Explainable ‘AI’ using Gradient Boosted randomized networks Pt2 (the Lasso)

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This post is about LSBoost, an Explainable ‘AI’ algorithm which uses Gradient Boosted randomized networks for pattern recognition. As we’ve discussed it last week LSBoost is a cousin of GFAGBM’s LS_Boost. In LSBoost, more specifically, the so called weak learners from LS_Boost are based on randomized neural networks’ components and variants of Least Squares regression models.

I’ve already presented some promising examples of use of LSBoost based on Ridge Regression weak learners. In mlsauce’s version 0.7.1, the Lasso can also be used as an alternative ingredient to the weak learners. Here is a comparison of the regression coefficients obtained by using mlsauce’s implementation of Ridge regression and the Lasso:

image-title-here

R example: LSBoostRegressor with Ridge regression and the Lasso

The following example is about training set error vs testing set error, as a function of the regularization parameter, both for Ridge regression and Lasso-based weak learners.

Packages and data

<span class="w">
</span><span class="c1"># 0 - Packages and data -------------------------------------------------------</span><span class="w">

</span><span class="n">library</span><span class="p">(</span><span class="n">devtools</span><span class="p">)</span><span class="w">
</span><span class="n">devtools</span><span class="o">::</span><span class="n">install_github</span><span class="p">(</span><span class="s2">"thierrymoudiki/mlsauce/R-package"</span><span class="p">)</span><span class="w">
</span><span class="n">library</span><span class="p">(</span><span class="n">mlsauce</span><span class="p">)</span><span class="w">
</span><span class="n">library</span><span class="p">(</span><span class="n">datasets</span><span class="p">)</span><span class="w">

</span><span class="n">print</span><span class="p">(</span><span class="n">summary</span><span class="p">(</span><span class="n">datasets</span><span class="o">::</span><span class="n">mtcars</span><span class="p">))</span><span class="w">

</span><span class="n">X</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">as.matrix</span><span class="p">(</span><span class="n">datasets</span><span class="o">::</span><span class="n">mtcars</span><span class="p">[,</span><span class="w"> </span><span class="m">-1</span><span class="p">])</span><span class="w">
</span><span class="n">y</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="nf">as.integer</span><span class="p">(</span><span class="n">datasets</span><span class="o">::</span><span class="n">mtcars</span><span class="p">[,</span><span class="w"> </span><span class="m">1</span><span class="p">])</span><span class="w">

</span><span class="n">n</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="nf">dim</span><span class="p">(</span><span class="n">X</span><span class="p">)[</span><span class="m">1</span><span class="p">]</span><span class="w">
</span><span class="n">p</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="nf">dim</span><span class="p">(</span><span class="n">X</span><span class="p">)[</span><span class="m">2</span><span class="p">]</span><span class="w">
</span><span class="n">set.seed</span><span class="p">(</span><span class="m">21341</span><span class="p">)</span><span class="w">
</span><span class="n">train_index</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">sample</span><span class="p">(</span><span class="n">x</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="o">:</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nf">floor</span><span class="p">(</span><span class="m">0.8</span><span class="o">*</span><span class="n">n</span><span class="p">),</span><span class="w"> </span><span class="n">replace</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">TRUE</span><span class="p">)</span><span class="w">
</span><span class="n">test_index</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="o">-</span><span class="n">train_index</span><span class="w">
</span><span class="n">X_train</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">as.matrix</span><span class="p">(</span><span class="n">X</span><span class="p">[</span><span class="n">train_index</span><span class="p">,</span><span class="w"> </span><span class="p">])</span><span class="w">
</span><span class="n">y_train</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="nf">as.double</span><span class="p">(</span><span class="n">y</span><span class="p">[</span><span class="n">train_index</span><span class="p">])</span><span class="w">
</span><span class="n">X_test</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">as.matrix</span><span class="p">(</span><span class="n">X</span><span class="p">[</span><span class="n">test_index</span><span class="p">,</span><span class="w"> </span><span class="p">])</span><span class="w">
</span><span class="n">y_test</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="nf">as.double</span><span class="p">(</span><span class="n">y</span><span class="p">[</span><span class="n">test_index</span><span class="p">])</span><span class="w">

</span>

LSBoost using Ridge regression

<span class="w">
</span><span class="c1"># 1 - Ridge -------------------------------------------------------------------</span><span class="w">

</span><span class="n">obj</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mlsauce</span><span class="o">::</span><span class="n">LSBoostRegressor</span><span class="p">()</span><span class="w"> </span><span class="c1"># default h is Ridge</span><span class="w">
</span><span class="n">print</span><span class="p">(</span><span class="n">obj</span><span class="o">$</span><span class="n">get_params</span><span class="p">())</span><span class="w">

</span><span class="n">n_lambdas</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="m">100</span><span class="w">
</span><span class="n">lambdas</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="m">10</span><span class="o">**</span><span class="n">seq</span><span class="p">(</span><span class="n">from</span><span class="o">=</span><span class="m">-6</span><span class="p">,</span><span class="w"> </span><span class="n">to</span><span class="o">=</span><span class="m">6</span><span class="p">,</span><span class="w"> 
                   </span><span class="n">length.out</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n_lambdas</span><span class="p">)</span><span class="w">
</span><span class="n">rmse_matrix</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">matrix</span><span class="p">(</span><span class="kc">NA</span><span class="p">,</span><span class="w"> </span><span class="n">nrow</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="n">ncol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n_lambdas</span><span class="p">)</span><span class="w">
</span><span class="n">rownames</span><span class="p">(</span><span class="n">rmse_matrix</span><span class="p">)</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="nf">c</span><span class="p">(</span><span class="s2">"training rmse"</span><span class="p">,</span><span class="w"> </span><span class="s2">"testing rmse"</span><span class="p">)</span><span class="w">

</span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1</span><span class="o">:</span><span class="n">n_lambdas</span><span class="p">)</span><span class="w">
</span><span class="p">{</span><span class="w">
  </span><span class="n">obj</span><span class="o">$</span><span class="n">set_params</span><span class="p">(</span><span class="n">reg_lambda</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">lambdas</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w">
  </span><span class="n">obj</span><span class="o">$</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span><span class="w"> </span><span class="n">y_train</span><span class="p">)</span><span class="w">
  </span><span class="n">rmse_matrix</span><span class="p">[,</span><span class="w"> </span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="nf">c</span><span class="p">(</span><span class="nf">sqrt</span><span class="p">(</span><span class="n">mean</span><span class="p">((</span><span class="n">obj</span><span class="o">$</span><span class="n">predict</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">y_train</span><span class="p">)</span><span class="o">**</span><span class="m">2</span><span class="p">)),</span><span class="w"> 
                        </span><span class="nf">sqrt</span><span class="p">(</span><span class="n">mean</span><span class="p">((</span><span class="n">obj</span><span class="o">$</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">y_test</span><span class="p">)</span><span class="o">**</span><span class="m">2</span><span class="p">)))</span><span class="w">
</span><span class="p">}</span><span class="w">

</span>

image-title-here

LSBoost using the Lasso

<span class="w">
</span><span class="c1"># 2 - Lasso -------------------------------------------------------------------</span><span class="w">

</span><span class="n">obj</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mlsauce</span><span class="o">::</span><span class="n">LSBoostRegressor</span><span class="p">(</span><span class="n">solver</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">"lasso"</span><span class="p">)</span><span class="w">
</span><span class="n">print</span><span class="p">(</span><span class="n">obj</span><span class="o">$</span><span class="n">get_params</span><span class="p">())</span><span class="w">

</span><span class="n">n_lambdas</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="m">100</span><span class="w">
</span><span class="n">lambdas</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="m">10</span><span class="o">**</span><span class="n">seq</span><span class="p">(</span><span class="n">from</span><span class="o">=</span><span class="m">-6</span><span class="p">,</span><span class="w"> </span><span class="n">to</span><span class="o">=</span><span class="m">6</span><span class="p">,</span><span class="w"> 
                   </span><span class="n">length.out</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n_lambdas</span><span class="p">)</span><span class="w">
</span><span class="n">rmse_matrix2</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">matrix</span><span class="p">(</span><span class="kc">NA</span><span class="p">,</span><span class="w"> </span><span class="n">nrow</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="n">ncol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n_lambdas</span><span class="p">)</span><span class="w">
</span><span class="n">rownames</span><span class="p">(</span><span class="n">rmse_matrix2</span><span class="p">)</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="nf">c</span><span class="p">(</span><span class="s2">"training rmse"</span><span class="p">,</span><span class="w"> </span><span class="s2">"testing rmse"</span><span class="p">)</span><span class="w">

</span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1</span><span class="o">:</span><span class="n">n_lambdas</span><span class="p">)</span><span class="w">
</span><span class="p">{</span><span class="w">
  </span><span class="n">obj</span><span class="o">$</span><span class="n">set_params</span><span class="p">(</span><span class="n">reg_lambda</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">lambdas</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w">
  </span><span class="n">obj</span><span class="o">$</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span><span class="w"> </span><span class="n">y_train</span><span class="p">)</span><span class="w">
  </span><span class="n">rmse_matrix2</span><span class="p">[,</span><span class="w"> </span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="nf">c</span><span class="p">(</span><span class="nf">sqrt</span><span class="p">(</span><span class="n">mean</span><span class="p">((</span><span class="n">obj</span><span class="o">$</span><span class="n">predict</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">y_train</span><span class="p">)</span><span class="o">**</span><span class="m">2</span><span class="p">)),</span><span class="w"> 
                         </span><span class="nf">sqrt</span><span class="p">(</span><span class="n">mean</span><span class="p">((</span><span class="n">obj</span><span class="o">$</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">y_test</span><span class="p">)</span><span class="o">**</span><span class="m">2</span><span class="p">)))</span><span class="w">
</span><span class="p">}</span><span class="w">

</span>

image-title-here

R session info

<span class="w">
</span><span class="o">></span><span class="w"> </span><span class="n">print</span><span class="p">(</span><span class="n">session_info</span><span class="p">())</span><span class="w">
</span><span class="err">─</span><span class="w"> </span><span class="n">Session</span><span class="w"> </span><span class="n">info</span><span class="w"> </span><span class="err">─────────────────────────────────────────────────────────────</span><span class="w">
 </span><span class="n">setting</span><span class="w">  </span><span class="n">value</span><span class="w">                       
 </span><span class="n">version</span><span class="w">  </span><span class="n">R</span><span class="w"> </span><span class="n">version</span><span class="w"> </span><span class="m">4.0.2</span><span class="w"> </span><span class="p">(</span><span class="m">2020-06-22</span><span class="p">)</span><span class="w">
 </span><span class="n">os</span><span class="w">       </span><span class="n">Ubuntu</span><span class="w"> </span><span class="m">16.04.6</span><span class="w"> </span><span class="n">LTS</span><span class="w">          
 </span><span class="n">system</span><span class="w">   </span><span class="n">x86_64</span><span class="p">,</span><span class="w"> </span><span class="n">linux</span><span class="o">-</span><span class="n">gnu</span><span class="w">           
 </span><span class="n">ui</span><span class="w">       </span><span class="n">RStudio</span><span class="w">                     
 </span><span class="n">language</span><span class="w"> </span><span class="p">(</span><span class="n">EN</span><span class="p">)</span><span class="w">                        
 </span><span class="n">collate</span><span class="w">  </span><span class="n">C.UTF</span><span class="m">-8</span><span class="w">                     
 </span><span class="n">ctype</span><span class="w">    </span><span class="n">C.UTF</span><span class="m">-8</span><span class="w">                     
 </span><span class="n">tz</span><span class="w">       </span><span class="n">Etc</span><span class="o">/</span><span class="n">UTC</span><span class="w">                     
 </span><span class="n">date</span><span class="w">     </span><span class="m">2020-07-31</span><span class="w">                  

</span><span class="err">─</span><span class="w"> </span><span class="n">Packages</span><span class="w"> </span><span class="err">─────────────────────────────────────────────────────────────────</span><span class="w">
 </span><span class="n">package</span><span class="w">     </span><span class="o">*</span><span class="w"> </span><span class="n">version</span><span class="w"> </span><span class="n">date</span><span class="w">       </span><span class="n">lib</span><span class="w"> </span><span class="n">source</span><span class="w">                                 
 </span><span class="n">assertthat</span><span class="w">    </span><span class="m">0.2.1</span><span class="w">   </span><span class="m">2019-03-21</span><span class="w"> </span><span class="p">[</span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="n">RSPM</span><span class="w"> </span><span class="p">(</span><span class="n">R</span><span class="w"> </span><span class="m">4.0.2</span><span class="p">)</span><span class="w">                         
 </span><span class="n">backports</span><span class="w">     </span><span class="m">1.1.8</span><span class="w">   </span><span class="m">2020-06-17</span><span class="w"> </span><span class="p">[</span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="n">RSPM</span><span class="w"> </span><span class="p">(</span><span class="n">R</span><span class="w"> </span><span class="m">4.0.2</span><span class="p">)</span><span class="w">                         
 </span><span class="n">callr</span><span class="w">         </span><span class="m">3.4.3</span><span class="w">   </span><span class="m">2020-03-28</span><span class="w"> </span><span class="p">[</span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="n">RSPM</span><span class="w"> </span><span class="p">(</span><span class="n">R</span><span class="w"> </span><span class="m">4.0.2</span><span class="p">)</span><span class="w">                         
 </span><span class="n">cli</span><span class="w">           </span><span class="m">2.0.2</span><span class="w">   </span><span class="m">2020-02-28</span><span class="w"> </span><span class="p">[</span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="n">RSPM</span><span class="w"> </span><span class="p">(</span><span class="n">R</span><span class="w"> </span><span class="m">4.0.2</span><span class="p">)</span><span class="w">                         
 </span><span class="n">crayon</span><span class="w">        </span><span class="m">1.3.4</span><span class="w">   </span><span class="m">2017-09-16</span><span class="w"> </span><span class="p">[</span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="n">RSPM</span><span class="w"> </span><span class="p">(</span><span class="n">R</span><span class="w"> </span><span class="m">4.0.2</span><span class="p">)</span><span class="w">                         
 </span><span class="n">curl</span><span class="w">          </span><span class="m">4.3</span><span class="w">     </span><span class="m">2019-12-02</span><span class="w"> </span><span class="p">[</span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="n">RSPM</span><span class="w"> </span><span class="p">(</span><span class="n">R</span><span class="w"> </span><span class="m">4.0.2</span><span class="p">)</span><span class="w">                         
 </span><span class="n">desc</span><span class="w">          </span><span class="m">1.2.0</span><span class="w">   </span><span class="m">2018-05-01</span><span class="w"> </span><span class="p">[</span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="n">RSPM</span><span class="w"> </span><span class="p">(</span><span class="n">R</span><span class="w"> </span><span class="m">4.0.2</span><span class="p">)</span><span class="w">                         
 </span><span class="n">devtools</span><span class="w">    </span><span class="o">*</span><span class="w"> </span><span class="m">2.3.1</span><span class="w">   </span><span class="m">2020-07-21</span><span class="w"> </span><span class="p">[</span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="n">RSPM</span><span class="w"> </span><span class="p">(</span><span class="n">R</span><span class="w"> </span><span class="m">4.0.2</span><span class="p">)</span><span class="w">                         
 </span><span class="n">digest</span><span class="w">        </span><span class="m">0.6.25</span><span class="w">  </span><span class="m">2020-02-23</span><span class="w"> </span><span class="p">[</span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="n">RSPM</span><span class="w"> </span><span class="p">(</span><span class="n">R</span><span class="w"> </span><span class="m">4.0.2</span><span class="p">)</span><span class="w">                         
 </span><span class="n">ellipsis</span><span class="w">      </span><span class="m">0.3.1</span><span class="w">   </span><span class="m">2020-05-15</span><span class="w"> </span><span class="p">[</span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="n">RSPM</span><span class="w"> </span><span class="p">(</span><span class="n">R</span><span class="w"> </span><span class="m">4.0.2</span><span class="p">)</span><span class="w">                         
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</span><span class="p">[</span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">/</span><span class="n">home</span><span class="o">/</span><span class="n">rstudio</span><span class="o">-</span><span class="n">user</span><span class="o">/</span><span class="n">R</span><span class="o">/</span><span class="n">x86_64</span><span class="o">-</span><span class="n">pc</span><span class="o">-</span><span class="n">linux</span><span class="o">-</span><span class="n">gnu</span><span class="o">-</span><span class="n">library</span><span class="o">/</span><span class="m">4.0</span><span class="w">
</span><span class="p">[</span><span class="m">2</span><span class="p">]</span><span class="w"> </span><span class="o">/</span><span class="n">opt</span><span class="o">/</span><span class="n">R</span><span class="o">/</span><span class="m">4.0.2</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">R</span><span class="o">/</span><span class="n">library</span><span class="w">

</span>

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