to fit the bias term.
       # @param bias_scale [Float] The scale of the bias term.
       # @param max_iter [Integer] The maximum number of epochs that indicates
       #   how many times the whole data is given to the training process.
-      # @param batch_size [Integer] The size of the mini batches.
       # @param tol [Float] The tolerance of loss for terminating optimization.
-      # @param n_jobs [Integer] The number of jobs for running the fit method in parallel.
-      #   If nil is given, the method does not execute in parallel.
-      #   If zero or less is given, it becomes equal to the number of processors.
-      #   This parameter is ignored if the Parallel gem is not loaded.
-      # @param verbose [Boolean] The flag indicating whether to output loss during iteration.
-      # @param random_seed [Integer] The seed value using to initialize the random generator.
-      def initialize(learning_rate: 0.01, decay: nil, momentum: 0.9,
-                     reg_param: 1.0, fit_bias: true, bias_scale: 1.0,
-                     max_iter: 1000, batch_size: 50, tol: 1e-4,
-                     n_jobs: nil, verbose: false, random_seed: nil)
+      def initialize(reg_param: 1.0, fit_bias: true, bias_scale: 1.0, max_iter: 1000, tol: 1e-4)
         super()
-        @params.merge!(method(:initialize).parameters.to_h { |_t, arg| [arg, binding.local_variable_get(arg)] })
-        @params[:decay] ||= @params[:reg_param] * @params[:learning_rate]
-        @params[:random_seed] ||= srand
-        @rng = Random.new(@params[:random_seed])
-        @penalty_type = L1_PENALTY
-        @loss_func = ::Rumale::LinearModel::Loss::MeanSquaredError.new
+        @params = {
+          reg_param: reg_param,
+          fit_bias: fit_bias,
+          bias_scale: bias_scale,
+          max_iter: max_iter,
+          tol: tol
+        }
       end
 
       # Fit the model with given training data.
       #
       # @param x [Numo::DFloat] (shape: [n_samples, n_features]) The training data to be used for fitting the model.
       # @param y [Numo::DFloat] (shape: [n_samples, n_outputs]) The target values to be used for fitting the model.
       # @return [Lasso] The learned regressor itself.
       def fit(x, y)
-        x = ::Rumale::Validation.check_convert_sample_array(x)
-        y = ::Rumale::Validation.check_convert_target_value_array(y)
-        ::Rumale::Validation.check_sample_size(x, y)
+        x = Rumale::Validation.check_convert_sample_array(x)
+        y = Rumale::Validation.check_convert_target_value_array(y)
+        Rumale::Validation.check_sample_size(x, y)
 
-        n_outputs = y.shape[1].nil? ? 1 : y.shape[1]
-        n_features = x.shape[1]
+        @n_iter = 0
+        x = expand_feature(x) if fit_bias?
 
-        if n_outputs > 1
-          @weight_vec = Numo::DFloat.zeros(n_outputs, n_features)
-          @bias_term = Numo::DFloat.zeros(n_outputs)
-          if enable_parallel?
-            models = parallel_map(n_outputs) { |n| partial_fit(x, y[true, n]) }
-            n_outputs.times { |n| @weight_vec[n, true], @bias_term[n] = models[n] }
-          else
-            n_outputs.times { |n| @weight_vec[n, true], @bias_term[n] = partial_fit(x, y[true, n]) }
-          end
-        else
-          @weight_vec, @bias_term = partial_fit(x, y)
-        end
+        @weight_vec, @bias_term = if single_target?(y)
+                                    partial_fit(x, y)
+                                  else
+                                    partial_fit_multi(x, y)
+                                  end
+
         self
       end
 
       # Predict values for samples.
       #
       # @param x [Numo::DFloat] (shape: [n_samples, n_features]) The samples to predict the values.
       # @return [Numo::DFloat] (shape: [n_samples, n_outputs]) Predicted values per sample.
       def predict(x)
-        x = ::Rumale::Validation.check_convert_sample_array(x)
+        x = Rumale::Validation.check_convert_sample_array(x)
 
         x.dot(@weight_vec.transpose) + @bias_term
+      end
+
+      private
+
+      def partial_fit(x, y)
+        n_features = x.shape[1]
+        w = Numo::DFloat.zeros(n_features)
+        x_norms = (x**2).sum(axis: 0)
+        residual = y - x.dot(w)
+
+        @params[:max_iter].times do |iter|
+          w_err = 0.0
+          n_features.times do |j|
+            next if x_norms[j].zero?
+
+            w_prev = w[j]
+
+            residual += w[j] * x[true, j]
+            z = x[true, j].dot(residual)
+            w[j] = soft_threshold(z, @params[:reg_param]).fdiv(x_norms[j])
+            residual -= w[j] * x[true, j]
+
+            w_err = [w_err, (w[j] - w_prev).abs].max
+          end
+
+          @n_iter = iter + 1
+
+          break if w_err <= @params[:tol]
+        end
+
+        split_weight(w)
+      end
+
+      def partial_fit_multi(x, y)
+        n_features = x.shape[1]
+        n_outputs = y.shape[1]
+        w = Numo::DFloat.zeros(n_outputs, n_features)
+        x_norms = (x**2).sum(axis: 0)
+        residual = y - x.dot(w.transpose)
+
+        @params[:max_iter].times do |iter|
+          w_err = 0.0
+          n_features.times do |j|
+            next if x_norms[j].zero?
+
+            w_prev = w[true, j]
+
+            residual += x[true, j].expand_dims(1) * w[true, j]
+            z = x[true, j].dot(residual)
+            w[true, j] = [1.0 - @params[:reg_param].fdiv(Math.sqrt((z**2).sum)), 0.0].max.fdiv(x_norms[j]) * z
+            residual -= x[true, j].expand_dims(1) * w[true, j]
+
+            w_err = [w_err, (w[true, j] - w_prev).abs.max].max
+          end
+
+          @n_iter = iter + 1
+
+          break if w_err <= @params[:tol]
+        end
+
+        split_weight(w)
+      end
+
+      def soft_threshold(z, threshold)
+        sign(z) * [z.abs - threshold, 0].max
+      end
+
+      def sign(z)
+        return 0.0 if z.zero?
+
+        z.positive? ? 1.0 : -1.0
+      end
+
+      def single_target?(y)
+        y.ndim == 1
       end
     end
   end
 end