{"id":7403,"date":"2021-03-27T19:58:03","date_gmt":"2021-03-27T10:58:03","guid":{"rendered":"https:\/\/pandanote.info\/?p=7403"},"modified":"2022-08-07T13:01:26","modified_gmt":"2022-08-07T04:01:26","slug":"%e8%a6%81%e7%b4%a0%e3%81%94%e3%81%a8%e3%81%ab%e8%a8%88%e7%ae%97%e3%81%97%e3%81%a6%e7%90%86%e8%a7%a3%e3%81%99%e3%82%8b%e6%ad%a3%e8%a6%8f%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%80%82","status":"publish","type":"post","link":"https:\/\/pandanote.info\/?p=7403","title":{"rendered":"\u8981\u7d20\u3054\u3068\u306b\u8a08\u7b97\u3057\u3066\u7406\u89e3\u3059\u308b\u6b63\u898f\u65b9\u7a0b\u5f0f\u3002"},"content":{"rendered":"<h2>\u306f\u3058\u3081\u306b<\/h2>\n<p>\u6a5f\u68b0\u5b66\u7fd2\u306e\u65b9\u9762\u3067\u306f\u8d85\u304a\u306a\u3058\u307f\u306e\u7dda\u5f62\u56de\u5e30\u5206\u6790\u3067\u3059\u304c\u3001\u7dda\u5f62\u56de\u5e30\u5206\u6790\u3068\u3044\u3048\u3070\u6700\u5c0f\u4e8c\u4e57\u6cd5\u304c\u307b\u307c\u5b9a\u756a\u3067\u3001\u6700\u5c0f\u4e8c\u4e57\u6cd5\u3068\u3044\u3048\u3070\u6b63\u898f\u65b9\u7a0b\u5f0f\u304c\u307b\u307c\u5fc5\u305a\u767b\u5834\u3057\u307e\u3059\u3002<\/p>\n<p>\u3088\u3063\u3066\u6b63\u898f\u65b9\u7a0b\u5f0f\u3082\u8d85\u304a\u306a\u3058\u307f\u306a\u308f\u3051\u3067\u3001\u6b63\u898f\u65b9\u7a0b\u5f0f\u306e\u5c0e\u51fa\u306e\u65b9\u6cd5\u306b\u3064\u3044\u3066Google\u5148\u751f\u306b\u5c0b\u306d\u3066\u307f\u308b\u3068\u3001\u884c\u5217\u3084\u30d9\u30af\u30c8\u30eb\u3092\u99c6\u4f7f\u3057\u307e\u304f\u308b\u65b9\u6cd5\u3084\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u6559\u3048\u3066\u304f\u308c\u307e\u3059\u3002<\/p>\n<p>\u3057\u304b\u3057\u3001\u3053\u306e\u60c5\u5831\u3060\u3051\u3060\u3068\u884c\u5217\u3084\u30d9\u30af\u30c8\u30eb\u306e\u8a08\u7b97\u304b\u3089\u4e00\u5ea6\u96e2\u308c\u3066\u4e00\u5468\u56de\u3063\u3066\u623b\u3063\u3066\u304d\u305f\u6642\u306b\u300c\u306a\u3093\u3067\u305d\u3046\u306a\u308b\u3093\u3060\u3063\u3051?\u300d\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u308a\u304b\u306d\u307e\u305b\u3093\u3002<\/p>\n<p>\u305d\u3053\u3067\u3001\u3053\u306e\u8a18\u4e8b\u3067\u306f\u6700\u5f8c\u306e\u5909\u5f62\u307e\u3067\u306f\u8868\u8a18\u3092\u7c21\u7565\u5316\u3059\u308b\u4ee5\u5916\u306e\u76ee\u7684\u3067\u306f\u884c\u5217\u3084\u30d9\u30af\u30c8\u30eb\u306e\u8a08\u7b97\u3092\u4f7f\u308f\u305a\u306b\u8981\u7d20\u3054\u3068\u306b\u8a08\u7b97\u3057\u3066\u5c0e\u51fa\u3057\u3066\u307f\u308b\u3053\u3068\u306b\u3057\u307e\u3059\u3002<\/p>\n<h2>\u7dda\u5f62\u56de\u5e30\u5206\u6790\u306e\u6982\u8981<\/h2>\n<p>\u7dda\u5f62\u56de\u5e30\u5206\u6790\u3068\u306f\u3001\u3042\u308b$n$\u500b\u304b\u3089\u306a\u308b\u30c7\u30fc\u30bf\u306e\u7d44$\\{x_1, \\cdots, x_n\\}$(\u3053\u308c\u3089\u306e\u6570\u3092\u8aac\u660e\u5909\u6570\u3068\u3044\u3044\u307e\u3059\u3002)\u304c\u3042\u3063\u305f\u3068\u304d\u306b\u6c42\u3081\u3089\u308c\u308b\u5024$y$(\u76ee\u7684\u5909\u6570\u3068\u3044\u3044\u307e\u3059\u3002)\u304c<br \/>\n\\begin{align}<br \/>\ny &#038;= \\sum_{i=1}^{n}a_ix_i \\label{eq:aixi}<br \/>\n\\end{align}<br \/>\n\u3068\u3044\u3046\u95a2\u4fc2\u5f0f\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3082\u306e\u3068\u4eee\u5b9a\u3057\u3001\u3069\u306e\u3088\u3046\u306a\u8aac\u660e\u5909\u6570\u3092\u4e0e\u3048\u3066\u3082\u3042\u308b\u7a0b\u5ea6\u6b63\u78ba\u305d\u3046\u306a\u76ee\u7684\u5909\u6570\u3092\u4e0e\u3048\u3066\u304f\u308c\u305d\u3046\u306a$\\{a_1, \\cdots, a_n\\}$\u306e\u3046\u3061\u6700\u826f\u306e\u3082\u306e\u3092\u6c42\u3081\u308b\u3053\u3068\u3092\u3044\u3044\u307e\u3059\u3002<\/p>\n<h2>\u6700\u5c0f\u4e8c\u4e57\u6cd5\u304b\u3089\u306e\u6b63\u898f\u65b9\u7a0b\u5f0f<\/h2>\n<h3>\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306e\u6982\u8981<\/h3>\n<p>\u3053\u306e\u3042\u308b\u7a0b\u5ea6\u6b63\u78ba\u305d\u3046\u306a\u72b6\u614b\u3092\u5b9a\u91cf\u7684\u306b\u8868\u3059\u305f\u3081\u306b\u3001\u8aac\u660e\u5909\u6570\u53ca\u3073\u76ee\u7684\u5909\u6570\u306e\u7d44\u3092\u7528\u610f\u3057\u307e\u3059\u3002\u3053\u306e\u8a18\u4e8b\u3067\u306f\u4eee\u306b$m$\u7d44\u306e\u8aac\u660e\u5909\u6570\u53ca\u3073$m$\u500b\u306e\u76ee\u7684\u5909\u6570\u304c\u7528\u610f\u3067\u304d\u305f\u3068\u3057\u3066\u3001\u305d\u306e\u3046\u3061\u306e$j$\u756a\u76ee$(1 \\le j \\le m)$\u306e\u8aac\u660e\u5909\u6570\u3092$\\boldsymbol{x}_j = (x_{j,1}, \\cdots, x_{j,n})$\u3068\u304a\u304f\u3053\u3068\u306b\u3057\u3001\u5bfe\u5fdc\u3059\u308b\u76ee\u7684\u5909\u6570\u3092$y_j$\u3068\u304a\u304f\u3053\u3068\u306b\u3057\u307e\u3059\u3002<\/p>\n<p>\u3053\u306e\u3068\u304d\u3001$\\boldsymbol{x}_j$\u304a\u3088\u3073$y_j$\u306e\u9593\u306b\u306f<br \/>\n\\begin{align}<br \/>\ny_j &#038;= \\sum_{i=1}^{n}a_ix_{j,i} \\label{eq:aixireal}<br \/>\n\\end{align}<br \/>\n\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3063\u3066\u6b32\u3057\u3044\u3068\u3053\u308d\u3067\u3059\u304c\u3001\u305d\u3082\u305d\u3082$\\{a_1, \\cdots, a_n\\}$\u306f\u307e\u3060\u6c42\u307e\u3063\u3066\u3044\u306a\u3044\u306e\u3067\u3059\u304b\u3089\u3001(\\ref{eq:aixireal})\u5f0f\u304c\u6210\u308a\u7acb\u3064\u4fdd\u8a3c\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<p>\u305d\u3053\u3067\u3001(\\ref{eq:aixireal})\u5f0f\u306e\u5de6\u8fba\u53ca\u3073\u53f3\u8fba\u306e\u5024\u304c\u4e00\u81f4\u3057\u306a\u3044\u3053\u3068\u3092\u524d\u63d0\u306b\u3001\u5de6\u8fba\u3068\u53f3\u8fba\u306e\u5dee\u3092\u4e8c\u4e57\u3057\u3001\u3055\u3089\u306b\u305d\u308c\u3092$1 \\le j \\le m$\u306e\u7bc4\u56f2\u3067\u8db3\u3057\u5408\u308f\u305b\u3066$m$\u3067\u5272\u3063\u305f\u3082\u306e\u3092$J(a_1, \\cdots, a_n) = J(\\boldsymbol{a})$\u3068\u304a\u304d\u307e\u3059\u3002<\/p>\n<p>\u3059\u308b\u3068\u3001$J(\\boldsymbol{a})$\u306f\u2026<br \/>\n\\begin{align}<br \/>\nJ(\\boldsymbol{a}) &#038;= \\sum_{j=1}^m\\left( y_j\\, &#8211; \\sum_{i=1}^{n}a_ix_{j,i} \\right)^2  \\label{eq:rss}<br \/>\n\\end{align}<br \/>\n\u3068\u66f8\u3051\u307e\u3059\u3002(\\ref{eq:rss})\u5f0f\u306f\u6b8b\u5dee\u5e73\u65b9\u548c(RSS: residual sum of squares)\u3068\u547c\u3070\u308c\u308b\u5f0f\u3067\u3059\u3002<\/p>\n<p>\u307e\u305f\u3001\u3053\u306e\u8a18\u4e8b\u3067\u306f\u76f4\u63a5\u306f\u4f7f\u7528\u3057\u307e\u305b\u3093\u304c\u3001(\\ref{eq:rss})\u5f0f\u306e\u4e21\u8fba\u3092$m$\u3067\u5272\u308b\u3068\u2026<\/p>\n<p>\\begin{align}<br \/>\n\\frac{J(\\boldsymbol{a})}{m} &#038;= \\frac{1}{m}\\sum_{j=1}^m\\left( y_j\\, &#8211; \\sum_{i=1}^{n}a_ix_{j,i} \\right)^2  \\label{eq:mse}<br \/>\n\\end{align}<br \/>\n\u3068\u66f8\u3051\u307e\u3059\u3002<\/p>\n<p>(\\ref{eq:mse})\u5f0f\u306f\u5e73\u5747\u4e8c\u4e57\u8aa4\u5dee(MSE: Mean Squared Error)\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>$J$\u3092$\\boldsymbol{a}$\u306e\u95a2\u6570\u3068\u8003\u3048\u3066\u3001$J$\u304c\u6700\u5c0f\u306b\u306a\u308b\u3088\u3046\u306a$\\boldsymbol{a}$\u3092\u6c42\u3081\u308b\u3053\u3068\u3092\u8003\u3048\u308b\u306e\u304c\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306e\u30ad\u30e2\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<h3>\u8981\u7d20\u3054\u3068\u306b\u504f\u5fae\u5206\u3002<\/h3>\n<p>\u3053\u3053\u304b\u3089\u306f\u8aac\u660e\u5909\u6570\u53ca\u3073\u76ee\u7684\u5909\u6570\u3068\u3057\u3066\u4e0e\u3048\u3089\u308c\u305f$\\boldsymbol{x}_j$\u304a\u3088\u3073$y_j$\u306f\u65e2\u77e5\u306e\u5b9a\u6570\u3067\u3042\u308b\u3068\u8003\u3048\u308b\u3053\u3068\u306b\u7559\u610f\u3057\u3064\u3064\u4ee5\u964d\u306e\u8a08\u7b97\u3092\u9032\u3081\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<p>(\\ref{eq:rss})\u5f0f\u5de6\u8fba\u306f$\\{a_1, \\cdots, a_n\\}$\u306e2\u6b21\u306e\u9805\u306e\u4fc2\u6570$\\{x_1^2, \\cdots, x_n^2\\}$\u306f\u8ca0\u3067\u306a\u3044\u5024\u306b\u306a\u308a\u307e\u3059\u306e\u3067$J$\u306f$\\{a_1, \\cdots, a_n\\}$\u306e\u305d\u308c\u305e\u308c\u306b\u3064\u3044\u3066\u9ad8\u30052\u6b21\u306e\u95a2\u6570\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001$J(\\boldsymbol{a})$\u3092$\\{a_1, \\cdots, a_n\\}$\u306e\u305d\u308c\u305e\u308c\u306b\u3064\u3044\u3066\u504f\u5fae\u5206\u3057\u305f\u7d50\u679c\u5f97\u3089\u308c\u308b\u5f0f\u304c0\u306b\u306a\u308b\u3068\u304d\u3001\u3059\u306a\u308f\u3061$1 \\le k \\le n$\u3092\u6e80\u305f\u3059\u6574\u6570$k$\u306b\u3064\u3044\u3066\u3001<br \/>\n\\begin{align}<br \/>\n\\frac{\\partial J(\\boldsymbol{a})}{\\partial a_k} &#038;= -2\\sum_{j=1}^mx_{j,k}\\left( y_j\\, &#8211; \\sum_{i=1}^{n}a_ix_{j,i} \\right) \\label{eq:partialderivative}<br \/>\n\\end{align}<br \/>\n\u304c\u3059\u3079\u30660\u306b\u306a\u308b\u3068\u304d\u306b$J(\\boldsymbol{a})$\u304c\u6700\u5c0f\u5024\u3092\u3068\u308a\u307e\u3059\u3002\u306a\u304a\u3001(\\ref{eq:partialderivative})\u5f0f\u306f<br \/>\n\\begin{align}<br \/>\n\\frac{\\partial}{\\partial a_k} \\left( y_j\\, &#8211; \\sum_{i=1}^{n}a_ix_{j,i} \\right) &#038;= x_{j,k} \\label{eq:partialderivativek}<br \/>\n\\end{align}<br \/>\n\u3068\u306a\u308b\u3053\u3068\u3092\u5229\u7528\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<h3>\u6b63\u898f\u65b9\u7a0b\u5f0f\u306e\u5c0e\u51fa<\/h3>\n<p>(\\ref{eq:partialderivative})\u5f0f\u306e\u53f3\u8fba\u304c0\u3068\u306a\u308b\u3068\u304d\u306b\u306f\u3001<br \/>\n\\begin{align}<br \/>\n\\sum_{j=1}^mx_{j,k}y_j &#038;= \\sum_{j=1}^mx_{j,k}\\sum_{i=1}^{n}a_ix_{j,i} \\label{eq:nefirst}<br \/>\n\\end{align}<br \/>\n\u306b\u306a\u308a\u307e\u3059\u306e\u3067\u3001\u3053\u308c\u3092\u884c\u5217\u304b\u30d9\u30af\u30c8\u30eb\u306e\u5f62\u5f0f\u3067\u307e\u3068\u3081\u3066\u66f8\u3051\u306a\u3044\u304b\u8003\u3048\u3066\u307f\u307e\u3059\u3002<\/p>\n<h4>\u307e\u305a\u5de6\u8fba\u3002<\/h4>\n<p>\u307e\u305a\u3001(\\ref{eq:nefirst})\u5f0f\u306e\u5de6\u8fba\u306b\u3064\u3044\u3066\u8003\u3048\u307e\u3059\u3002\u3053\u308c\u306f\u3001<br \/>\n\\begin{align}<br \/>\n\\sum_{j=1}^mx_{j,k}y_j &#038;=<br \/>\n\\begin{pmatrix}<br \/>\nx_{1,k} &#038; \\cdots &#038; x_{m,k}<br \/>\n\\end{pmatrix}<br \/>\n\\begin{pmatrix}<br \/>\ny_1 \\cr<br \/>\n\\vdots \\cr<br \/>\ny_m<br \/>\n\\end{pmatrix}\\label{eq:nesecond}<br \/>\n\\end{align}<br \/>\n\u3068\u66f8\u3051\u307e\u3059\u3002$k$\u306f$1 \\le k \\le n$\u3092\u6e80\u305f\u3059\u6574\u6570\u3067\u3042\u3063\u305f\u3053\u3068\u3092\u601d\u3044\u51fa\u3059\u3068\u3001(\\ref{eq:nesecond})\u5f0f\u306f\u7e26\u65b9\u5411\u306b\u4e26\u3079\u308b\u3053\u3068\u304c\u3067\u304d\u3066\u2026<br \/>\n\\begin{align}<br \/>\n\\begin{pmatrix}<br \/>\n\\displaystyle\\sum_{j=1}^mx_{j,1}y_j \\cr<br \/>\n\\vdots \\cr<br \/>\n\\displaystyle\\sum_{j=1}^mx_{j,n}y_j<br \/>\n\\end{pmatrix} &#038;=<br \/>\n\\begin{pmatrix}<br \/>\nx_{1,1} &#038; \\cdots &#038; x_{m,1} \\cr<br \/>\n\\vdots &#038; \\ddots &#038; \\vdots \\cr<br \/>\nx_{1,n} &#038; \\cdots &#038; x_{m,n} \\cr<br \/>\n\\end{pmatrix}<br \/>\n\\begin{pmatrix}<br \/>\ny_1 \\cr<br \/>\n\\vdots \\cr<br \/>\ny_m<br \/>\n\\end{pmatrix}<br \/>\n\\label{eq:nethird}<br \/>\n\\end{align}<br \/>\n\u3068\u66f8\u3051\u307e\u3059\u3002<\/p>\n<p>\u3053\u3053\u3067\u3001$X = \\begin{pmatrix}<br \/>\nx_{1,1} &#038; \\cdots &#038; x_{1,n} \\cr<br \/>\n\\vdots &#038; \\ddots &#038; \\vdots \\cr<br \/>\nx_{m,1} &#038; \\cdots &#038; x_{m,n} \\cr<br \/>\n\\end{pmatrix} $, $\\boldsymbol{y} = (y_1, \\cdots y_n)^T$(\u53f3\u80a9\u306e$T$\u306f\u884c\u5217\u307e\u305f\u306f\u30d9\u30af\u30c8\u30eb\u306e\u8ee2\u7f6e\u3092\u8868\u3057\u307e\u3059\u3002\u4ee5\u4e0b\u540c\u3058\u3002)\u3068\u304a\u304f\u3068\u3001(\\ref{eq:nethird})\u5f0f\u306e\u53f3\u8fba\u306f<\/p>\n<p>\\begin{align}<br \/>\n\\begin{pmatrix}<br \/>\nx_{1,1} &#038; \\cdots &#038; x_{m,1} \\cr<br \/>\n\\vdots &#038; \\ddots &#038; \\vdots \\cr<br \/>\nx_{1,n} &#038; \\cdots &#038; x_{m,n} \\cr<br \/>\n\\end{pmatrix}<br \/>\n\\begin{pmatrix}<br \/>\ny_1 \\cr<br \/>\n\\vdots \\cr<br \/>\ny_m<br \/>\n\\end{pmatrix} &#038;= X^T\\boldsymbol{y} \\label{eq:nefourth}<br \/>\n\\end{align}<br \/>\n\u3068\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<h4>\u6b21\u306b\u53f3\u8fba\u3002<\/h4>\n<p>\u6b21\u306b\u3001(\\ref{eq:nefirst})\u5f0f\u306e\u5de6\u8fba\u306b\u3064\u3044\u3066\u8003\u3048\u307e\u3059\u3002<\/p>\n<p>\u5de6\u8fba\u306f\u7dcf\u548c\u30922\u56de\u3068\u308b\u5f62\u306b\u306a\u3063\u3066\u3044\u3066\u4e00\u898b\u3084\u3084\u3053\u3057\u3044\u306e\u3067\u3001\u3068\u308a\u3042\u3048\u305a\u3001<br \/>\n\\begin{align}<br \/>\n\\sum_{i=1}^{n}a_ix_{j,i} &#038;= \\sum_{i=1}^{n}a_ix_{j,i} \\nonumber \\cr<br \/>\n&#038;= b_j \\label{eq:bj}<br \/>\n\\end{align}<br \/>\n\u3068\u304a\u3044\u3066\u307f\u307e\u3059\u3002\u3059\u308b\u3068\u2026<br \/>\n\\begin{align}<br \/>\n\\sum_{j=1}^mx_{j,k}\\sum_{i=1}^{n}a_ix_{j,i} &#038;= \\sum_{j=1}^mx_{j,k}b_j \\nonumber \\cr<br \/>\n&#038;= \\begin{pmatrix}<br \/>\nx_{1,k} &#038; \\cdots &#038; x_{m,k}<br \/>\n\\end{pmatrix}<br \/>\n\\begin{pmatrix}<br \/>\nb_1 \\cr<br \/>\n\\vdots \\cr<br \/>\nb_m<br \/>\n\\end{pmatrix} \\label{eq:nefifth}<br \/>\n\\end{align}<br \/>\n\u3053\u3053\u3067\u518d\u5ea6$k$\u304c$1 \\le k \\le n$\u3092\u6e80\u305f\u3059\u6574\u6570\u3067\u3042\u3063\u305f\u3053\u3068\u3092\u601d\u3044\u51fa\u3059\u3068\u3001(\\ref{eq:nefifth})\u5f0f\u306f\u7e26\u65b9\u5411\u306b\u4e26\u3079\u308b\u3053\u3068\u304c\u3067\u304d\u3066\u2026<br \/>\n\\begin{align}<br \/>\n\\begin{pmatrix}<br \/>\n\\displaystyle\\sum_{j=1}^mx_{j,1}b_j \\cr<br \/>\n\\vdots \\cr<br \/>\n\\displaystyle\\sum_{j=1}^mx_{j,n}b_j<br \/>\n\\end{pmatrix} &#038;=<br \/>\n\\begin{pmatrix}<br \/>\nx_{1,1} &#038; \\cdots &#038; x_{m,1} \\cr<br \/>\n\\vdots &#038; \\ddots &#038; \\vdots \\cr<br \/>\nx_{1,n} &#038; \\cdots &#038; x_{m,n} \\cr<br \/>\n\\end{pmatrix}<br \/>\n\\begin{pmatrix}<br \/>\nb_1 \\cr<br \/>\n\\vdots \\cr<br \/>\nb_m<br \/>\n\\end{pmatrix} \\nonumber \\cr<br \/>\n&#038;= X^T\\boldsymbol{b}\\label{eq:nesixth}<br \/>\n\\end{align}<br \/>\n\u3068\u66f8\u3051\u307e\u3059\u3002\u306a\u304a\u3001$\\boldsymbol{b} = (b_1, \\cdots b_m)^T$\u3068\u304a\u3044\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>(\\ref{eq:bj})\u5f0f\u3092\u7528\u3044\u308b\u3068$\\boldsymbol{b}$\u306f\u3001<br \/>\n\\begin{align}<br \/>\n\\begin{pmatrix}<br \/>\nb_1\\cr<br \/>\n\\vdots\\cr<br \/>\nb_j\\cr<br \/>\n\\vdots\\cr<br \/>\nb_n\\cr<br \/>\n\\end{pmatrix} &#038;= \\begin{pmatrix}<br \/>\n\\displaystyle\\sum_{i=1}^{n}x_{1,i}a_i \\cr<br \/>\n\\vdots \\cr<br \/>\n\\displaystyle\\sum_{i=1}^{n}x_{j,i}a_i \\cr<br \/>\n\\vdots \\cr<br \/>\n\\displaystyle\\sum_{i=1}^{n}x_{m,i}a_i<br \/>\n\\end{pmatrix} \\nonumber \\cr<br \/>\n&#038;= \\begin{pmatrix}<br \/>\nx_{1,1} &#038; \\cdots &#038; x_{1,n} \\cr<br \/>\n\\vdots &#038; \\ddots &#038; \\vdots \\cr<br \/>\nx_{j,1} &#038; \\cdots &#038; x_{j,n} \\cr<br \/>\n\\vdots &#038; \\ddots &#038; \\vdots \\cr<br \/>\nx_{m,1} &#038; \\cdots &#038; x_{m,n} \\cr<br \/>\n\\end{pmatrix}<br \/>\n\\begin{pmatrix}<br \/>\na_1 \\cr<br \/>\n\\vdots \\cr<br \/>\na_n<br \/>\n\\end{pmatrix} \\nonumber \\cr<br \/>\n&#038;= X\\boldsymbol{a} \\label{eq:bjsecond}<br \/>\n\\end{align}<br \/>\n\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u3053\u3053\u307e\u3067(\\ref{eq:nefirst})\u5f0f\u306e\u5de6\u8fba\u53ca\u3073\u53f3\u8fba\u306b\u5bfe\u3057\u3066\u7b49\u5f0f\u3092\u7e26\u306b\u4e26\u3079\u308b\u3068\u3044\u3046\u64cd\u4f5c\u30921\u56de\u305a\u3064\u884c\u3063\u3066\u3044\u308b\u305f\u3081\u306b\u3001(\\ref{eq:nefourth})\u5f0f\u53ca\u3073(\\ref{eq:nesixth})\u5f0f\u304c\u7b49\u3057\u3044\u3068\u304a\u304f\u3053\u3068\u304c\u3067\u304d\u3066\u3001\u3055\u3089\u306b(\\ref{eq:bjsecond})\u5f0f\u306e\u7d50\u679c\u3068\u5408\u308f\u305b\u308b\u3068\u2026<br \/>\n\\begin{align}<br \/>\nX^T\\boldsymbol{y} &#038;= X^TX\\boldsymbol{a} \\label{eq:normalequation}<br \/>\n\\end{align}<br \/>\n\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p>\u306a\u3093\u3068\u304b\u6b63\u898f\u65b9\u7a0b\u5f0f\u306b\u305f\u3069\u308a\u7740\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<p>\u7279\u306b$X^TX$\u304c\u6b63\u5247\u884c\u5217\u3067\u3042\u308b\u5834\u5408\u306b\u306f$(X^TX)^{-1}$\u304c\u8a08\u7b97\u3067\u304d\u307e\u3059\u306e\u3067\u3001<br \/>\n\\begin{align}<br \/>\n\\boldsymbol{a} &#038;= (X^TX)^{-1}X^T\\boldsymbol{y} \\label{eq:normalequationsolution}<br \/>\n\\end{align}<br \/>\n\u3068\u8a08\u7b97\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001$\\boldsymbol{a}$\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002$\\blacksquare$<\/p>\n<h2>\u307e\u3068\u3081<\/h2>\n<p>\u3053\u3053\u307e\u3067\u306e\u8a08\u7b97\u3067\u884c\u5217\u306e\u8981\u7d20\u3054\u3068\u306b\u8a08\u7b97\u3092\u884c\u3046\u3053\u3068\u3067\u3001\u6b63\u898f\u65b9\u7a0b\u5f0f\u3092\u5c0e\u51fa\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<p>\u884c\u5217\u3084\u30d9\u30af\u30c8\u30eb\u306e\u8a08\u7b97\u6642\u306b\u4f7f\u3048\u308b\u95a2\u4fc2\u5f0f\u3092\u5fd8\u308c\u3066\u3082\u8a08\u7b97\u3067\u304d\u308b\u65b9\u6cd5\u3067\u3059\u306e\u3067\u3001\u3054\u53c2\u8003\u306b\u3057\u3066\u3044\u305f\u3060\u3051\u308b\u3068\u5e78\u3044\u3067\u3059\u3002<\/p>\n<p>\u3053\u306e\u8a18\u4e8b\u306f\u4ee5\u4e0a\u3067\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u306f\u3058\u3081\u306b \u6a5f\u68b0\u5b66\u7fd2\u306e\u65b9\u9762\u3067\u306f\u8d85\u304a\u306a\u3058\u307f\u306e\u7dda\u5f62\u56de\u5e30\u5206\u6790\u3067\u3059\u304c\u3001\u7dda\u5f62\u56de\u5e30\u5206\u6790\u3068\u3044\u3048\u3070\u6700\u5c0f\u4e8c\u4e57\u6cd5\u304c\u307b\u307c\u5b9a\u756a\u3067\u3001\u6700\u5c0f\u4e8c\u4e57\u6cd5\u3068\u3044\u3048\u3070\u6b63\u898f\u65b9\u7a0b\u5f0f\u304c\u307b\u307c\u5fc5\u305a\u767b\u5834\u3057\u307e\u3059\u3002 \u3088\u3063\u3066\u6b63\u898f\u65b9\u7a0b\u5f0f\u3082\u8d85\u304a\u306a\u3058\u307f\u306a\u308f\u3051\u3067\u3001\u6b63\u898f\u65b9\u7a0b\u5f0f\u306e\u5c0e\u51fa\u306e\u65b9\u6cd5\u306b\u3064\u3044\u3066Google\u5148\u751f\u306b\u5c0b\u306d\u3066\u307f\u308b\u3068\u3001\u884c\u5217\u3084\u30d9\u30af\u30c8\u30eb\u3092\u99c6\u4f7f\u3057\u307e\u304f\u308b\u65b9\u6cd5\u3084\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u6559\u3048\u3066\u304f\u308c\u307e\u3059\u3002 \u3057\u304b\u3057\u3001\u3053\u306e\u60c5\u5831\u3060\u3051\u3060\u3068\u884c\u5217\u3084\u30d9\u30af\u30c8\u30eb\u306e\u8a08\u7b97\u304b\u3089\u4e00\u5ea6\u96e2\u308c\u3066\u4e00\u5468\u56de\u3063\u3066\u623b\u3063\u3066\u304d\u305f\u6642\u2026 <span class=\"read-more\"><a href=\"https:\/\/pandanote.info\/?p=7403\">Read More &raquo;<\/a><\/span><\/p>\n","protected":false},"author":1,"featured_media":7420,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[33,13],"tags":[],"class_list":["post-7403","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-panda","category-13"],"_links":{"self":[{"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/posts\/7403","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/pandanote.info\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=7403"}],"version-history":[{"count":21,"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/posts\/7403\/revisions"}],"predecessor-version":[{"id":9400,"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/posts\/7403\/revisions\/9400"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/media\/7420"}],"wp:attachment":[{"href":"https:\/\/pandanote.info\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7403"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pandanote.info\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7403"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pandanote.info\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7403"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}