What loss function to use when labels are probabilities?





.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ margin-bottom:0;
}







1












$begingroup$


What loss function is most appropriate when training a model with target values that are probabilities? For example, I have a 3-output model with x=[some features] and y=[0.2, 0.3, 0.5].



It seems like something like cross-entropy doesn't make sense here since it assumes that a single target is the correct label.



Would something like MSE (after applying softmax) make sense, or is there a better loss function?






neural-networks loss-functions probability-distribution







share|improve this question







New contributor




Thomas Johnson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$



















    1












    $begingroup$


    What loss function is most appropriate when training a model with target values that are probabilities? For example, I have a 3-output model with x=[some features] and y=[0.2, 0.3, 0.5].



    It seems like something like cross-entropy doesn't make sense here since it assumes that a single target is the correct label.



    Would something like MSE (after applying softmax) make sense, or is there a better loss function?






    neural-networks loss-functions probability-distribution







    share|improve this question







    New contributor




    Thomas Johnson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.







    $endgroup$















      1












      1








      1





      $begingroup$


      What loss function is most appropriate when training a model with target values that are probabilities? For example, I have a 3-output model with x=[some features] and y=[0.2, 0.3, 0.5].



      It seems like something like cross-entropy doesn't make sense here since it assumes that a single target is the correct label.



      Would something like MSE (after applying softmax) make sense, or is there a better loss function?






      neural-networks loss-functions probability-distribution







      share|improve this question







      New contributor




      Thomas Johnson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.







      $endgroup$




      What loss function is most appropriate when training a model with target values that are probabilities? For example, I have a 3-output model with x=[some features] and y=[0.2, 0.3, 0.5].



      It seems like something like cross-entropy doesn't make sense here since it assumes that a single target is the correct label.



      Would something like MSE (after applying softmax) make sense, or is there a better loss function?






      neural-networks loss-functions probability-distribution




      neural-networks loss-functions probability-distribution






      share|improve this question







      New contributor




      Thomas Johnson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      share|improve this question







      New contributor




      Thomas Johnson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      share|improve this question




      share|improve this question






      New contributor




      Thomas Johnson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      asked 5 hours ago









      Thomas JohnsonThomas Johnson

      1083




      1083




      New contributor




      Thomas Johnson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.





      New contributor





      Thomas Johnson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.






      Thomas Johnson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.






















          1 Answer
          1






          active

          oldest

          votes


















          1












          $begingroup$

          Actually, the cross-entropy loss function would be appropriate here, since it measures the "distance" between a distribution $q$ and the "true" distribution $p$.



          You are right, though, that using a loss function called "cross_entropy" in many APIs would be a mistake. This is because these functions, as you said, assume a one-hot label. You would need to use the general cross-entropy function,



          $$H(p,q)=-sum_{xin X} p(x) log q(x).$$
          $ $



          Note that one-hot labels would mean that
          $$
          p(x) =
          begin{cases}
          1 & text{if }x text{ is the true label}\
          0 & text{otherwise}
          end{cases}$$



          which causes the cross-entropy $H(p,q)$ to reduce to the form you're familiar with:



          $$H(p,q) = -log q(x_{label})$$






          share|improve this answer









          $endgroup$














            Your Answer








            StackExchange.ready(function() {
            var channelOptions = {
            tags: "".split(" "),
            id: "658"
            };
            initTagRenderer("".split(" "), "".split(" "), channelOptions);

            StackExchange.using("externalEditor", function() {
            // Have to fire editor after snippets, if snippets enabled
            if (StackExchange.settings.snippets.snippetsEnabled) {
            StackExchange.using("snippets", function() {
            createEditor();
            });
            }
            else {
            createEditor();
            }
            });

            function createEditor() {
            StackExchange.prepareEditor({
            heartbeatType: 'answer',
            autoActivateHeartbeat: false,
            convertImagesToLinks: false,
            noModals: true,
            showLowRepImageUploadWarning: true,
            reputationToPostImages: null,
            bindNavPrevention: true,
            postfix: "",
            imageUploader: {
            brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
            contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
            allowUrls: true
            },
            noCode: true, onDemand: true,
            discardSelector: ".discard-answer"
            ,immediatelyShowMarkdownHelp:true
            });


            }
            });






            Thomas Johnson is a new contributor. Be nice, and check out our Code of Conduct.










            draft saved

            draft discarded


















            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fai.stackexchange.com%2fquestions%2f11816%2fwhat-loss-function-to-use-when-labels-are-probabilities%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown

























            1 Answer
            1






            active

            oldest

            votes








            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            1












            $begingroup$

            Actually, the cross-entropy loss function would be appropriate here, since it measures the "distance" between a distribution $q$ and the "true" distribution $p$.



            You are right, though, that using a loss function called "cross_entropy" in many APIs would be a mistake. This is because these functions, as you said, assume a one-hot label. You would need to use the general cross-entropy function,



            $$H(p,q)=-sum_{xin X} p(x) log q(x).$$
            $ $



            Note that one-hot labels would mean that
            $$
            p(x) =
            begin{cases}
            1 & text{if }x text{ is the true label}\
            0 & text{otherwise}
            end{cases}$$



            which causes the cross-entropy $H(p,q)$ to reduce to the form you're familiar with:



            $$H(p,q) = -log q(x_{label})$$






            share|improve this answer









            $endgroup$


















              1












              $begingroup$

              Actually, the cross-entropy loss function would be appropriate here, since it measures the "distance" between a distribution $q$ and the "true" distribution $p$.



              You are right, though, that using a loss function called "cross_entropy" in many APIs would be a mistake. This is because these functions, as you said, assume a one-hot label. You would need to use the general cross-entropy function,



              $$H(p,q)=-sum_{xin X} p(x) log q(x).$$
              $ $



              Note that one-hot labels would mean that
              $$
              p(x) =
              begin{cases}
              1 & text{if }x text{ is the true label}\
              0 & text{otherwise}
              end{cases}$$



              which causes the cross-entropy $H(p,q)$ to reduce to the form you're familiar with:



              $$H(p,q) = -log q(x_{label})$$






              share|improve this answer









              $endgroup$
















                1












                1








                1





                $begingroup$

                Actually, the cross-entropy loss function would be appropriate here, since it measures the "distance" between a distribution $q$ and the "true" distribution $p$.



                You are right, though, that using a loss function called "cross_entropy" in many APIs would be a mistake. This is because these functions, as you said, assume a one-hot label. You would need to use the general cross-entropy function,



                $$H(p,q)=-sum_{xin X} p(x) log q(x).$$
                $ $



                Note that one-hot labels would mean that
                $$
                p(x) =
                begin{cases}
                1 & text{if }x text{ is the true label}\
                0 & text{otherwise}
                end{cases}$$



                which causes the cross-entropy $H(p,q)$ to reduce to the form you're familiar with:



                $$H(p,q) = -log q(x_{label})$$






                share|improve this answer









                $endgroup$



                Actually, the cross-entropy loss function would be appropriate here, since it measures the "distance" between a distribution $q$ and the "true" distribution $p$.



                You are right, though, that using a loss function called "cross_entropy" in many APIs would be a mistake. This is because these functions, as you said, assume a one-hot label. You would need to use the general cross-entropy function,



                $$H(p,q)=-sum_{xin X} p(x) log q(x).$$
                $ $



                Note that one-hot labels would mean that
                $$
                p(x) =
                begin{cases}
                1 & text{if }x text{ is the true label}\
                0 & text{otherwise}
                end{cases}$$



                which causes the cross-entropy $H(p,q)$ to reduce to the form you're familiar with:



                $$H(p,q) = -log q(x_{label})$$







                share|improve this answer












                share|improve this answer



                share|improve this answer










                answered 5 hours ago









                Philip RaeisghasemPhilip Raeisghasem

                963119




                963119






















                    Thomas Johnson is a new contributor. Be nice, and check out our Code of Conduct.










                    draft saved

                    draft discarded


















                    Thomas Johnson is a new contributor. Be nice, and check out our Code of Conduct.













                    Thomas Johnson is a new contributor. Be nice, and check out our Code of Conduct.












                    Thomas Johnson is a new contributor. Be nice, and check out our Code of Conduct.
















                    Thanks for contributing an answer to Artificial Intelligence Stack Exchange!


                    • Please be sure to answer the question. Provide details and share your research!

                    But avoid …



                    • Asking for help, clarification, or responding to other answers.

                    • Making statements based on opinion; back them up with references or personal experience.


                    Use MathJax to format equations. MathJax reference.


                    To learn more, see our tips on writing great answers.




                    draft saved


                    draft discarded














                    StackExchange.ready(
                    function () {
                    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fai.stackexchange.com%2fquestions%2f11816%2fwhat-loss-function-to-use-when-labels-are-probabilities%23new-answer', 'question_page');
                    }
                    );

                    Post as a guest















                    Required, but never shown





















































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown

































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown







                    -

                    Popular posts from this blog

                    How to label and detect the document text images

                    Image
                    1 $begingroup$ This is what I mean as document text image: I want to label the texts in image as separate blocks and my model should detect these labels as classes. NOTE: This is how the end result should be like: The labels like Block 1, Block 2, Block 3,.. should be Logo, Title, Date,.. Others, etc. Work done: First approach : I tried to implement this method via Object Detection, it didn't work. It didn't even detect any text. Second approach : Then I tried it using PixelLink. As this model is build for scene text detection, it detected each and every text in the image. But this method can detect multiple lines of text if the threshold values are increased. But I have no idea how do I add labels to the text blocks. PIXEL_CLS_WEIGHT_all_ones = 'PIXEL_CLS_WEIGHT_all_ones' PIXEL_C...
                    Read more

                    Vallis Paradisi

                    Image
                    Coordinata: .mw-parser-output .geo-default,.mw-parser-output .geo-dms,.mw-parser-output .geo-dec{display:inline}.mw-parser-output .geo-nondefault,.mw-parser-output .geo-multi-punct{display:none}.mw-parser-output .longitude,.mw-parser-output .latitude{white-space:nowrap} 33°03′S 71°37′W  /  33.05°S 71.617°W  / -33.05; -71.617 Vallis Paradisi Res apud Vicidata repertae: Civitas : Chilia Numerus incolarum : 296 655 Zona horaria : UTC-4 Situs interretialis Nomen officiale : Valparaíso Gubernium Consilium : municipal council of Valparaíso Geographia Superficies : 401 600 000 Metrum quadratum Coniunctiones urbium Urbes gemellae : Ovetum , Badalona , Santa Fe , Ora longa , Sciamhaevum , Quantunia , Callao , Bat Yam , Melaka , Novorossiysk , Busan , Corduba , Odessa , Rosario , Malacca , Barcino , Soteropolis , Franciscopolis (California) , Guanajuato, Silao Tabula aut despectus Despectus in portum sinumque et urbem Vallis Paradisi Vallis Para...
                    Read more

                    Tabula Rosettana

                    Image
                    Tabula multilinguis Rosettana in Museo Britannico ostenditur. Tabula Rosettana, [1] etiam titulo OGIS 90 agnita, est stela decreto de rebus sacris in Aegypto anno 196 a.C.n. lato inscripta. Tabula iuxta Rosettam Aegypti, urbem in delta Nili et ad oram maris Mediterranei iacentem, anno 1799 a milite Francico reperta est. Inventio stelae, linguis duabus scripturisque tribus inscriptae, eruditis Instituti Aegypti statim nuntiata est; ibi enim iussu imperatoris Napoleonis eruditi omnium scientiarum (sub aegide Commissionis Scientiarum et Artium) properaverant cum expeditione Francica. Qua a Britannis mox debellata, tabula Rosettana Londinium missa hodie apud Museum Britannicum iacet. Textus Graecus cito lectus interpretationi textuum Aegyptiorum (in formis hieroglyphica et demotica expressorum) gradatim adiuvit. Denique textum plene interpretatus est Ioannes Franciscus Champollion. Ab opere eruditorum cumulativo coepit hodiernus scripturae hieroglyphicae linguaeque Aegyptiae a...
                    Read more