[{"data":1,"prerenderedAt":314},["ShallowReactive",2],{"content-query-PCr8FTzfb8":3},{"_path":4,"_dir":5,"_draft":6,"_partial":6,"_locale":7,"title":8,"description":9,"date":10,"cover":11,"type":12,"category":13,"body":14,"_type":308,"_id":309,"_source":310,"_file":311,"_stem":312,"_extension":313},"/technology-blogs/zh/577","zh",false,"","【跟着小Mi一起机器学习吧！】单变量线性回归（一）","什么是机器学习，什么是机器学习，如果你想知道什么是机器学习，那么小Mi带你一起研究！","2021-05-31","https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2021/05/31/06ff751913c54df7ad687a78635b0159.png","technology-blogs","基础知识",{"type":15,"children":16,"toc":302},"root",[17,25,31,37,45,61,68,73,84,91,102,108,115,138,145,152,157,168,173,180,185,192,199,226,232,239,244,251,262,269,274,291],{"type":18,"tag":19,"props":20,"children":22},"element","h1",{"id":21},"跟着小mi一起机器学习吧单变量线性回归一",[23],{"type":24,"value":8},"text",{"type":18,"tag":26,"props":27,"children":28},"p",{},[29],{"type":24,"value":30},"几天不见，动力不减！话说回来，我们要正式开始挑起大梁干大事了，前面一段时间，小Mi已经带大家初步了解了机器学习，复习了机器学习中需要用到的线性代数知识点，这次我们就要开始正式学习监督学习下的单变量线性回归（那么后面是不是还有多变量线性回归？Bingo！答对了！）啦。那就废话不多说，抓紧时间跟小Mi一起机器学习吧~",{"type":18,"tag":19,"props":32,"children":34},{"id":33},"_1-模型描述",[35],{"type":24,"value":36},"1 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，使得h(x)与y之间的差值尽可能的小。于是就选取了可以使得建模误差的平方和能够最小的模型参数。即：使得",{"type":18,"tag":41,"props":163,"children":165},{"alt":7,"src":164},"https://bbs-img.huaweicloud.com/data/forums/attachment/forum/202105/29/173558cb8vonnejsiby6un.png",[],{"type":24,"value":167},"最小，这样的一个函数我们也称之为代价函数。",{"type":18,"tag":26,"props":169,"children":170},{},[171],{"type":24,"value":172},"代价函数也被称为平方误差函数，或平方误差代价函数。之所以要求出误差的平方和，是因为误差平方代价函数，对于大多数问题，特别是回归问题，都是一个合理的选择。还有其他的代价函数也能很好地发挥作用，但是平方误差代价函数可能是解决回归问题最常用的手段了。",{"type":18,"tag":174,"props":175,"children":177},"h2",{"id":176},"_21-代价函数图形解释一",[178],{"type":24,"value":179},"2.1 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代价函数图形解释（二）",{"type":18,"tag":26,"props":233,"children":234},{},[235],{"type":18,"tag":41,"props":236,"children":238},{"alt":7,"src":237},"https://bbs-img.huaweicloud.com/data/forums/attachment/forum/202105/29/173120ltreyntgyvnm085x.png",[],{"type":18,"tag":26,"props":240,"children":241},{},[242],{"type":24,"value":243},"在标准形式下， 小Mi觉得大家可以想象一下，既然一维参数是抛物线，那么二维参数是不是就是一个立体空间上的碗状形式？没错，下图可以参考下，高度即为代价函数的值，可以看到它仍然有着最小值的，而到达更多的参数的时候就无法像这样可视化了，但是原理都是相似的。",{"type":18,"tag":26,"props":245,"children":246},{},[247],{"type":18,"tag":41,"props":248,"children":250},{"alt":7,"src":249},"https://bbs-img.huaweicloud.com/data/forums/attachment/forum/202105/29/172640lutraqym3jewis6q.png",[],{"type":18,"tag":26,"props":252,"children":253},{},[254,256,260],{"type":24,"value":255},"我们还可以把上面的这个三维图像映射到二维平面上，这样的图像叫做等高图像，每一条颜色线上的点都具有相同的",{"type":18,"tag":41,"props":257,"children":259},{"alt":7,"src":258},"https://bbs-img.huaweicloud.com/data/forums/attachment/forum/202105/29/172753apa3h8brssrqhum5.png",[],{"type":24,"value":261},"值。",{"type":18,"tag":26,"props":263,"children":264},{},[265],{"type":18,"tag":41,"props":266,"children":268},{"alt":7,"src":267},"https://bbs-img.huaweicloud.com/data/forums/attachment/forum/202105/29/172817u7lyjpondsse5zxf.png",[],{"type":18,"tag":26,"props":270,"children":271},{},[272],{"type":24,"value":273},"通过这些图形，我们能够更好地理解这些代价函数J所代表的值是什么样的，它们对应的假设是什么样的，以及什么样的假设对应的点，更接近于代价函数J的最小值。",{"type":18,"tag":26,"props":275,"children":276},{},[277,279,283,285,289],{"type":24,"value":278},"当然，我们真正需要的是一种有效的算法，能够自动地找出这些使代价函数J取最小值的参数",{"type":18,"tag":41,"props":280,"children":282},{"alt":7,"src":281},"https://bbs-img.huaweicloud.com/data/forums/attachment/forum/202105/29/172914gosfg3ggp0ur1ihf.png",[],{"type":24,"value":284},"来。小Mi认为编个程序把这些点画出来，然后人工的方法来读出这些点的数值，这依然无法真正实现机器学习，隔靴搔痒一样。我们也会遇到更复杂、更高维度、更多参数的情况，而这些情况是很难画出图的，因此更无法将其可视化，因此我们真正需要的是编写程序来找出这些最小化代价函数的",{"type":18,"tag":41,"props":286,"children":288},{"alt":7,"src":287},"https://bbs-img.huaweicloud.com/data/forums/attachment/forum/202105/29/172934zcrjd6ks3sjwrhjj.png",[],{"type":24,"value":290},"的值。",{"type":18,"tag":26,"props":292,"children":293},{},[294,296,300],{"type":24,"value":295},"在下一节，小Mi将介绍一种算法，能够自动地找出能使代价函数J最小化的参数",{"type":18,"tag":41,"props":297,"children":299},{"alt":7,"src":298},"https://bbs-img.huaweicloud.com/data/forums/attachment/forum/202105/29/173015d5pnx0scddagnkws.png",[],{"type":24,"value":301},"的值,是不是很开心，这才是真正的机器学习嘛！好了，今天小Mi带着大家学习了单变量线性回归算法的模型表示，并且从数形结合的角度描述了代价函数的存在意义，但是更精彩的还在等着大家，我们下期再见~",{"title":7,"searchDepth":303,"depth":303,"links":304},4,[305,307],{"id":176,"depth":306,"text":179},2,{"id":228,"depth":306,"text":231},"markdown","content:technology-blogs:zh:577.md","content","technology-blogs/zh/577.md","technology-blogs/zh/577","md",1776506138090]