From d63de51bea837d66aabb22a755a8215212782e9d Mon Sep 17 00:00:00 2001
From: unknown <Brano@Toshibicka.(none)>
Date: Fri, 2 Mar 2012 01:54:14 -0800
Subject: Algorithms

---
 algorithm.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

(limited to 'algorithm.tex')

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.
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