diff options
| -rw-r--r-- | algorithm.tex | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/algorithm.tex b/algorithm.tex index df2fdf9..450f881 100644 --- a/algorithm.tex +++ b/algorithm.tex @@ -29,11 +29,11 @@ The prediction $\hat{y}$ is accepted when the classifier is sufficiently confide \subsection{Sequential hypothesis testing} \label{sec:SHT} -The mixture of Gaussians model can be extended to temporal inference through sequential hypothesis testing. Sequential hypothesis testing \cite{wald47sequential} is an established statistical framework, in which a subject is sequentially tested for belonging to one of many classes. The probability that a sequence of data $\bx^{(1)}, \dots, \bx^{(t)}$ belongs to the class $y$ at time $t$ is given by: +The mixture of Gaussians model can be extended to temporal inference through sequential hypothesis testing. Sequential hypothesis testing \cite{wald47sequential} is an established statistical framework, where a subject is sequentially tested for belonging to one of several classes. The probability that a sequence of data $\bx^{(1)}, \dots, \bx^{(t)}$ belongs to the class $y$ at time $t$ is given by: \begin{align} P(y | \bx^{(1)}, \dots, \bx^{(t)}) = \frac{\prod_{i = 1}^t \cN(\bx^{(i)} | \bar{\bx}_y, \Sigma) P(y)} {\sum_y \prod_{i = 1}^t \cN(\bx^{(i)} | \bar{\bx}_y, \Sigma) P(y)}. \label{eq:SHT} \end{align} -The result $\hat{y} = \arg\max_y P(y | \bx^{(1)}, \dots, \bx^{(t)})$ is accepted when $P(\hat{y} | \bx^{(1)}, \dots, \bx^{(t)}) > h$, where the threshold $h \in (0, 1)$ controls the precision and recall of the predictor. +The result $\hat{y} = \arg\max_y P(y | \bx^{(1)}, \dots, \bx^{(t)})$ is accepted when $P(\hat{y} | \bx^{(1)}, \dots, \bx^{(t)}) > h$, where the threshold $h \in (0, 1)$ controls the precision and recall of the predictor. In practice, sequential hypothesis testing smooths out the predictions of the base model. As a result, the new predictions are more precise at the same recall. |