Bayesian　estimation　of　parameters　in　the　Dirichlet　mixture　process　of　the　Beta-Liouville　distribution　(i.e.,　the　infinite　Beta-Liouville　mixture　model)　has　recently　gained　considerable　attention　due　to　its　modeling　capability　for　proportional　data.　However,　applying　the　conventional　variational　inference　(VI)　framework　cannot　derive　an　analytically　tractable　solution　since　the　variational　objective　function　cannot　be　explicitly　calculated.　In　this　paper,　we　adopt　the　recently　proposed　extended　VI　framework　to　derive　the　closed-form　solution　by　further　lower　bounding　the　original　variational　objective　function　in　the　VI　framework.　This　method　is　capable　of　simultaneously　determining　the　model＇s　complexity　and　estimating　the　model＇s　parameters.　Moreover,　due　to　the　nature　of　Bayesian　nonparametric　approaches,　it　can　also　avoid　the　problems　of　underfitting　and　overfitting.　Extensive　experiments　were　conducted　on　both　synthetic　and　real　data,　generated　from　two　real-world　challenging　applications,　namely,　object　detection　and　text　categorization,　and　its　superior　performance　and　effectiveness　of　the　proposed　method　have　been　demonstrated.　©　2021　Wiley　Periodicals　LLC.