Language Modeling for Soft Keyboards
Joshua Goodman, Gina Venolia, Keith Steury, and Chauncey Parker
Microsoft Research
Summary: By combining language models and a pen down position model, we can reduce error rates for soft keyboards by a factor of 1.7 to 1.9
Soft Keyboard: An image of a keyboard that can be tapped with a stylus.  Perhaps the fastest way to enter text on handheld computers.
Language Model: Computes probability of sequences of letters.  Probabilities are determined by counting occurrences in real text.
Language models are used in speech recognition, handwriting recognition, information retrieval, etc.
Experiments: 8 users were asked to type four sets of 1000 characters, two sets with the language model, and two sets without, counterbalancing the order. No significant difference in speed was observed.  Error rate using the language model was reduced by a factor of 1.7 to 1.9.
Pen Down Position Model: Probability of pen position given intended key.  A simple Gaussian works well, but the mean of the Gaussian is shifted from the center of the key, and there is some covariance between x and y.  Other factors, such as pen up position, and error at previous time were not useful.
Conclusion: Language models can be used to substantially reduce error rates.  The technique could be applied to many different input types.
Intuition: If the user taps on or near key boundaries, we can use the language model to guess the intended letters.  For instance, if user taps “q” and then taps between “u” and “i”, he intended “qu” 
In fact, even if the user hits inside “i”, he probably meant “qu”:
Future information can change our guess for the past.
= qu
= qu
= we
Mathematics: Find the most probable letter sequence given the observed pen down positions:
Blue letters may change later.  When user hits the r, the system corrects the error.