模块2.6.1 · 数学与统计能力 · 机器学习理论
监督学习基础
machine-learning · statistical-learning · supervised-learning · erm · loss-functions · bayes-optimal · bias-variance · generalization
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中文题目课程监督学习基础 · 机器学习理论
偏差-方差分解与泛化
偏差 方差分解与泛化 Hook：周一的因子复盘 上海某私募的因子研究员周一收到了风控的复盘邮件。他原本用 6 个 Barra 风格因子在沪深300 成份股上做截面回归预测次日超额收益,样本内 公式,模型经理觉得「不够性感」。一周后他把因子从 6 个铺到 36 个——叠加了 28 个行业哑变量、过去 30 日动量分位、几个高频微观结构特征——样本内 公式 一跃...
打开 →题目4312 · 机器学习
Before Adding Augmentation
A teammate proposes aggressive data augmentation as a universal fix. What is the first check you should make before accepting that plan?
打开 →题目4311 · 机器学习
Before Raising Dropout
You are tempted to raise dropout from 0.2 to 0.6 after one mediocre run. What is the first diagnostic question you should answer before doing that?
打开 →题目4314 · 机器学习
Before Trusting Early Stopping
Your validation metric is noisy day to day. Before treating the first local peak as the stopping point, what should you calibrate?
打开 →题目4309 · 机器学习
Co-Adapted Hidden Units
Two hidden layers memorize pairs of co-occurring signals. In-sample metrics look great, but when one signal in the pair shifts slightly out of sample, performance collapses. Which control is most naturally aimed at reducing this co-adaptation?
打开 →题目4296 · 机器学习
Dropout Noise Level 1
Keep eta = 0.1, gradient g = 0.3, and current weight w = 2.0. In the decoupled update w_new = (1 - eta*lambda)w - eta*g, lambda rises from 0.05 to 0.10. By how much does the updated weight decrease relative to the old lambda case?
打开 →题目4297 · 机器学习
Dropout Noise Level 2
A unit has activation 2.0 before standard dropout, meaning dropped units become 0 and kept units stay at 2.0. If keep probability falls from 0.8 to 0.5, what happens to the expected post-dropout activation?
打开 →题目4298 · 机器学习
Dropout Noise Level 3
A 5-class model uses label smoothing with epsilon distributed uniformly across all classes. If epsilon rises from 0.1 to 0.3, by how much does the true-class target change?
打开 →题目4300 · 机器学习
Dropout Noise Level 5
A proximal L1 step uses sign(w)*max(|w| - tau, 0). If the pre-step weight is 0.6, what output do you get when tau rises from 0.2 to 0.5?
打开 →题目4308 · 机器学习
Noisy Labels And Overconfidence
A classifier already has good accuracy, but on borderline names it assigns 99% probability too often and the labels are believed to contain small noise. Which regularization change best targets that failure mode?
打开 →题目4315 · 机器学习
Regularization Is Not Isolated
In an overparameterized network, why is it a mistake to discuss regularization strength without also looking at optimizer and data pipeline choices?
打开 →题目4310 · 机器学习
Safe Invariance Available
You are training on a small image-like signal dataset where small translations and mirror flips preserve the label by construction. The network fits the training set too easily. What regularization lever should move to the front of the queue?
打开 →题目4306 · 机器学习
Sparse Weights Blow Up
A wide MLP on 8k tabular rows drives training AUC to 0.99 while validation AUC stalls at 0.76. Feature semantics do not support label-preserving augmentation, and the largest weights sit on sparse one-hot inputs. Which regularization control should you try first?
打开 →题目4307 · 机器学习
Validation Peak Then Drift
Training loss keeps improving every epoch, but validation Sharpe peaks around epoch 11 and then gradually drifts lower. You are not changing architecture or dataset. What regularization move is most justified?
打开 →题目4291 · 机器学习
Weight Decay Shrinkage 1
A hidden unit has pre-dropout activation 3.2. You apply inverted dropout with keep probability 0.8. If the unit is kept on this training pass, what value is forwarded after dropout?
打开 →题目4292 · 机器学习
Weight Decay Shrinkage 2
A 4-class classifier uses label smoothing with epsilon = 0.2, distributing epsilon uniformly across all 4 classes including the true class. If class 3 is the correct label, what smoothed target vector do you train on?
打开 →题目4293 · 机器学习
Weight Decay Shrinkage 3
A parameter has current value w = 2.0 and gradient g = 0.3. Using a decoupled weight-decay update w_new = (1 - eta*lambda) w - eta*g with eta = 0.1 and lambda = 0.05, what is the updated weight after one step?
打开 →题目4294 · 机器学习
Weight Decay Shrinkage 4
A layer weight vector is w = (3, 4), so its norm is 5. You enforce max-norm regularization with cap c = 4 by rescaling only when the norm exceeds c. What vector is stored after clipping?
打开 →题目4295 · 机器学习
Weight Decay Shrinkage 5
An optimizer uses the proximal L1 shrinkage step sign(w)*max(|w| - tau, 0). If the pre-step weight is w = 0.7 and tau = 0.2, what weight remains after shrinkage?
打开 →题目4313 · 机器学习
When Weight Decay Starts Hurting
Performance falls as you increase weight decay. Before concluding that regularization is bad, what structural question should you ask about the signal?
打开 →课程监督学习基础 · 机器学习理论
分类损失与 Logistic 回归
分类损失与 Logistic 回归 Hook：二元跑赢信号 上海某私募的因子研究员把上一节的 5 因子载荷在沪深300 全样本上重新拟过一遍,现在 PM 把问题反过来问:「不要预测下月超额收益率,直接给我一个『这只票下月跑赢沪深300 的概率』。」目标变量从连续的 公式 收缩成二值的 公式,这条信号要直接驱动一个多空叠加层(long/short overla...
打开 →课程监督学习基础 · 机器学习理论
正则化与模型选择
正则化与模型选择 Hook：一次「翻牌」事件 你在上海一家私募基金负责沪深300 选股策略。上周你按第 3 课的做法，用普通最小二乘（ordinary least squares, OLS）把 5 个 Barra 风格因子——估值、质量、动量、规模、低波动——回归到下一期超额收益上，得到一组 公式。这周把估计窗口前移 5 个交易日重跑，价值因子载荷从 公式 ...
打开 →课程监督学习基础 · 机器学习理论
线性回归作为监督学习的基线
线性回归作为监督学习的基线 Hook：周二早会的 OLS 提问 周二早会上，你向一家头部私募（private fund）的 PM 汇报上周的因子归因。你用沪深300 成份股过去 60 个交易日的横截面数据，对 5 个 Barra 风格因子——市值、估值、动量、质量、低波动——跑了一次普通最小二乘（ordinary least squares, OLS），这是...
打开 →课程监督学习基础 · 机器学习理论
统计学习框架：损失、风险与经验风险最小化
统计学习框架：损失、风险与经验风险最小化 开篇场景（Hook）：下月信号要不要照搬 上海一家私募的量化研究员把过去三年沪深300（CSI 300）成分股的月度超额收益（excess return）整理成一张表：每一行是一只股票在某月的 公式，公式 是当月末的因子向量（规模、价值、动量、低波），公式 是下月的超额收益。她准备在这张大约一万行的样本里挑一个预测器...
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