1. Carnegie Mellon School of Computer Science Understanding SMT without the “S” (Statistics) Robert Frederking

2. 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

3. Carnegie Mellon School of Computer Science

4. Carnegie Mellon School of Computer Science

5. Carnegie Mellon School of Computer Science y = a*x + b Err = sqrt(sum(d i ^2))

6. Carnegie Mellon School of Computer Science X Y y = a*x + b

7. Carnegie Mellon School of Computer Science

8. Carnegie Mellon School of Computer Science

9. Carnegie Mellon School of Computer Science y = a*x + b Err = sqrt(sum(d i ^2))

10. Carnegie Mellon School of Computer Science y = a*x + b X Y??

11. Carnegie Mellon School of Computer Science X Y2 Y1 Err = sqrt(sum(d i ^2)) (Y-y0)^2/a + (X-x0)^2/b = r^2

12. 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