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    <p>Speaking as an ignorant, lurker/nonuser of sklearn, the way I see
      this being handled in neural nets is</p>
    <blockquote>
      <p><br>
        <font size="+2"><span style="color: rgb(0, 0, 0); font-family: SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", Courier, monospace; font-size: 12px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: pre; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;"><a href="https://keras.io/examples/cifar10_cnn/">https://keras.io/examples/cifar10_cnn/</a></span></font></p>
      <p><font size="+2"><span style="color: rgb(0, 0, 0); font-family: SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", Courier, monospace; font-size: 12px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: pre; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;">model.add(Dense(num_classes))  
model.add(Activation('softmax'))
</span><span style="color: rgb(0, 0, 0); font-family: SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", Courier, monospace; font-size: 12px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: pre; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;"></span></font></p>
    </blockquote>
    <div class="moz-cite-prefix">Not sure if that will map to sklearn.</div>
    <div class="moz-cite-prefix"><br>
    </div>
    <div class="moz-cite-prefix">Bill</div>
    <div class="moz-cite-prefix"><br>
    </div>
    <div class="moz-cite-prefix">On 2/9/20 12:21 PM, Paul Chike Ofoche
      via scikit-learn wrote:<br>
    </div>
    <blockquote type="cite"
      cite="mid:2075352869.868953.1581279707668@mail.yahoo.com">
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            <p style="color: rgb(0, 0, 0); font-size: 11pt; line-height:
              107%; margin: 0in 0in 8pt; text-align: justify;"><span
                style="border-color: currentcolor; border-style: none;
                border-width: 0px; color: inherit; font-family: inherit;
                font-size: 12pt; font-stretch: inherit; font-style:
                inherit; font-weight: inherit; line-height: inherit;
                margin: 0px; padding: 0px; vertical-align: baseline;">Hello
                all,</span></p>
            <span style="color: inherit; font-style: inherit;
              font-weight: inherit; font-stretch: inherit; font-size:
              inherit; line-height: inherit; font-family: inherit;">
            </span>
            <p style="color: rgb(0, 0, 0); font-size: 11pt; line-height:
              107%; margin: 0in 0in 8pt; text-align: justify;">
              <span style="border-color: currentcolor; border-style:
                none; border-width: 0px; color: inherit; font-family:
                inherit; font-size: 12pt; font-stretch: inherit;
                font-style: inherit; font-weight: inherit; line-height:
                inherit; margin: 0px; padding: 0px; vertical-align:
                baseline;">My name is Paul and I am enthused about data
                science. I have been using Python and other programming
                languages for close to two years. There is an issue that
                I have been facing since I began applying Python to the
                analysis of my research work.</span></p>
            <span style="color: inherit; font-style: inherit;
              font-weight: inherit; font-stretch: inherit; font-size:
              inherit; line-height: inherit; font-family: inherit;">
            </span>
            <p style="color: rgb(0, 0, 0); font-size: 11pt; line-height:
              107%; margin: 0in 0in 8pt; text-align: justify;">
              <span style="border-color: currentcolor; border-style:
                none; border-width: 0px; color: inherit; font-family:
                inherit; font-size: 12pt; font-stretch: inherit;
                font-style: inherit; font-weight: inherit; line-height:
                inherit; margin: 0px; padding: 0px; vertical-align:
                baseline;"><br>
              </span></p>
            <span style="color: inherit; font-style: inherit;
              font-weight: inherit; font-stretch: inherit; font-size:
              inherit; line-height: inherit; font-family: inherit;">
            </span>
            <p style="color: rgb(0, 0, 0); font-size: 11pt; line-height:
              107%; margin: 0in 0in 8pt; text-align: justify;">
              <span style="background-attachment: scroll;
                background-image: none; background-size: auto; border:
                0px none currentcolor; color: inherit; font-family:
                inherit; font-size: 12pt; font-stretch: inherit;
                font-style: inherit; font-weight: inherit; line-height:
                inherit; margin: 0px; padding: 0px; vertical-align:
                baseline;">My question has remained unanswered for
                months. Has anybody not run into the need to work with
                data whereby the regression results are a multiple
                output, in which the output parameters are correlated
                with each other? This is called a multi-output
                multivariate problem. A version of random forest that
                handles multiple outputs is referred to as the
                multivariate random forest. It is implemented in the
                programming language, R (see attached reference
                documentation below).</span></p>
            <span style="color: inherit; font-style: inherit;
              font-weight: inherit; font-stretch: inherit; font-size:
              inherit; line-height: inherit; font-family: inherit;">
            </span>
            <p style="color: rgb(0, 0, 0); font-size: 11pt; line-height:
              107%; margin: 0in 0in 8pt; text-align: justify;">
              <span style="border-color: currentcolor; border-style:
                none; border-width: 0px; color: inherit; font-family:
                inherit; font-size: 12pt; font-stretch: inherit;
                font-style: inherit; font-weight: inherit; line-height:
                inherit; margin: 0px; padding: 0px; vertical-align:
                baseline;"><br>
                <span style="background-attachment: scroll;
                  background-image: none; background-size: auto; border:
                  0px none currentcolor; color: inherit; font-style:
                  inherit; font-weight: inherit; font-stretch: inherit;
                  font-size: inherit; line-height: inherit; font-family:
                  inherit; margin: 0px; padding: 0px; vertical-align:
                  baseline;"><span style="border-color: currentcolor;
                    border-style: none; border-width: 0px; color:
                    inherit; font-family: inherit; font-size: inherit;
                    font-stretch: inherit; font-style: inherit;
                    font-weight: inherit; line-height: inherit; margin:
                    0px; padding: 0px; vertical-align: baseline;">Till
                    date, there exists no such package in Python. My
                    question is whether anybody knows how to go about
                    implementing this. The random forest univariate
                    regression case utilizes the Euclidean distance as
                    the measurement criteria, whereas the multivariate
                    regression case uses the Mahalanobis distance, which
                    takes into account the inter-relationships between
                    the multiple outputs. I have inquired about an
                    equivalent capability in Python for many years, but
                    it has still not been addressed. Such a multivariate
                    random forest mode is very applicable to the type of
                    research and analysis that I do. Could someone help,
                    please?
                  </span></span></span></p>
            <span style="color: inherit; font-style: inherit;
              font-weight: inherit; font-stretch: inherit; font-size:
              inherit; line-height: inherit; font-family: inherit;">
            </span>
            <p style="color: rgb(0, 0, 0); font-size: 11pt; line-height:
              107%; margin: 0in 0in 8pt; text-align: justify;">
              <span style="background-attachment: scroll;
                background-image: none; background-size: auto; border:
                0px none currentcolor; color: inherit; font-family:
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                font-style: inherit; font-weight: inherit; line-height:
                inherit; margin: 0px; padding: 0px; vertical-align:
                baseline;">Thank you,</span></p>
            <span style="color: inherit; font-style: inherit;
              font-weight: inherit; font-stretch: inherit; font-size:
              inherit; line-height: inherit; font-family: inherit;">
            </span>
            <p style="color: rgb(0, 0, 0); font-size: 11pt; line-height:
              107%; margin: 0in 0in 8pt; text-align: justify;">
              <span style="background-attachment: scroll;
                background-image: none; background-size: auto; border:
                0px none currentcolor; color: inherit; font-family:
                inherit; font-size: 12pt; font-stretch: inherit;
                font-style: inherit; font-weight: inherit; line-height:
                inherit; margin: 0px; padding: 0px; vertical-align:
                baseline;">Paul Ofoche</span></p>
            <span style="color: inherit; font-style: inherit;
              font-weight: inherit; font-stretch: inherit; font-size:
              inherit; line-height: inherit; font-family: inherit;">
            </span>
            <p style="color: rgb(0, 0, 0); font-size: 11pt; line-height:
              107%; margin: 0in 0in 8pt; text-align: justify;">
              <span style="background-attachment: scroll;
                background-image: none; background-size: auto; border:
                0px none currentcolor; color: inherit; font-family:
                inherit; font-size: 12pt; font-stretch: inherit;
                font-style: inherit; font-weight: inherit; line-height:
                inherit; margin: 0px; padding: 0px; vertical-align:
                baseline;"> </span></p>
            <span style="color: inherit; font-style: inherit;
              font-weight: inherit; font-stretch: inherit; font-size:
              inherit; line-height: inherit; font-family: inherit;">
            </span>
            <p style="color: rgb(0, 0, 0); font-size: 11pt; line-height:
              107%; margin: 0in 0in 8pt; text-align: justify;">
              <span style="background-attachment: scroll;
                background-image: none; background-size: auto; border:
                0px none currentcolor; color: inherit; font-family:
                inherit; font-size: 12pt; font-stretch: inherit;
                font-style: inherit; font-weight: inherit; line-height:
                inherit; margin: 0px; padding: 0px; vertical-align:
                baseline;">PS: This is an important need for
                multivariate output analysis as a technique to solving
                practical research problems. Here are some posted
                questions by various other Python users concerning this
                same issue.</span></p>
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              107%; margin: 0in 0in 8pt; text-align: justify;">
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                baseline;"> </span></p>
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              107%; margin: 0in 0in 8pt; text-align: justify;">
              <a
href="https://datascience.stackexchange.com/questions/21637/code-for-multivariate-random-forest-in-python-r"
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                padding: 0px; vertical-align: baseline;"
                data-auth="NotApplicable" rel="nofollow" target="_blank"
                moz-do-not-send="true"><b><span style="border-color:
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                    font-weight: inherit; line-height: normal; margin:
                    0px; padding: 0in; vertical-align: baseline;">https://datascience.stackexchange.com/questions/21637/code-for-multivariate-random-forest-in-python-r</span></b></a></p>
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              <a
href="https://stackoverflow.com/questions/49391637/multi-output-regression"
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                data-auth="NotApplicable" rel="nofollow" target="_blank"
                class="enhancr_card_1438705237" moz-do-not-send="true">Multi-output
                regression</a></p>
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                                </table>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <table class="ydpd279c0a0card-info
                                  ydpd279c0a0yahoo-ignore-table"
style="background:#fff;position:relative;z-index:2;width:100%;max-width:400px;border-radius:0
                                  0 2px 2px;border-top:1px solid
                                  rgb(224, 228, 233)" cellspacing="0"
                                  cellpadding="0" border="0"
                                  align="center">
                                  <tbody>
                                    <tr>
                                      <td
                                        style="background-color:#ffffff;padding:16px
                                        0 16px
                                        12px;vertical-align:top;border-radius:0
                                        0 0 2px"><br>
                                      </td>
                                      <td
                                        style="vertical-align:middle;padding:12px
                                        24px 16px
                                        12px;width:99%;font-family:"Helvetica
                                        Neue", "Segoe
                                        UI", Helvetica, Arial,
                                        sans-serif;border-radius:0 0 2px
                                        0">
                                        <h2
                                          class="ydpd279c0a0card-title"
                                          style="font-size: 14px;
                                          line-height: 19px; margin: 0px
                                          0px 6px; font-family:
                                          "Helvetica Neue",
                                          "Segoe UI",
                                          Helvetica, Arial, sans-serif;
                                          color: rgb(38, 40, 42);">Multi-output
                                          regression</h2>
                                        <p
                                          class="ydpd279c0a0card-description"
                                          style="font-size: 12px;
                                          line-height: 16px; margin:
                                          0px; color: rgb(151, 155,
                                          167);">I have been looking in
                                          to Multi-output regression the
                                          last view weeks. I am working
                                          with the scikit learn
                                          packag...</p>
                                      </td>
                                    </tr>
                                  </tbody>
                                </table>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </td>
                    </tr>
                  </tbody>
                </table>
              </a></div>
            <div><br>
            </div>
            <div><br>
            </div>
          </div>
          <br>
        </div>
      </div>
      <br>
      <fieldset class="mimeAttachmentHeader"></fieldset>
      <pre class="moz-quote-pre" wrap="">_______________________________________________
scikit-learn mailing list
<a class="moz-txt-link-abbreviated" href="mailto:scikit-learn@python.org">scikit-learn@python.org</a>
<a class="moz-txt-link-freetext" href="https://mail.python.org/mailman/listinfo/scikit-learn">https://mail.python.org/mailman/listinfo/scikit-learn</a>
</pre>
    </blockquote>
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