# [SRILM User List] Interpolating LMs with different smoothing

Anand Venkataraman venkataraman.anand at gmail.com
Wed Jul 18 14:29:13 PDT 2018

```Cool - Central Limit Theorem in action :-)

&

On Wed, Jul 18, 2018 at 11:06 AM, Andreas Stolcke <stolcke at icsi.berkeley.edu
> wrote:

>
> This is as expected.  You have two estimators (of conditional word
> probabilities, i.e., LMs), each with random deviations from the true
> probabilities.  By averaging their predictions you reduce the deviation
> from the truth (assuming the deviations are randomly distributed).
>
> For this reason you can almost always get a win out of interpolating
> models that are approximately on par in their individual performance.
> Other examples are
>
> - random forest models
> - sets of neural LMs initialized with different initial random weights
> - log-linear combination of forward and backward running LMs
> - sets of LMs trained on random samples from the same training set
>
> These techniques all reduce the "variance" part of the modeling error
> Other techniques (like interpolating models trained on different genres) do
> a similar thing for the "bias"  part of the error.
>
> Andreas
>
> On 7/17/2018 9:22 PM, Fed Ang wrote:
>
> Hi,
>
> I don't know if it has been asked before, but does it make sense to
> interpolate on the basis of smoothing instead of domain/genre?  What should
> be the assumptions in considering this when the resulting perplexity is
> lower than any of the two separately?
>
> Let's say: 5-gram Katz yields 100, and 5-gram Modified KN yields 90
> Then best-mix of the two yields 87
>
> On a theoretical perspective, is it sound to simply trust that the
> interpolated LM is better/generalizable to different smoothing combinations?
>
> -Fred
>
>
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