Glossary
B
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- Bayes risk
- Optimal (smallest) risk achievable by any predictor on a problem.
C
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- Classification error or loss (aka 0/1 error or loss)
- Used in classification to measure quality of predictor h(x): $\ell_{0/1}(h,y) = \textbf{1}(h(x) \ne y)$. We are often interested in 0–1 risk: $L_{0/1}(h) = \textbfĒ_(x,y)[\textbf{1}(h(x) \ne y)]$.
- Conditional Independence
- X is conditionally independent of Y given Z if $P(X=x \mid Y=y, Z=z)= P(X=x \mid Z=z), \; \forall x,y,z$ or equivalently, $P(X=x,Y=y\mid Z=z) = P(X=x\mid Z=z)P(Y=y\mid Z=z), \; \forall x,y,z$.
D
- Decision stump
- A decision tree with one internal node.
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I
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- Independence
- X is independent of Y if $P(X=x \mid Y=y)= P(X=x), \; \forall x,y$ or equivalently, $P(X=x,Y=y) = P(X=x)P(Y=y), \; \forall x,y$.
L
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- Linear separability
-
A dataset $\{\textbf{x}_i,y_i\}_{i=1}^{n}$ is linearly separable if
$$\exists w_0, \textbf{w}, {\rm such} \; {\rm that}:
\left\{
\begin{align}
w_0 + \textbf{w}^\top \textbf{x}_i > 0 &\; {\rm if}\; y_i=1
w_0 + \textbf{w}^\top \textbf{x}_i < 0 &\; {\rm if}\; y_i=0
\end{align}
\right.
$$
- Loss
- A function used to measure error of a predictor h(x), $\ell(h,y)$, for example, squared error or 0–1 error.
R
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- Risk
- Expected loss of a predictor h(x): $L(h) = \textbfĒ_(x,y)[\ell(h(x),y)]$.
S
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- Squared error or loss
- Often used in regression to measure quality of predictor h(x): $\ell_{2}(h,y) = (h(x) - y)^2$. We are usually interested in expected squared error, or risk: $L_2(h) = \textbfĒ_(x,y)[(h(x) - y)^2]$.
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