{"id":200,"date":"2023-06-09T11:27:09","date_gmt":"2023-06-09T03:27:09","guid":{"rendered":"http:\/\/106.52.213.145:21080\/?p=200"},"modified":"2023-06-10T04:02:59","modified_gmt":"2023-06-09T20:02:59","slug":"200","status":"publish","type":"post","link":"https:\/\/apifj.com\/index.php\/2023\/06\/09\/200\/","title":{"rendered":"[\u5b66\u4e60\u7b14\u8bb0]BPR \uff08Bayesian Personalized Ranking\uff09\u63a8\u8350\u7b97\u6cd5"},"content":{"rendered":"<h2>BPR \u4ecb\u7ecd<\/h2>\n<p>BPR\uff08Bayesian Personalized Ranking\uff09\u8d1d\u53f6\u65af\u4e2a\u6027\u5316\u6392\u5e8f\u662f\u4e00\u79cd\u7528\u4e8e\u534f\u540c\u8fc7\u6ee4\u63a8\u8350\u7b97\u6cd5\u7684\u6a21\u578b\uff0c\u5b83\u901a\u8fc7\u6700\u5927\u5316\u7528\u6237\u9879\u5bf9\u4e4b\u95f4\u7684\u6392\u540d\u987a\u5e8f\u7684\u6982\u7387\u6765\u8fdb\u884c\u8bad\u7ec3\u3002<\/p>\n<p>\u5bf9\u4e8e\u6211\u4eec\u4e4b\u524d\u7684\u77e9\u9635\u5206\u89e3MF\uff0c\u76f4\u63a5\u5c06\u7528\u6237\u6ca1\u6709\u770b\u8fc7\u7684\u4e1c\u897f\u4e0e\u4e0d\u559c\u6b22\u7684\u4e1c\u897f\u76f4\u63a5\u8bbe\u5b9a\u4e3a\u201c0\u201d\u5143\u7d20\uff0c\u5e76\u5c06\u8fd9\u4e2a0\u5143\u7d20\u4e0e\u6b63\u5e38\u7684\u8bc4\u5206\u505aMSE\uff0c\u8fd9\u6837\u4e0d\u80fd\u5f88\u597d\u7684\u4f53\u73b0\u51fa\u7528\u6237\u6240\u559c\u6b22\u7684\u5143\u7d20\u3002\u800c\u8d1d\u53f6\u65af\u4e2a\u6027\u5316\u6392\u5e8f\u662f\u9884\u6d4b\u4e00\u4e2a\u6392\u5e8f\u7684\u987a\u5e8f\uff0c\u800c\u4e0d\u662f\u9884\u6d4b\u8bc4\u5206\uff0c\u4f20\u7edf\u7684MF\u7b97\u6cd5\u901a\u5e38\u5c06\u96f6\u5143\u7d20\u89c6\u4e3a\u7f3a\u5931\u503c\u6216\u65e0\u5174\u8da3\uff0c\u65e0\u6cd5\u533a\u5206\u7528\u6237\u5bf9\u7269\u54c1\u7684\u559c\u597d\u7a0b\u5ea6\u3002<\/p>\n<p>\u5bf9\u6bd4MF\uff0cBPR\u6709\u5982\u4e0b\u4f18\u70b9\uff1a<\/p>\n<ol>\n<li>\n<p>\u6392\u5e8f\u76ee\u6807\uff1aBPR\u7b97\u6cd5\u7684\u76ee\u6807\u662f\u76f4\u63a5\u8fdb\u884c\u7269\u54c1\u7684\u76f8\u5bf9\u6392\u5e8f\uff0c\u800c\u4e0d\u662f\u9884\u6d4b\u5177\u4f53\u7684\u8bc4\u5206\u3002\u8fd9\u4f7f\u5f97BPR\u7b97\u6cd5\u66f4\u52a0\u9002\u5408\u4e8e\u9690\u5f0f\u53cd\u9988\u6570\u636e\u7684\u63a8\u8350\u4efb\u52a1\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u4f20\u7edf\u7684MF\u7b97\u6cd5\u4e3b\u8981\u7528\u4e8e\u9884\u6d4b\u7528\u6237\u5bf9\u7269\u54c1\u7684\u8bc4\u5206\uff0c\u5bf9\u4e8e\u9690\u5f0f\u53cd\u9988\u6570\u636e\u7684\u5904\u7406\u76f8\u5bf9\u4e0d\u8db3\u3002<\/p>\n<\/li>\n<li>\n<p>\u91c7\u6837\u7b56\u7565\uff1aBPR\u7b97\u6cd5\u91c7\u7528\u4e86\u8d1f\u91c7\u6837\u7684\u7b56\u7565\uff0c\u901a\u8fc7\u6784\u5efa\u7528\u6237\u5bf9\u672a\u89c2\u5bdf\u5230\u7269\u54c1\u7684\u504f\u597d\u5bf9\u6765\u8bad\u7ec3\u6a21\u578b\u3002\u8fd9\u79cd\u91c7\u6837\u7b56\u7565\u907f\u514d\u4e86\u76f4\u63a5\u4f7f\u7528\u96f6\u5143\u7d20\u7684\u95ee\u9898\uff0c\u80fd\u591f\u66f4\u597d\u5730\u5229\u7528\u9690\u5f0f\u53cd\u9988\u6570\u636e\u4e2d\u7684\u6b63\u6837\u672c\u3002\u800c\u4f20\u7edf\u7684MF\u7b97\u6cd5\u901a\u5e38\u5c06\u96f6\u5143\u7d20\u89c6\u4e3a\u7f3a\u5931\u503c\u6216\u65e0\u5174\u8da3\uff0c\u65e0\u6cd5\u533a\u5206\u7528\u6237\u5bf9\u7269\u54c1\u7684\u559c\u597d\u7a0b\u5ea6\u3002<\/p>\n<\/li>\n<li>\n<p>\u635f\u5931\u51fd\u6570\uff1aBPR\u7b97\u6cd5\u4f7f\u7528\u4e86\u57fa\u4e8e\u6392\u540d\u7684\u635f\u5931\u51fd\u6570\uff0c\u5373\u91c7\u7528\u4e86Pairwise Ranking Loss\uff0c\u76ee\u6807\u662f\u6700\u5927\u5316\u6b63\u786e\u7684\u504f\u597d\u5bf9\u7684\u76f8\u5bf9\u6392\u5e8f\u6982\u7387\uff0c\u4ece\u800c\u4f7f\u5f97\u6b63\u786e\u7684\u7269\u54c1\u5728\u6392\u5e8f\u4e2d\u6392\u5728\u8d1f\u6837\u672c\u4e4b\u524d\u3002\u8fd9\u6837\u7684\u635f\u5931\u51fd\u6570\u66f4\u52a0\u7b26\u5408\u63a8\u8350\u7cfb\u7edf\u4e2d\u7684\u6392\u5e8f\u76ee\u6807\uff0c\u80fd\u591f\u66f4\u597d\u5730\u5b66\u4e60\u5230\u7528\u6237\u7684\u504f\u597d\u548c\u6392\u5e8f\u89c4\u5219\u3002<\/p>\n<\/li>\n<\/ol>\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th>BPR<\/th>\n<th>MF<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u5b9e\u73b0\u65b9\u5f0f<\/td>\n<td>\u901a\u8fc7\u6700\u5927\u5316Pairwise Ranking Loss\u8bad\u7ec3\u6a21\u578b<\/td>\n<td>\u901a\u8fc7\u6700\u5c0f\u5316\u8bc4\u5206\u9884\u6d4b\u4e0e\u771f\u5b9e\u8bc4\u5206\u4e4b\u95f4\u7684\u5dee\u8ddd\u6765\u8bad\u7ec3\u6a21\u578b<\/td>\n<\/tr>\n<tr>\n<td>\u76ee\u6807<\/td>\n<td>\u7269\u54c1\u7684\u76f8\u5bf9\u6392\u5e8f<\/td>\n<td>\u7528\u6237\u5bf9\u7269\u54c1\u7684\u8bc4\u5206\u9884\u6d4b<\/td>\n<\/tr>\n<tr>\n<td>\u4f18\u5316\u76ee\u6807<\/td>\n<td>\u6700\u5927\u5316\u6b63\u786e\u7684\u504f\u597d\u5bf9\u7684\u76f8\u5bf9\u6392\u5e8f\u6982\u7387<\/td>\n<td>\u9884\u6d4b\u7528\u6237\u5bf9\u7269\u54c1\u7684\u8bc4\u5206<\/td>\n<\/tr>\n<tr>\n<td>\u6570\u636e\u5904\u7406<\/td>\n<td>\u7269\u54c1\u7684\u76f8\u5bf9\u6392\u5e8f<\/td>\n<td>\u5c06\u96f6\u5143\u7d20\u89c6\u4e3a\u7f3a\u5931\u503c\u6216\u65e0\u5174\u8da3<\/td>\n<\/tr>\n<tr>\n<td>\u91c7\u6837\u7b56\u7565<\/td>\n<td>\u8d1f\u91c7\u6837<\/td>\n<td>\u65e0\u91c7\u6837<\/td>\n<\/tr>\n<tr>\n<td>\u635f\u5931\u51fd\u6570<\/td>\n<td>Pairwise Ranking Loss<\/td>\n<td>\u5747\u65b9\u5dee\u635f\u5931\u6216\u4ea4\u53c9\u71b5\u635f\u5931\u7b49<\/td>\n<\/tr>\n<tr>\n<td>\u6a21\u578b\u53c2\u6570\u521d\u59cb\u5316<\/td>\n<td>\u968f\u673a\u521d\u59cb\u5316<\/td>\n<td>\u968f\u673a\u521d\u59cb\u5316<\/td>\n<\/tr>\n<tr>\n<td>\u9884\u6d4b\u8bc4\u5206<\/td>\n<td>\u4e0d\u9884\u6d4b\u5177\u4f53\u8bc4\u5206<\/td>\n<td>\u9884\u6d4b\u7528\u6237\u5bf9\u7269\u54c1\u7684\u8bc4\u5206<\/td>\n<\/tr>\n<tr>\n<td>\u63a8\u8350\u7ed3\u679c<\/td>\n<td>\u76f8\u5bf9\u6392\u5e8f\u7684\u7269\u54c1\u5217\u8868<\/td>\n<td>\u9884\u6d4b\u8bc4\u5206\u9ad8\u7684\u7269\u54c1\u5217\u8868<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u5411\u524d\u4f20\u64ad<\/h2>\n<p>\u5047\u8bbe\u6709\u4e00\u4e2a\u7528\u6237\u96c6\u5408U\u3001\u7269\u54c1\u96c6\u5408I\u548c\u4e00\u4e2a\u4e8c\u8fdb\u5236\u7684\u7528\u6237-\u7269\u54c1\u4ea4\u4e92\u77e9\u9635R\uff0c\u5176\u4e2dR(u, i)\u8868\u793a\u7528\u6237u\u662f\u5426\u4e0e\u7269\u54c1i\u6709\u8fc7\u4ea4\u4e92\u3002BPR\u7b97\u6cd5\u7684\u76ee\u6807\u662f\u5b66\u4e60\u4e00\u4e2a\u7528\u6237\u5411\u91cf\u548c\u4e00\u4e2a\u7269\u54c1\u5411\u91cf\u7684\u8868\u793a\uff0c\u4ee5\u4fbf\u5728\u672a\u89c2\u5bdf\u5230\u7684\u7528\u6237-\u7269\u54c1\u5bf9\u4e0a\u8fdb\u884c\u9884\u6d4b\u3002<\/p>\n<ol>\n<li>\u521d\u59cb\u5316\u53c2\u6570\uff1a\n<ul>\n<li>\u5b66\u4e60\u7387\uff08learning rate\uff09\uff1a<code class=\"katex-inline\">\\alpha<\/code><\/li>\n<li>\u6b63\u5219\u5316\u53c2\u6570\uff08regularization parameter\uff09\uff1a<code class=\"katex-inline\">\\lambda<\/code><\/li>\n<li>\u7528\u6237\u5411\u91cf\u96c6\u5408\uff1a<code class=\"katex-inline\">U = {u_1, u_2, ..., u_m}<\/code><\/li>\n<li>\u7269\u54c1\u5411\u91cf\u96c6\u5408\uff1a<code class=\"katex-inline\">V = {v_1, v_2, ..., v_n}<\/code><\/li>\n<\/ul>\n<\/li>\n<li>\u5bf9\u4e8e\u6bcf\u4e2a\u8bad\u7ec3\u6837\u672c<code class=\"katex-inline\">(u, i, j)<\/code>\uff0c\u5176\u4e2d<code class=\"katex-inline\">u<\/code>\u662f\u7528\u6237\u7279\u5f81\u5411\u91cf\uff0c<code class=\"katex-inline\">i<\/code>\u662f\u7528\u6237u\u4ea4\u4e92\u8fc7\u7684\u7269\u54c1\uff08\u6b63\u6837\u672c\uff09\u7279\u5f81\u5411\u91cf\uff0c<code class=\"katex-inline\">j<\/code>\u662f\u7528\u6237u\u672a\u4ea4\u4e92\u8fc7\u7684\u7269\u54c1\uff08\u8d1f\u6837\u672c\uff09\u7279\u5f81\u5411\u91cf\uff1a\n<ul>\n<li>\u8ba1\u7b97\u7528\u6237u\u548c\u7269\u54c1i\u4e4b\u95f4\u7684\u5185\u79ef\uff1a<code class=\"katex-inline\">x_{ui} = \\langle u, i \\rangle<\/code><\/li>\n<li>\u8ba1\u7b97\u7528\u6237u\u548c\u7269\u54c1j\u4e4b\u95f4\u7684\u5185\u79ef\uff1a<code class=\"katex-inline\">x_{uj} = \\langle u, j \\rangle<\/code><\/li>\n<li>\u8ba1\u7b97\u7528\u6237u\u5bf9\u7269\u54c1i\u548c\u7269\u54c1j\u7684\u5dee\u503c\uff1a<code class=\"katex-inline\">x_{uij} = x_{ui} - x_{uj}<\/code><\/li>\n<li>\u8ba1\u7b97\u7528\u6237u\u5bf9\u7269\u54c1i\u548c\u7269\u54c1j\u7684sigmoid\u51fd\u6570\u503c\uff1a<code class=\"katex-inline\">\\sigma(x_{uij}) = \\frac{1}{1 + e^{-x_{uij}}}<\/code><\/li>\n<\/ul>\n<\/li>\n<li>\u8ba1\u7b97BPR\u635f\u5931\u51fd\u6570\uff1a\n<ul>\n<li>\u5bf9\u4e8e\u6bcf\u4e2a\u8bad\u7ec3\u6837\u672c<code class=\"katex-inline\">(u, i, j)<\/code>\uff0c\u8ba1\u7b97\u4ea4\u53c9\u71b5\u635f\u5931\uff1a<code class=\"katex-inline\">loss = -\\log(\\sigma(x_{uij}))<\/code><\/li>\n<li>\u52a0\u4e0a\u6b63\u5219\u5316\u9879\uff1a<code class=\"katex-inline\">loss = loss + \\frac{\\lambda}{2} (\\lVert u \\rVert^2 + \\lVert i \\rVert^2 + \\lVert j \\rVert^2)<\/code><\/li>\n<\/ul>\n<\/li>\n<li>\u66f4\u65b0\u7528\u6237\u548c\u7269\u54c1\u5411\u91cf\uff1a\n<ul>\n<li>\u8ba1\u7b97\u635f\u5931\u51fd\u6570\u5bf9\u7528\u6237\u5411\u91cf<code class=\"katex-inline\">u<\/code>\u7684\u68af\u5ea6\uff1a<code class=\"katex-inline\">\\frac{\\partial loss}{\\partial u} = -\\frac{\\partial \\log(\\sigma(x_{uij}))}{\\partial u} + \\lambda u<\/code><\/li>\n<li>\u8ba1\u7b97\u635f\u5931\u51fd\u6570\u5bf9\u7269\u54c1\u5411\u91cf<code class=\"katex-inline\">i<\/code>\u7684\u68af\u5ea6\uff1a<code class=\"katex-inline\">\\frac{\\partial loss}{\\partial i} = -\\frac{\\partial \\log(\\sigma(x_{uij}))}{\\partial i} + \\lambda i<\/code><\/li>\n<li>\u8ba1\u7b97\u635f\u5931\u51fd\u6570\u5bf9\u7269\u54c1\u5411\u91cf<code class=\"katex-inline\">j<\/code>\u7684\u68af\u5ea6\uff1a<code class=\"katex-inline\">\\frac{\\partial loss}{\\partial j} = -\\frac{\\partial \\log(\\sigma(x_{uij}))}{\\partial j} + \\lambda j<\/code><\/li>\n<li>\u4f7f\u7528\u68af\u5ea6\u4e0b\u964d\u6cd5\u66f4\u65b0\u7528\u6237\u548c\u7269\u54c1\u5411\u91cf\uff1a <code class=\"katex-inline\">u \\leftarrow u - \\alpha \\frac{\\partial loss}{\\partial u}<\/code> <code class=\"katex-inline\">i \\leftarrow i - \\alpha \\frac{\\partial loss}{\\partial i}<\/code> <code class=\"katex-inline\">j \\leftarrow j - \\alpha \\frac{\\partial loss}{\\partial j}<\/code><\/li>\n<\/ul>\n<\/li>\n<li>\u91cd\u590d\u6b65\u9aa42\u52304\uff0c\u76f4\u5230\u6536\u655b\u6216\u8fbe\u5230\u9884\u5b9a\u7684\u8fed\u4ee3\u6b21\u6570\u3002<\/li>\n<\/ol>\n<h2>\u516c\u5f0f\u63a8\u5bfc<\/h2>\n<h3>\u8d1d\u53f6\u65af\u516c\u5f0f<\/h3>\n<p>\u6982\u7387\u8f6e\u91cc\uff0c\u82e5A\u5df2\u7ecf\u53d1\u751f\uff0c\u6267\u679c\u7d22\u56e0\uff0c\u6709<\/p>\n<pre><code class=\"language-katex\">\nP(A_j|B)=\\frac{P(A_jB)}{P(B)}=\\frac{P(A)P(B|A)}{P(B)}\n<\/code><\/pre>\n<p>\u7531\u6b64\uff0c\u6211\u4eec\u5b9a\u4e49<code class=\"katex-inline\">\\theta<\/code>\u662f\u6a21\u578b\u7684\u53c2\u6570\uff0c<code class=\"katex-inline\">>_u<\/code> \u662f\u7528\u6237\u5df2\u7ecf\u6709\u7684\u504f\u597d\uff0c<code class=\"katex-inline\">i>_uj<\/code> \u8868\u793a\u7528\u6237u\u5bf9<code class=\"katex-inline\">i<\/code>\u7684\u559c\u6b22\u7a0b\u5ea6\u5927\u8fc7\u4e8e<code class=\"katex-inline\">j<\/code><\/p>\n<h3>BPR\u516c\u5f0f<\/h3>\n<p><code class=\"katex-inline\">P(\\theta|>_u)<\/code> \u4e3a\u5728\u7528\u6237\u73b0\u5728\u5df2\u6709\u7684\u504f\u597d\u4e0b\uff0c\u53c2\u6570\u4e3a<code class=\"katex-inline\">\\theta<\/code> \u7684\u6982\u7387\u662f\u591a\u5c11\uff0c\u6211\u4eec\u901a\u8fc7\u4e0a\u9762\u8d1d\u53f6\u65af\u516c\u5f0f\u53ef\u5f97\uff1a<\/p>\n<pre><code class=\"language-katex\">\nP(\\theta|&gt;_u)=\\frac{P(\\theta)P(&gt;_u|\\theta)}{P(&gt;_u)}\n<\/code><\/pre>\n<p>\u7531\u4e8e\u4e00\u4e2a\u7528\u6237\u5bf9\u4e8e\u5df2\u7ecf\u6709\u7684\u504f\u597d\u7684\u6982\u7387\u662f\u5e38\u6570\uff0c\u6709<\/p>\n<pre><code class=\"language-katex\">\nP(\\theta|&gt;_u)\\propto P(\\theta)P(&gt;_u|\\theta)\n<\/code><\/pre>\n<p><code class=\"katex-inline\">\\propto<\/code>\u8868\u793a\u6b63\u76f8\u5173\uff0c\u6211\u4eec\u9700\u8981\u6539\u53d8<code class=\"katex-inline\">\\theta<\/code>\u6765\u8ba9<code class=\"katex-inline\">P(\\theta|>_u)<\/code> \u6700\u5927\uff0c\u4e5f\u5c31\u662f\u8bf4\u6211\u4eec\u9700\u8981\u4f18\u5316 <code class=\"katex-inline\">P(\\theta)P(>_u|\\theta)<\/code> \u6765\u8fbe\u5230\u6700\u5927<\/p>\n<p>\u9996\u5148\u662f\u6700\u5927\u5316<code class=\"katex-inline\">P(\\theta)<\/code> ,\u8fd9\u91cc\u7684<code class=\"katex-inline\">\\theta<\/code> \u662f\u6211\u4eec\u8bad\u7ec3\u51fa\u6765\u7684\uff0c\u6211\u4eec\u8bad\u7ec3\u6a21\u578b\u7684\u65f6\u5019\u9700\u8981\u6b63\u5219\u5316\uff0c\u4e5f\u5c31\u662f<code class=\"katex-inline\">\\lambda||\\theta||^2<\/code> ,\u6240\u4ee5\u6211\u4eec\u4ee4<\/p>\n<pre><code class=\"language-katex\">\nln\\ P(\\theta) =\\lambda||\\theta||^2\n<\/code><\/pre>\n<p>\u8fd9\u6837\u6211\u4eec\u540e\u9762\u505a\u635f\u5931\u51fd\u6570\u7684\u65f6\u5019\u5c31\u975e\u5e38\u4e4b\u65b9\u4fbf<\/p>\n<p>\u63a5\u7740\u6211\u4eec\u6700\u5927\u5316<code class=\"katex-inline\">P(>_u|\\theta)<\/code> \uff0c\u6211\u4eec\u5b9a\u4e49<\/p>\n<pre><code class=\"language-katex\">\n\\overline{x}_{ui}=&lt;u,i&gt;=\\sum_{j=1}^k u_ji_j=u_1\u00b7i_1+\u00b7\u00b7\u00b7+u_k\u00b7i_k\n<\/code><\/pre>\n<p>\u8fd9\u91cc&lt;u,i&gt;\u8868\u793a\u5185\u79ef<code class=\"katex-inline\">u,i<\/code> \u662f\u7528\u6237\u7279\u5f81\u77e9\u9635\u4e0e\u56fe\u7247\u77e9\u9635\u4e2dU\u3001I\u7684\u5411\u91cf<\/p>\n<pre><code class=\"language-katex\">\n\\overline{x}_{uij}=\\overline{x}_{ui}-\\overline{x}_{uj}\n<\/code><\/pre>\n<p><code class=\"katex-inline\">\\overline{x}_{uij}<\/code> \u6765\u8868\u793a\u7528\u6237\u7684i\u3001j\u7269\u54c1\u7684\u5173\u7cfb\u8ddd\u79bb\uff0c\u7136\u540e\u63a5\u7740\u6211\u4eec\u901a\u8fc7<code class=\"katex-inline\">\\sigma(x) = sigmoid(x)<\/code>\u5c06\u4ed6\u7684\u5173\u7cfb\u8f6c\u5316\u52300-1\u4e4b\u95f4\uff0c\u4e5f\u5c31\u662f\u5982\u4e0b<\/p>\n<pre><code class=\"language-katex\">\nP(i&gt;_u j|\\theta)=\\sigma(\\overline{x}_{uij}(\\theta))\n<\/code><\/pre>\n<p>\u7531\u4e8e\u7528\u6237\u4e4b\u95f4\u76f8\u4e92\u72ec\u7acb\uff08BPR\u4e0d\u8003\u8651\u7528\u6237\u4e4b\u95f4\u7684\u76f8\u4e92\u5f71\u54cd\uff09\uff0c\u6211\u4eec\u6709<\/p>\n<pre><code class=\"language-katex\">\n\\prod P(i&gt;_uj|\\theta)=\\prod\\sigma(\\overline{x}_{uij}(\\theta))\n<\/code><\/pre>\n<p>\u7efc\u4e0a\uff0c\u6211\u4eec\u6709\u5982\u4e0b\u4f18\u5316\u76ee\u6807<\/p>\n<pre><code class=\"language-katex\">\nBPR-Opt:=lnP(\\theta|&gt;_u) \\\\\n=lnP(&gt;_u|\\theta)P(\\theta) \\\\\n=ln \\prod \\sigma(\\overline{x}_{uij})+lnP(\\theta)\\\\\n=\\sum ln \\sigma(\\overline{x}_{uij})+\\lambda||\\theta||^2\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>BPR \u4ecb\u7ecd BPR\uff08Bayesian Personalized Ranking\uff09\u8d1d\u53f6\u65af\u4e2a\u6027\u5316\u6392\u5e8f\u662f\u4e00\u79cd\u7528\u4e8e\u534f&#8230; &raquo; <a class=\"read-more-link\" href=\"https:\/\/apifj.com\/index.php\/2023\/06\/09\/200\/\">\u9605\u8bfb\u5168\u6587<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,7],"tags":[],"class_list":["post-200","post","type-post","status-publish","format-standard","hentry","category-dl","category-xuexibiji"],"_links":{"self":[{"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/posts\/200","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/comments?post=200"}],"version-history":[{"count":15,"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/posts\/200\/revisions"}],"predecessor-version":[{"id":215,"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/posts\/200\/revisions\/215"}],"wp:attachment":[{"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/media?parent=200"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/categories?post=200"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/tags?post=200"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}