Supervised Learning

模块目标

Write a loss, a gradient step, and a validation protocol as three different objects, and refuse to treat training error as expected risk.

课程大纲

1. 01 Objectives and models 20h

   学习结果 Distinguish a prediction task, a model class, and a training objective.

   形成性检查 四选一检查

2. 02 Linear regression as an optimisation problem 20h

   学习结果 Derive the normal equations from squared loss and say when the design is linear in parameters.

   形成性检查 书面推导

3. 03 Logistic classification and likelihood 20h

   学习结果 Derive binary cross-entropy from a Bernoulli likelihood.

   形成性检查 书面推导

4. 04 Gradients and local descent 20h

   学习结果 Justify the negative gradient as a local descent direction and state the first-order remainder.

   形成性检查 书面推导

5. 05 Gradient descent and learning rates 15h

   学习结果 For a one-dimensional quadratic, derive a constant-step interval that contracts.

   形成性检查 书面推导

6. 06 Regularisation and inductive bias 15h

   学习结果 Prove uniqueness of the ridge solution for a strictly positive penalty parameter even when X is rank deficient.

   形成性检查 书面推导

7. 07 Validation, leakage and generalisation 20h

   学习结果 Design a split that respects how new data arrive and exhibit a leakage failure.

   形成性检查 反例

8. 08 Examination synthesis 20h

   学习结果 Assemble objective, optimiser caveat, and evaluation into one short written argument.

   形成性检查 书面推导

学习结果

Given a prediction task, specify a model class, a loss, an optimiser limitation, and a leakage-aware evaluation.

学科技能

Empirical risk, linear and logistic models, gradients, ridge, train/validation/test splits.

可迁移技能

Report what a number measures; keep evaluation independent of fitting choices.

相关入门主题

01Objectives and models3 个主题

1. Empirical risk and loss functions
2. Linear regression as an optimisation problem
3. Logistic classification and likelihood

章节链接

02Optimisation and regularisation3 个主题

1. Gradients and local descent
2. Gradient descent and learning rates
3. Regularisation and inductive bias

章节链接

03Evaluation and examination synthesis2 个主题

1. Validation, leakage and generalisation
2. Supervised-learning examination synthesis

章节链接