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$(2,0),(-2,0),(0,1),(0,-1)$。均值为零，按四个样本取平均的协方差为diag(2,0.5)。PCA只保留一维时选择横轴：前两点不变，后两点投影为原点。平均平方重建误差为 $(0+0+1+1)/4=0.5$；若选纵轴，则为2。","sha256":"afb4b88eb02b7c896b6906f158c3b8e8f4b422a9c200eba1c04397589e0b2461","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-masked-prediction","title":"限制可见信息，怎样构成可验证的重建任务？"},"page":{"id":"reading-opening","title":"保留最大方差，不等于保留任务答案","number":1},"sectionTitle":"保留最大方差，不等于保留任务答案","currentQuestion":"保留最大方差，不等于保留任务答案","sourceSlides":[],"knowledgeBlock":null,"formulas":[{"latex":"(2,0),(-2,0),(0,1),(0,-1)","definitionContext":"保留最大方差，不等于保留任务答案"},{"latex":"(0+0+1+1)/4=0.5","definitionContext":"保留最大方差，不等于保留任务答案"}],"previousBlock":"b-4b859112f48b1753a8e22786","nextBlock":"b-842c9c2b8e385a29f68ffa58","prerequisites":[{"id":"b-b97b309740b539b0d0018d50","url":"#b-b97b309740b539b0d0018d50","role":"section-title"},{"id":"b-4b859112f48b1753a8e22786","url":"#b-4b859112f48b1753a8e22786","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-842c9c2b8e385a29f68ffa58","type":"p","scope":"pca-reconstruction-worked-example","url":"https://codingai-lec03.pages.dev/course/blocks/pca-reconstruction-worked-example.html#b-842c9c2b8e385a29f68ffa58","content":"在“尽量重建输入”这个题目下，横轴合理。但若任务要区分纵坐标正负，两点落在原点后就无法再区分。问题不在PCA算错，而在重建目标和未来用途不完全一致。","sha256":"23fb328ddea3c580d00a3d6063033a3a285a22d74ef6bf1a9caf5a2b575485d0","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-masked-prediction","title":"限制可见信息，怎样构成可验证的重建任务？"},"page":{"id":"reading-opening","title":"保留最大方差，不等于保留任务答案","number":1},"sectionTitle":"保留最大方差，不等于保留任务答案","currentQuestion":"保留最大方差，不等于保留任务答案","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-aad90eb6374cefb0a100c804","nextBlock":"b-2cf984868ca0f475e80803ea","prerequisites":[{"id":"b-b97b309740b539b0d0018d50","url":"#b-b97b309740b539b0d0018d50","role":"section-title"},{"id":"b-4b859112f48b1753a8e22786","url":"#b-4b859112f48b1753a8e22786","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-2cf984868ca0f475e80803ea","type":"p","scope":"pca-reconstruction-worked-example","url":"https://codingai-lec03.pages.dev/course/blocks/pca-reconstruction-worked-example.html#b-2cf984868ca0f475e80803ea","content":"这个反例同样提醒我们理解深层重建：低像素误差是一个有意义的成绩，却不是所有语义任务的替代指标。需要另外检验表示能否支持类别、颜色或空间读出。","sha256":"3ee6b967c2180d7471f95f260440fb5df461b94fb66bc1cad9c30e0cf8519c32","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-masked-prediction","title":"限制可见信息，怎样构成可验证的重建任务？"},"page":{"id":"reading-opening","title":"保留最大方差，不等于保留任务答案","number":1},"sectionTitle":"保留最大方差，不等于保留任务答案","currentQuestion":"保留最大方差，不等于保留任务答案","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-842c9c2b8e385a29f68ffa58","nextBlock":"b-9eb75b4322c76e1b9891d4b3","prerequisites":[{"id":"b-b97b309740b539b0d0018d50","url":"#b-b97b309740b539b0d0018d50","role":"section-title"},{"id":"b-4b859112f48b1753a8e22786","url":"#b-4b859112f48b1753a8e22786","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-9eb75b4322c76e1b9891d4b3","type":"h2","scope":"pca-reconstruction-worked-example","url":"https://codingai-lec03.pages.dev/course/blocks/pca-reconstruction-worked-example.html#b-9eb75b4322c76e1b9891d4b3","content":"## 继续阅读与实验","sha256":"2b9ccef7e1220e2250cceff1abd8bdd736b42f8da5a223f26b029f44b962e807","chapter":{"id":"I","title":"学习信号与表示"},"unit":{"id":"i-masked-prediction","title":"限制可见信息，怎样构成可验证的重建任务？"},"page":{"id":"reading-opening","title":"保留最大方差，不等于保留任务答案","number":1},"sectionTitle":"保留最大方差，不等于保留任务答案","currentQuestion":"保留最大方差，不等于保留任务答案","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-2cf984868ca0f475e80803ea","nextBlock":null,"prerequisites":[{"id":"b-b97b309740b539b0d0018d50","url":"#b-b97b309740b539b0d0018d50","role":"section-title"},{"id":"b-4b859112f48b1753a8e22786","url":"#b-4b859112f48b1753a8e22786","role":"problem-context"}],"relatedBlocks":[]}]}