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<h1>Source code for MRCpy.mrc</h1><div class="highlight"><pre>
<span></span><span class="sd">'''Minimax Risk Classification.'''</span>
<span class="kn">import</span> <span class="nn">itertools</span> <span class="k">as</span> <span class="nn">it</span>
<span class="kn">import</span> <span class="nn">warnings</span>
<span class="kn">import</span> <span class="nn">cvxpy</span> <span class="k">as</span> <span class="nn">cvx</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">scipy.special</span> <span class="k">as</span> <span class="nn">scs</span>
<span class="kn">from</span> <span class="nn">sklearn.utils</span> <span class="kn">import</span> <span class="n">check_array</span>
<span class="kn">from</span> <span class="nn">sklearn.utils.validation</span> <span class="kn">import</span> <span class="n">check_is_fitted</span>
<span class="c1"># Import the MRC super class</span>
<span class="kn">from</span> <span class="nn">MRCpy</span> <span class="kn">import</span> <span class="n">BaseMRC</span>
<div class="viewcode-block" id="MRC"><a class="viewcode-back" href="../../generated/MRCpy.MRC.html#MRCpy.MRC">[docs]</a><span class="k">class</span> <span class="nc">MRC</span><span class="p">(</span><span class="n">BaseMRC</span><span class="p">):</span>
<span class="sd">'''</span>
<span class="sd"> Minimax Risk Classifier</span>
<span class="sd"> MRCs using the default constraints and</span>
<span class="sd"> implements two kinds of loss functions, namely 0-1 and log loss.</span>
<span class="sd"> This is a subclass of the super class BaseMRC.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> loss : `str` {'0-1', 'log'}, default='0-1'</span>
<span class="sd"> The type of loss function to use for the risk minimization.</span>
<span class="sd"> s : float, default=0.3</span>
<span class="sd"> For tuning the estimation of expected values</span>
<span class="sd"> of feature mapping function.</span>
<span class="sd"> Must be a positive float value and</span>
<span class="sd"> expected to be in the 0 to 1 in general cases.</span>
<span class="sd"> deterministic : bool, default=None</span>
<span class="sd"> For determining if the prediction of the labels</span>
<span class="sd"> should be done in a deterministic way or not.</span>
<span class="sd"> For '0-1' loss, the non-deterministic ('False') approach</span>
<span class="sd"> works well.</span>
<span class="sd"> For 'log' loss, the deterministic ('True') approach</span>
<span class="sd"> works well.</span>
<span class="sd"> If the user doesnot specify the value, the default value</span>
<span class="sd"> is set according to loss function.</span>
<span class="sd"> random_state : int, RandomState instance, default=None</span>
<span class="sd"> Used when 'fourier' and 'relu' options for feature mappings are used</span>
<span class="sd"> to produce the random weights.</span>
<span class="sd"> fit_intercept : bool, default=True</span>
<span class="sd"> Whether to calculate the intercept for MRCs</span>
<span class="sd"> If set to false, no intercept will be used in calculations</span>
<span class="sd"> (i.e. data is expected to be already centered).</span>
<span class="sd"> warm_start : bool, default=False</span>
<span class="sd"> When set to True,</span>
<span class="sd"> reuse the solution of the previous call to fit as initialization,</span>
<span class="sd"> otherwise, just erase the previous solution.</span>
<span class="sd"> use_cvx : bool, default=False</span>
<span class="sd"> If True, use CVXpy library for the optimization</span>
<span class="sd"> instead of the subgradient methods.</span>
<span class="sd"> solver : str {'SCS', 'ECOS', 'MOSEK'}, default='MOSEK'</span>
<span class="sd"> The type of CVX solver to use for solving the problem.</span>
<span class="sd"> In some cases, one solver might not work,</span>
<span class="sd"> so you might need to change solver depending on the problem.</span>
<span class="sd"> 'MOSEK' is a commercial solver for which one might need to</span>
<span class="sd"> request for a license. A free license can be requested</span>
<span class="sd"> `here <https://www.mosek.com/products/academic-licenses/>`_</span>
<span class="sd"> max_iters : int, default=10000</span>
<span class="sd"> The maximum number of iterations to use</span>
<span class="sd"> for finding the solution of optimization</span>
<span class="sd"> using the subgradient approach.</span>
<span class="sd"> phi : str {'fourier', 'relu', 'threshold', 'linear'} or</span>
<span class="sd"> `BasePhi` instance (custom features), default='linear'</span>
<span class="sd"> The type of feature mapping function to use for mapping the input data</span>
<span class="sd"> 'fourier', 'relu', 'threshold' and 'linear'</span>
<span class="sd"> are the currenlty available feature mapping methods.</span>
<span class="sd"> The users can also implement their own feature mapping object</span>
<span class="sd"> (should be a `BasePhi` instance) and pass it to this argument.</span>
<span class="sd"> To implement a feature mapping, please go through the</span>
<span class="sd"> :ref:`Feature Mapping` section.</span>
<span class="sd"> **phi_kwargs : Additional parameters for feature mappings.</span>
<span class="sd"> Groups the multiple optional parameters</span>
<span class="sd"> for the corresponding feature mappings(phi).</span>
<span class="sd"> For example in case of fourier features,</span>
<span class="sd"> the number of features is given by `n_components`</span>
<span class="sd"> parameter which can be passed as argument -</span>
<span class="sd"> `MRC(loss='log', phi='fourier', n_components=500)`</span>
<span class="sd"> The list of arguments for each feature mappings class</span>
<span class="sd"> can be found in the corresponding documentation.</span>
<span class="sd"> Attributes</span>
<span class="sd"> ----------</span>
<span class="sd"> is_fitted_ : bool</span>
<span class="sd"> True if the classifier is fitted i.e., the parameters are learnt.</span>
<span class="sd"> tau_ : array-like of shape (n_features) or float</span>
<span class="sd"> The mean estimates</span>
<span class="sd"> for the expectations of feature mappings.</span>
<span class="sd"> lambda_ : array-like of shape (n_features) or float</span>
<span class="sd"> The variance in the mean estimates</span>
<span class="sd"> for the expectations of the feature mappings.</span>
<span class="sd"> mu_ : array-like of shape (n_features) or float</span>
<span class="sd"> Parameters learnt by the optimization.</span>
<span class="sd"> nu_ : float</span>
<span class="sd"> Parameter learnt by the optimization.</span>
<span class="sd"> mu_l_ : array-like of shape (n_features) or float</span>
<span class="sd"> Parameters learnt by solving the lower bound optimization of MRC.</span>
<span class="sd"> upper_ : float</span>
<span class="sd"> Optimized upper bound of the MRC classifier.</span>
<span class="sd"> lower_ : float</span>
<span class="sd"> Optimized lower bound of the MRC classifier.</span>
<span class="sd"> upper_params_ : a dictionary</span>
<span class="sd"> Stores the optimal points and best value</span>
<span class="sd"> for the upper bound of the function</span>
<span class="sd"> when the warm_start=True.</span>
<span class="sd"> params_ : a dictionary</span>
<span class="sd"> Stores the optimal points and best value</span>
<span class="sd"> for the lower bound of the function</span>
<span class="sd"> when the warm_start=True.</span>
<span class="sd"> '''</span>
<div class="viewcode-block" id="MRC.minimax_risk"><a class="viewcode-back" href="../../generated/MRCpy.MRC.html#MRCpy.MRC.minimax_risk">[docs]</a> <span class="k">def</span> <span class="nf">minimax_risk</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">tau_</span><span class="p">,</span> <span class="n">lambda_</span><span class="p">,</span> <span class="n">n_classes</span><span class="p">):</span>
<span class="sd">'''</span>
<span class="sd"> Solves the minimax risk problem</span>
<span class="sd"> for different types of loss (0-1 and log loss).</span>
<span class="sd"> The solution of the default MRC optimization</span>
<span class="sd"> gives the upper bound of the error.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> X : array-like of shape (n_samples, n_dimensions)</span>
<span class="sd"> Training instances used for solving</span>
<span class="sd"> the minimax risk optimization problem.</span>
<span class="sd"> tau_ : array-like of shape (n_features * n_classes)</span>
<span class="sd"> The mean estimates</span>
<span class="sd"> for the expectations of feature mappings.</span>
<span class="sd"> lambda_ : array-like of shape (n_features * n_classes)</span>
<span class="sd"> The variance in the mean estimates</span>
<span class="sd"> for the expectations of the feature mappings.</span>
<span class="sd"> n_classes : int</span>
<span class="sd"> Number of labels in the dataset.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> self :</span>
<span class="sd"> Fitted estimator</span>
<span class="sd"> '''</span>
<span class="c1"># Set the parameters for the optimization</span>
<span class="bp">self</span><span class="o">.</span><span class="n">n_classes</span> <span class="o">=</span> <span class="n">n_classes</span>
<span class="bp">self</span><span class="o">.</span><span class="n">tau_</span> <span class="o">=</span> <span class="n">check_array</span><span class="p">(</span><span class="n">tau_</span><span class="p">,</span> <span class="n">accept_sparse</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">ensure_2d</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">lambda_</span> <span class="o">=</span> <span class="n">check_array</span><span class="p">(</span><span class="n">lambda_</span><span class="p">,</span> <span class="n">accept_sparse</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
<span class="n">ensure_2d</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="n">phi</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">phi</span><span class="o">.</span><span class="n">eval_x</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="n">phi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">unique</span><span class="p">(</span><span class="n">phi</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="c1"># Constants</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">phi</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
<span class="n">n</span> <span class="o">=</span> <span class="n">phi</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="c1"># Save the phi configurations for finding the lower bounds</span>
<span class="bp">self</span><span class="o">.</span><span class="n">lowerPhiConfigs</span> <span class="o">=</span> <span class="n">phi</span>
<span class="c1"># Supress the depreciation warnings</span>
<span class="n">warnings</span><span class="o">.</span><span class="n">simplefilter</span><span class="p">(</span><span class="s1">'ignore'</span><span class="p">)</span>
<span class="c1"># In case of 0-1 loss, learn constraints using the phi</span>
<span class="c1"># These constraints are used in the optimization instead of phi</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">loss</span> <span class="o">==</span> <span class="s1">'0-1'</span><span class="p">:</span>
<span class="c1"># Summing up the phi configurations</span>
<span class="c1"># for all possible subsets of classes for each instance</span>
<span class="n">F</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">phi</span><span class="p">[:,</span> <span class="n">S</span><span class="p">,</span> <span class="p">],</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="k">for</span> <span class="n">numVals</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_classes</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
<span class="k">for</span> <span class="n">S</span> <span class="ow">in</span> <span class="n">it</span><span class="o">.</span><span class="n">combinations</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_classes</span><span class="p">),</span>
<span class="n">numVals</span><span class="p">)))</span>
<span class="c1"># Compute the corresponding length of the subset of classes</span>
<span class="c1"># for which sums computed for each instance</span>
<span class="n">cardS</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_classes</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span><span class="o">.</span>\
<span class="n">repeat</span><span class="p">([</span><span class="n">n</span> <span class="o">*</span> <span class="n">scs</span><span class="o">.</span><span class="n">comb</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_classes</span><span class="p">,</span> <span class="n">numVals</span><span class="p">)</span>
<span class="k">for</span> <span class="n">numVals</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span>
<span class="bp">self</span><span class="o">.</span><span class="n">n_classes</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)])</span>
<span class="n">M</span> <span class="o">=</span> <span class="n">F</span> <span class="o">/</span> <span class="p">(</span><span class="n">cardS</span><span class="p">[:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">])</span>
<span class="n">h</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">cardS</span><span class="p">)</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">use_cvx</span><span class="p">:</span>
<span class="c1"># Use CVXpy for the convex optimization of the MRC.</span>
<span class="c1"># Variables</span>
<span class="n">mu</span> <span class="o">=</span> <span class="n">cvx</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">loss</span> <span class="o">==</span> <span class="s1">'0-1'</span><span class="p">:</span>
<span class="k">def</span> <span class="nf">neg_nu</span><span class="p">(</span><span class="n">mu</span><span class="p">):</span>
<span class="k">return</span> <span class="n">cvx</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">M</span> <span class="o">@</span> <span class="n">mu</span> <span class="o">+</span> <span class="n">h</span><span class="p">)</span>
<span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">loss</span> <span class="o">==</span> <span class="s1">'log'</span><span class="p">:</span>
<span class="n">numConstr</span> <span class="o">=</span> <span class="n">phi</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="k">def</span> <span class="nf">neg_nu</span><span class="p">(</span><span class="n">mu</span><span class="p">):</span>
<span class="k">return</span> <span class="n">cvx</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">cvx</span><span class="o">.</span><span class="n">hstack</span><span class="p">(</span><span class="n">cvx</span><span class="o">.</span><span class="n">log_sum_exp</span><span class="p">(</span><span class="n">phi</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="p">:,</span> <span class="p">:]</span> <span class="o">@</span>
<span class="n">mu</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">numConstr</span><span class="p">)))</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">'The given loss function is not available '</span> <span class="o">+</span>
<span class="s1">'for this classifier'</span><span class="p">)</span>
<span class="c1"># Objective function</span>
<span class="n">objective</span> <span class="o">=</span> <span class="n">cvx</span><span class="o">.</span><span class="n">Minimize</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">lambda_</span> <span class="o">@</span> <span class="n">cvx</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">mu</span><span class="p">)</span> <span class="o">-</span>
<span class="bp">self</span><span class="o">.</span><span class="n">tau_</span> <span class="o">@</span> <span class="n">mu</span> <span class="o">+</span>
<span class="n">neg_nu</span><span class="p">(</span><span class="n">mu</span><span class="p">))</span>
<span class="bp">self</span><span class="o">.</span><span class="n">mu_</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">upper_</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">try_solvers</span><span class="p">(</span><span class="n">objective</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="n">mu</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">nu_</span> <span class="o">=</span> <span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">neg_nu</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">mu_</span><span class="p">)</span><span class="o">.</span><span class="n">value</span><span class="p">)</span>
<span class="k">elif</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">use_cvx</span><span class="p">:</span>
<span class="c1"># Use the subgradient approach for the convex optimization of MRC</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">loss</span> <span class="o">==</span> <span class="s1">'0-1'</span><span class="p">:</span>
<span class="n">M_t</span> <span class="o">=</span> <span class="n">M</span><span class="o">.</span><span class="n">transpose</span><span class="p">()</span>
<span class="c1"># Define the subobjective function and</span>
<span class="c1"># its gradient for the 0-1 loss function.</span>
<span class="k">def</span> <span class="nf">f_</span><span class="p">(</span><span class="n">mu</span><span class="p">):</span>
<span class="k">return</span> <span class="n">M</span> <span class="o">@</span> <span class="n">mu</span> <span class="o">+</span> <span class="n">h</span>
<span class="k">def</span> <span class="nf">g_</span><span class="p">(</span><span class="n">mu</span><span class="p">,</span> <span class="n">idx</span><span class="p">):</span>
<span class="k">return</span> <span class="n">M_t</span><span class="p">[:,</span> <span class="n">idx</span><span class="p">]</span>
<span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">loss</span> <span class="o">==</span> <span class="s1">'log'</span><span class="p">:</span>
<span class="c1"># Define the subobjective function and</span>
<span class="c1"># its gradient for the log loss function.</span>
<span class="k">def</span> <span class="nf">f_</span><span class="p">(</span><span class="n">mu</span><span class="p">):</span>
<span class="k">return</span> <span class="n">scs</span><span class="o">.</span><span class="n">logsumexp</span><span class="p">((</span><span class="n">phi</span> <span class="o">@</span> <span class="n">mu</span><span class="p">),</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">g_</span><span class="p">(</span><span class="n">mu</span><span class="p">,</span> <span class="n">idx</span><span class="p">):</span>
<span class="n">phi_xi</span> <span class="o">=</span> <span class="n">phi</span><span class="p">[</span><span class="n">idx</span><span class="p">,</span> <span class="p">:,</span> <span class="p">:]</span>
<span class="n">expPhi_xi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="n">phi_xi</span> <span class="o">@</span> <span class="n">mu</span><span class="p">)</span>
<span class="k">return</span> <span class="p">(</span><span class="n">expPhi_xi</span> <span class="o">@</span> <span class="n">phi_xi</span><span class="p">)</span><span class="o">.</span><span class="n">transpose</span><span class="p">()</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">expPhi_xi</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">'The given loss function is not available '</span> <span class="o">+</span>
<span class="s1">'for this classifier'</span><span class="p">)</span>
<span class="c1"># Calculate the upper bound</span>
<span class="c1"># Check if the warm start is true</span>
<span class="c1"># to reuse the solution from previous call to fit.</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">warm_start</span><span class="p">:</span>
<span class="c1"># Start from a previous solution.</span>
<span class="k">try</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">upper_params_</span> <span class="o">=</span> \
<span class="bp">self</span><span class="o">.</span><span class="n">nesterov_optimization</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">upper_params_</span><span class="p">,</span>
<span class="n">f_</span><span class="p">,</span> <span class="n">g_</span><span class="p">)</span>
<span class="k">except</span> <span class="ne">AttributeError</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">upper_params_</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">nesterov_optimization</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span>
<span class="n">f_</span><span class="p">,</span> <span class="n">g_</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">upper_params_</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">nesterov_optimization</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span>
<span class="n">f_</span><span class="p">,</span> <span class="n">g_</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">mu_</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">upper_params_</span><span class="p">[</span><span class="s1">'mu'</span><span class="p">]</span>
<span class="bp">self</span><span class="o">.</span><span class="n">nu_</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">upper_params_</span><span class="p">[</span><span class="s1">'nu'</span><span class="p">]</span>
<span class="bp">self</span><span class="o">.</span><span class="n">upper_</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">upper_params_</span><span class="p">[</span><span class="s1">'best_value'</span><span class="p">]</span>
<span class="bp">self</span><span class="o">.</span><span class="n">is_fitted_</span> <span class="o">=</span> <span class="kc">True</span>
<span class="k">return</span> <span class="bp">self</span></div>
<div class="viewcode-block" id="MRC.get_upper_bound"><a class="viewcode-back" href="../../generated/MRCpy.MRC.html#MRCpy.MRC.get_upper_bound">[docs]</a> <span class="k">def</span> <span class="nf">get_upper_bound</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">'''</span>
<span class="sd"> Returns the upper bound on the expected loss for the fitted classifier.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> upper : float</span>
<span class="sd"> The upper bound of the expected loss for the fitted classifier.</span>
<span class="sd"> '''</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">upper_</span></div>
<div class="viewcode-block" id="MRC.get_lower_bound"><a class="viewcode-back" href="../../generated/MRCpy.MRC.html#MRCpy.MRC.get_lower_bound">[docs]</a> <span class="k">def</span> <span class="nf">get_lower_bound</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">'''</span>
<span class="sd"> Obtains the lower bound on the expected loss for the fitted classifier.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> lower : float</span>
<span class="sd"> The lower bound of the error for the fitted classifier.</span>
<span class="sd"> '''</span>
<span class="c1"># Classifier should be fitted to obtain the lower bound</span>
<span class="n">check_is_fitted</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s2">"is_fitted_"</span><span class="p">)</span>
<span class="c1"># Learned feature mappings</span>
<span class="n">phi</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">lowerPhiConfigs</span>
<span class="c1"># Variables</span>
<span class="n">n</span> <span class="o">=</span> <span class="n">phi</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">phi</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">loss</span> <span class="o">==</span> <span class="s1">'0-1'</span><span class="p">:</span>
<span class="c1"># To define the objective function and</span>
<span class="c1"># the gradient for the 0-1 loss function.</span>
<span class="c1"># epsilon</span>
<span class="n">eps</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">clip</span><span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">phi</span> <span class="o">@</span> <span class="bp">self</span><span class="o">.</span><span class="n">mu_</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">nu_</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
<span class="n">c</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">eps</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">zeros</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">isclose</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="n">c</span><span class="p">[</span><span class="n">zeros</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">eps</span><span class="p">[</span><span class="n">zeros</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_classes</span>
<span class="n">eps</span> <span class="o">=</span> <span class="n">eps</span> <span class="o">/</span> <span class="p">(</span><span class="n">c</span><span class="p">[:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">])</span>
<span class="c1"># Using negative of epsilon</span>
<span class="c1"># for the nesterov accelerated optimization</span>
<span class="n">eps</span> <span class="o">=</span> <span class="n">eps</span> <span class="o">-</span> <span class="mi">1</span>
<span class="c1"># Reshape it for the optimization function</span>
<span class="n">eps</span> <span class="o">=</span> <span class="n">eps</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="n">n</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_classes</span><span class="p">,))</span>
<span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">loss</span> <span class="o">==</span> <span class="s1">'log'</span><span class="p">:</span>
<span class="c1"># To define the objective function and</span>
<span class="c1"># the gradient for the log loss function.</span>
<span class="c1"># Using negative of epsilon</span>
<span class="c1"># for the nesterov accelerated optimization</span>
<span class="n">eps</span> <span class="o">=</span> <span class="n">phi</span> <span class="o">@</span> <span class="bp">self</span><span class="o">.</span><span class="n">mu_</span> <span class="o">-</span> \
<span class="n">scs</span><span class="o">.</span><span class="n">logsumexp</span><span class="p">(</span><span class="n">phi</span> <span class="o">@</span> <span class="bp">self</span><span class="o">.</span><span class="n">mu_</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)[:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">]</span>
<span class="n">eps</span> <span class="o">=</span> <span class="n">eps</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="n">n</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_classes</span><span class="p">,))</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">'The given loss function is not available '</span> <span class="o">+</span>
<span class="s1">'for this classifier'</span><span class="p">)</span>
<span class="n">phi</span> <span class="o">=</span> <span class="n">phi</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="n">n</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_classes</span><span class="p">,</span> <span class="n">m</span><span class="p">))</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">use_cvx</span><span class="p">:</span>
<span class="c1"># Use CVXpy for the convex optimization of the MRC</span>
<span class="n">low_mu</span> <span class="o">=</span> <span class="n">cvx</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
<span class="c1"># Objective function</span>
<span class="n">objective</span> <span class="o">=</span> <span class="n">cvx</span><span class="o">.</span><span class="n">Minimize</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">lambda_</span> <span class="o">@</span> <span class="n">cvx</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">low_mu</span><span class="p">)</span> <span class="o">-</span>
<span class="bp">self</span><span class="o">.</span><span class="n">tau_</span> <span class="o">@</span> <span class="n">low_mu</span> <span class="o">+</span>
<span class="n">cvx</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">phi</span> <span class="o">@</span> <span class="n">low_mu</span> <span class="o">+</span> <span class="n">eps</span><span class="p">))</span>
<span class="bp">self</span><span class="o">.</span><span class="n">mu_l_</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">lower_</span> <span class="o">=</span> \
<span class="bp">self</span><span class="o">.</span><span class="n">try_solvers</span><span class="p">(</span><span class="n">objective</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="n">low_mu</span><span class="p">)</span>
<span class="c1"># Maximize the function</span>
<span class="bp">self</span><span class="o">.</span><span class="n">lower_</span> <span class="o">=</span> <span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">lower_</span>
<span class="k">elif</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">use_cvx</span><span class="p">:</span>
<span class="c1"># Use the subgradient approach for the convex optimization of MRC</span>
<span class="c1"># Defining the partial objective and its gradient.</span>
<span class="k">def</span> <span class="nf">f_</span><span class="p">(</span><span class="n">mu</span><span class="p">):</span>
<span class="k">return</span> <span class="n">phi</span> <span class="o">@</span> <span class="n">mu</span> <span class="o">+</span> <span class="n">eps</span>
<span class="k">def</span> <span class="nf">g_</span><span class="p">(</span><span class="n">mu</span><span class="p">,</span> <span class="n">idx</span><span class="p">):</span>
<span class="k">return</span> <span class="n">phi</span><span class="o">.</span><span class="n">transpose</span><span class="p">()[:,</span> <span class="n">idx</span><span class="p">]</span>
<span class="c1"># Lower bound</span>
<span class="c1"># Check if the warm start is true</span>
<span class="c1"># to reuse the solution from previous call to fit.</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">warm_start</span><span class="p">:</span>
<span class="c1"># Start from a previous solution.</span>
<span class="k">try</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">lower_params_</span> <span class="o">=</span> \
<span class="bp">self</span><span class="o">.</span><span class="n">nesterov_optimization</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">lower_params_</span><span class="p">,</span>
<span class="n">f_</span><span class="p">,</span> <span class="n">g_</span><span class="p">)</span>
<span class="k">except</span> <span class="ne">AttributeError</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">lower_params_</span> <span class="o">=</span> \
<span class="bp">self</span><span class="o">.</span><span class="n">nesterov_optimization</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="n">f_</span><span class="p">,</span> <span class="n">g_</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">lower_params_</span> <span class="o">=</span> \
<span class="bp">self</span><span class="o">.</span><span class="n">nesterov_optimization</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="n">f_</span><span class="p">,</span> <span class="n">g_</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">mu_l_</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">lower_params_</span><span class="p">[</span><span class="s1">'mu'</span><span class="p">]</span>
<span class="bp">self</span><span class="o">.</span><span class="n">lower_</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">lower_params_</span><span class="p">[</span><span class="s1">'best_value'</span><span class="p">]</span>
<span class="c1"># Maximize the function</span>
<span class="c1"># as the nesterov optimization gives the minimum</span>
<span class="bp">self</span><span class="o">.</span><span class="n">lower_</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">lower_</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">lower_</span></div>
<span class="k">def</span> <span class="nf">nesterov_optimization</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">m</span><span class="p">,</span> <span class="n">params_</span><span class="p">,</span> <span class="n">f_</span><span class="p">,</span> <span class="n">g_</span><span class="p">):</span>
<span class="sd">'''</span>
<span class="sd"> Solution of the MRC convex optimization(minimization)</span>
<span class="sd"> using the Nesterov accelerated approach.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> m : int</span>
<span class="sd"> Length of the feature mapping vector</span>
<span class="sd"> params_ : a dictionary</span>
<span class="sd"> A dictionary of parameters values</span>
<span class="sd"> obtained from the previous call to fit</span>
<span class="sd"> used as the initial values for the current optimization</span>
<span class="sd"> when warm_start is True.</span>
<span class="sd"> f_ : a lambda function of the form - f_(mu)</span>
<span class="sd"> It is expected to be a lambda function</span>
<span class="sd"> calculating a part of the objective function</span>
<span class="sd"> depending on the type of loss function chosen</span>
<span class="sd"> by taking the parameters(mu) of the optimization as input.</span>
<span class="sd"> g_ : a lambda function of the form - g_(mu, idx)</span>
<span class="sd"> It is expected to be a lambda function</span>
<span class="sd"> calculating the part of the subgradient of the objective function</span>
<span class="sd"> depending on the type of the loss function chosen.</span>
<span class="sd"> It takes the as input -</span>
<span class="sd"> parameters (mu) of the optimization and</span>
<span class="sd"> the index corresponding to the maximum value of data matrix</span>
<span class="sd"> obtained from the instances.</span>
<span class="sd"> Return</span>
<span class="sd"> ------</span>
<span class="sd"> mu : array-like, shape (m,)</span>
<span class="sd"> The parameters corresponding to the optimized function value</span>
<span class="sd"> nu : float</span>
<span class="sd"> The parameter corresponding to the optimized function value</span>
<span class="sd"> f_best_value : float</span>
<span class="sd"> The optimized value of the function in consideration i.e.,</span>
<span class="sd"> the upper bound of the minimax risk classification.</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> [1] The strength of Nesterov’s extrapolation</span>
<span class="sd"> in the individual convergence of nonsmooth optimization.</span>
<span class="sd"> Wei Tao, Zhisong Pan, Gao wei Wu, and Qing Tao.</span>
<span class="sd"> In IEEE Transactions on Neural Networks and Learning System.</span>
<span class="sd"> (https://ieeexplore.ieee.org/document/8822632)</span>
<span class="sd"> '''</span>
<span class="c1"># Initial values for the parameters</span>
<span class="n">theta_k</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">theta_k_prev</span> <span class="o">=</span> <span class="mi">1</span>
<span class="c1"># Initial values for points</span>
<span class="k">if</span> <span class="n">params_</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">y_k</span> <span class="o">=</span> <span class="n">params_</span><span class="p">[</span><span class="s1">'mu'</span><span class="p">]</span>
<span class="n">w_k</span> <span class="o">=</span> <span class="n">params_</span><span class="p">[</span><span class="s1">'w_k'</span><span class="p">]</span>
<span class="n">w_k_prev</span> <span class="o">=</span> <span class="n">params_</span><span class="p">[</span><span class="s1">'w_k_prev'</span><span class="p">]</span>
<span class="c1"># Length of the points array might change</span>
<span class="c1"># depending on the new dataset in case of warm_start=True,</span>
<span class="c1"># as the length of feature mapping might</span>
<span class="c1"># change with the new dataset.</span>
<span class="n">old_m</span> <span class="o">=</span> <span class="n">y_k</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="k">if</span> <span class="n">old_m</span> <span class="o">!=</span> <span class="n">m</span><span class="p">:</span>
<span class="c1"># Length of each class</span>
<span class="c1"># in the feature mapping depending on old dataset</span>
<span class="n">old_len</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">old_m</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_classes</span><span class="p">)</span>
<span class="c1"># Length of each class</span>
<span class="c1"># in the feature mapping depending on new dataset</span>
<span class="n">new_len</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">m</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_classes</span><span class="p">)</span>
<span class="c1"># New points array with increased size</span>
<span class="c1"># while restoring the old values of points.</span>
<span class="n">new_y_k</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float</span><span class="p">)</span>
<span class="n">new_w_k</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float</span><span class="p">)</span>
<span class="n">new_w_k_prev</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float</span><span class="p">)</span>
<span class="c1"># Restoring the old values of the points</span>
<span class="c1"># obtained from previous call to fit.</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_classes</span><span class="p">):</span>
<span class="n">new_start</span> <span class="o">=</span> <span class="n">new_len</span> <span class="o">*</span> <span class="n">i</span>
<span class="n">old_start</span> <span class="o">=</span> <span class="n">old_len</span> <span class="o">*</span> <span class="n">i</span>
<span class="k">if</span> <span class="n">old_m</span> <span class="o"><</span> <span class="n">m</span><span class="p">:</span>
<span class="c1"># Increase the size by appending zeros</span>
<span class="c1"># at the end of each class segment.</span>
<span class="n">new_y_k</span><span class="p">[</span><span class="n">new_start</span><span class="p">:</span><span class="n">new_start</span> <span class="o">+</span> <span class="n">old_len</span><span class="p">]</span> <span class="o">=</span> \
<span class="n">y_k</span><span class="p">[</span><span class="n">old_start</span><span class="p">:</span><span class="n">old_start</span> <span class="o">+</span> <span class="n">old_len</span><span class="p">]</span>
<span class="n">new_w_k</span><span class="p">[</span><span class="n">new_start</span><span class="p">:</span><span class="n">new_start</span> <span class="o">+</span> <span class="n">old_len</span><span class="p">]</span> <span class="o">=</span> \
<span class="n">w_k</span><span class="p">[</span><span class="n">old_start</span><span class="p">:</span><span class="n">old_start</span> <span class="o">+</span> <span class="n">old_len</span><span class="p">]</span>
<span class="n">new_w_k_prev</span><span class="p">[</span><span class="n">new_start</span><span class="p">:</span><span class="n">new_start</span> <span class="o">+</span> <span class="n">old_len</span><span class="p">]</span> <span class="o">=</span> \
<span class="n">w_k_prev</span><span class="p">[</span><span class="n">old_start</span><span class="p">:</span><span class="n">old_start</span> <span class="o">+</span> <span class="n">old_len</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># Decrease the size</span>
<span class="c1"># by taking the starting values of each class segment.</span>
<span class="n">new_y_k</span><span class="p">[</span><span class="n">new_start</span><span class="p">:</span><span class="n">new_start</span> <span class="o">+</span> <span class="n">new_len</span><span class="p">]</span> <span class="o">=</span> \
<span class="n">y_k</span><span class="p">[</span><span class="n">old_start</span><span class="p">:</span><span class="n">old_start</span> <span class="o">+</span> <span class="n">new_len</span><span class="p">]</span>
<span class="n">new_w_k</span><span class="p">[</span><span class="n">new_start</span><span class="p">:</span><span class="n">new_start</span> <span class="o">+</span> <span class="n">new_len</span><span class="p">]</span> <span class="o">=</span> \
<span class="n">w_k</span><span class="p">[</span><span class="n">old_start</span><span class="p">:</span><span class="n">old_start</span> <span class="o">+</span> <span class="n">new_len</span><span class="p">]</span>
<span class="n">new_w_k_prev</span><span class="p">[</span><span class="n">new_start</span><span class="p">:</span><span class="n">new_start</span> <span class="o">+</span> <span class="n">new_len</span><span class="p">]</span> <span class="o">=</span> \
<span class="n">w_k_prev</span><span class="p">[</span><span class="n">old_start</span><span class="p">:</span><span class="n">old_start</span> <span class="o">+</span> <span class="n">new_len</span><span class="p">]</span>
<span class="c1"># Updating values.</span>
<span class="n">y_k</span> <span class="o">=</span> <span class="n">new_y_k</span>
<span class="n">w_k</span> <span class="o">=</span> <span class="n">new_w_k</span>
<span class="n">w_k_prev</span> <span class="o">=</span> <span class="n">new_w_k_prev</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">y_k</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float</span><span class="p">)</span>
<span class="n">w_k</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float</span><span class="p">)</span>
<span class="n">w_k_prev</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float</span><span class="p">)</span>
<span class="c1"># Setting initial values for the objective function and other results</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">f_</span><span class="p">(</span><span class="n">y_k</span><span class="p">)</span>
<span class="n">mnu</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="n">f_best_value</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">lambda_</span> <span class="o">@</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">y_k</span><span class="p">)</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">tau_</span> <span class="o">@</span> <span class="n">y_k</span> <span class="o">+</span> <span class="n">mnu</span>
<span class="n">mu</span> <span class="o">=</span> <span class="n">y_k</span>
<span class="n">nu</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">mnu</span>
<span class="c1"># Iteration for finding the optimal values</span>
<span class="c1"># using Nesterov's extrapolation</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">max_iters</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)):</span>
<span class="n">y_k</span> <span class="o">=</span> <span class="n">w_k</span> <span class="o">+</span> <span class="n">theta_k</span> <span class="o">*</span> <span class="p">((</span><span class="mi">1</span> <span class="o">/</span> <span class="n">theta_k_prev</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">w_k</span> <span class="o">-</span> <span class="n">w_k_prev</span><span class="p">)</span>
<span class="c1"># Calculating the subgradient of the objective function at y_k</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">f_</span><span class="p">(</span><span class="n">y_k</span><span class="p">)</span>
<span class="n">idx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="n">g_0</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">lambda_</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">y_k</span><span class="p">)</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">tau_</span> <span class="o">+</span> <span class="n">g_</span><span class="p">(</span><span class="n">y_k</span><span class="p">,</span> <span class="n">idx</span><span class="p">)</span>
<span class="c1"># Update the parameters</span>
<span class="n">theta_k_prev</span> <span class="o">=</span> <span class="n">theta_k</span>
<span class="n">theta_k</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="n">k</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">alpha_k</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">power</span><span class="p">((</span><span class="n">k</span> <span class="o">+</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">3</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)))</span>
<span class="c1"># Calculate the new points</span>
<span class="n">w_k_prev</span> <span class="o">=</span> <span class="n">w_k</span>
<span class="n">w_k</span> <span class="o">=</span> <span class="n">y_k</span> <span class="o">-</span> <span class="n">alpha_k</span> <span class="o">*</span> <span class="n">g_0</span>
<span class="c1"># Check if there is an improvement</span>
<span class="c1"># in the value of the objective function</span>
<span class="n">mnu</span> <span class="o">=</span> <span class="n">v</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
<span class="n">f_value</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">lambda_</span> <span class="o">@</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">y_k</span><span class="p">)</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">tau_</span> <span class="o">@</span> <span class="n">y_k</span> <span class="o">+</span> <span class="n">mnu</span>
<span class="k">if</span> <span class="n">f_value</span> <span class="o"><</span> <span class="n">f_best_value</span><span class="p">:</span>
<span class="n">f_best_value</span> <span class="o">=</span> <span class="n">f_value</span>
<span class="n">mu</span> <span class="o">=</span> <span class="n">y_k</span>
<span class="n">nu</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">mnu</span>
<span class="c1"># Check for possible improvement of the objective value</span>
<span class="c1"># for the last generated value of w_k</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">f_</span><span class="p">(</span><span class="n">w_k</span><span class="p">)</span>
<span class="n">mnu</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="n">f_value</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">lambda_</span> <span class="o">@</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">w_k</span><span class="p">)</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">tau_</span> <span class="o">@</span> <span class="n">w_k</span> <span class="o">+</span> <span class="n">mnu</span>
<span class="k">if</span> <span class="n">f_value</span> <span class="o"><</span> <span class="n">f_best_value</span><span class="p">:</span>
<span class="n">f_best_value</span> <span class="o">=</span> <span class="n">f_value</span>
<span class="n">mu</span> <span class="o">=</span> <span class="n">w_k</span>
<span class="n">nu</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">mnu</span>
<span class="c1"># Return the optimized values in a dictionary</span>
<span class="n">new_params_</span> <span class="o">=</span> <span class="p">{</span><span class="s1">'w_k'</span><span class="p">:</span> <span class="n">w_k</span><span class="p">,</span>
<span class="s1">'w_k_prev'</span><span class="p">:</span> <span class="n">w_k_prev</span><span class="p">,</span>
<span class="s1">'mu'</span><span class="p">:</span> <span class="n">mu</span><span class="p">,</span>
<span class="s1">'nu'</span><span class="p">:</span> <span class="n">nu</span><span class="p">,</span>
<span class="s1">'best_value'</span><span class="p">:</span> <span class="n">f_best_value</span><span class="p">,</span>
<span class="p">}</span>
<span class="k">return</span> <span class="n">new_params_</span>
<div class="viewcode-block" id="MRC.predict_proba"><a class="viewcode-back" href="../../generated/MRCpy.MRC.html#MRCpy.MRC.predict_proba">[docs]</a> <span class="k">def</span> <span class="nf">predict_proba</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">X</span><span class="p">):</span>
<span class="sd">'''</span>
<span class="sd"> Conditional probabilities corresponding to each class</span>
<span class="sd"> for each unlabeled instance</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> X : array-like of shape (n_samples, n_dimensions)</span>
<span class="sd"> Testing instances for which</span>
<span class="sd"> the prediction probabilities are calculated for each class.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> hy_x : ndarray of shape (n_samples, n_classes)</span>
<span class="sd"> The probabilities (p(y|x)) corresponding to the predictions</span>
<span class="sd"> for each class.</span>
<span class="sd"> '''</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">check_array</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">accept_sparse</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">check_is_fitted</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s2">"is_fitted_"</span><span class="p">)</span>
<span class="n">phi</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">phi</span><span class="o">.</span><span class="n">eval_x</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">loss</span> <span class="o">==</span> <span class="s1">'0-1'</span><span class="p">:</span>
<span class="c1"># Constraints in case of 0-1 loss function</span>
<span class="c1"># Unnormalized conditional probabilityes</span>
<span class="n">hy_x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">clip</span><span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">phi</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">mu_</span><span class="p">)</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">nu_</span><span class="p">,</span> <span class="mf">0.</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
<span class="c1"># normalization constraint</span>
<span class="n">c</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">hy_x</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="c1"># check when the sum is zero</span>
<span class="n">zeros</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">isclose</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="n">c</span><span class="p">[</span><span class="n">zeros</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">hy_x</span><span class="p">[</span><span class="n">zeros</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_classes</span>
<span class="n">c</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">tile</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_classes</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">transpose</span><span class="p">()</span>
<span class="n">hy_x</span> <span class="o">=</span> <span class="n">hy_x</span> <span class="o">/</span> <span class="n">c</span>
<span class="c1"># Set the approach for prediction to non-deterministic</span>
<span class="c1"># if not provided by user.</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">deterministic</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">deterministic</span> <span class="o">=</span> <span class="kc">False</span>
<span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">loss</span> <span class="o">==</span> <span class="s1">'log'</span><span class="p">:</span>
<span class="c1"># Constraints in case of log loss function</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">phi</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">mu_</span><span class="p">)</span>
<span class="c1"># Normalizing conditional probabilities</span>
<span class="n">hy_x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="n">v</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">tile</span><span class="p">(</span><span class="n">v</span><span class="p">[:,</span> <span class="n">i</span><span class="p">],</span>
<span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_classes</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">transpose</span><span class="p">()),</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_classes</span><span class="p">))</span><span class="o">.</span><span class="n">transpose</span><span class="p">()</span>
<span class="n">hy_x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reciprocal</span><span class="p">(</span><span class="n">hy_x</span><span class="p">)</span>
<span class="c1"># Set the approach for prediction to deterministic</span>
<span class="c1"># if not provided by user.</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">deterministic</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">deterministic</span> <span class="o">=</span> <span class="kc">True</span>
<span class="k">return</span> <span class="n">hy_x</span></div></div>
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