Understanding SMT
without the “S”
(Statistics)
Robert Frederking
Carnegie Mellon
School of Computer Science
Statistical modelling
• Think about statistical modelling as
fitting a curve to data points
– Start with parameterized function,
error metric, and data points
– After fitting the function to data using
parameters, you can make
predictions
Carnegie Mellon
School of Computer Science
Carnegie Mellon
School of Computer Science
Carnegie Mellon
School of Computer Science
y = a*x + b
Err = sqrt(sum(di^2))
Carnegie Mellon
School of Computer Science
y = a*x + b
Y
X
Carnegie Mellon
School of Computer Science
Carnegie Mellon
School of Computer Science
Carnegie Mellon
School of Computer Science
y = a*x + b
Err = sqrt(sum(di^2))
Carnegie Mellon
School of Computer Science
y = a*x + b
Y??
X
Carnegie Mellon
School of Computer Science
Y2
(Y-y0)^2/a +
(X-x0)^2/b
= r^2
Y1
Err = sqrt(sum(di^2))
X
Carnegie Mellon
School of Computer Science
Statistical modelling
• Think about statistical modelling as
fitting a curve to data points
– Parameterized function, error metric, data
points
– After fitting parameters, you can make
predictions
– But you will get some fit for any data set
• Human researchers need to come up
with “good” family of functions, and
error metric, for the data you see
– Want low error number, good predictions
– Tractable, both in training and decoding
• including data availability, sparseness issues
Carnegie Mellon
School of Computer Science