Overview
Definition
- Field of study that gives computers the ability to learn without explicitly programmed. Arthur Samuel(1959)
- A computer program is said to learn from experience E with respect to some task T and some performance measure P, if its performance on T, as measured by P, improves with experience E. Tom Mitchell(1998)
Type of problem
| Regression | Classification | |
|---|---|---|
| Outcome | Continuous value | Discrete value |
| Example | Housing price | Breast cancer |
| Algorithm | Linear regression | Logistic regression, SVM |
Type of model
| Discriminative model | Generative model | |
|---|---|---|
| Goal | Estimate $P(y|x)$ directly | Estimate $P(x|y)$ then deduce $P(y|x)$ |
| What's learned | Desicion boundary | Probability distribution of data |
| Algorithm | Logistic regression, SVM | Naive Bayes, Latent Dirichlet Allocation(LDA) |
Notations
Hypothesis: The hypothesis is denotes as $h_{\theta}$ and is the model we want to select. For a given data $x^{i}$ the model prediction is $h_{\theta}(x^{(i)})$
Loss function: The difference between the predicted value $z$ according to the selected model and the real data value $y$. The common loss functions include least square error, logistic loss, hinge loss, and cross entropy loss.
Cost function: The cost function $J$ is used to measure the performance of a model, and is defined with loss function as follows:
\[ J(\theta) = \sum_{i=1}^{m} L(h_{\theta}(x^{i}, y^{i})) \]
- Gradient descent: The update rule to optimize the model parameters by the set learning rate $\alpha$ and the computed gradient of each parameter.
\[\theta \gets \theta - \alpha\nabla J(\theta)\]
and more explicitly:
\[ \text{repeat until convergence} \{ \theta_{j} := \theta_{j} - \alpha \frac{\partial}{\partial \theta_{j}} J(\theta) \} \]