The problem posed is the classic one, along these lines (although Mac Kay presents it slightly differently): given that a biased die averaged 4.5 on a large number of tosses, assign probabilities for the next toss, x.
This problem can seemingly be solved by Bayesian Inference, or by Max Ent with a constraint on the expected value of x: E(x) =4.5. Given the success of Bayes, I was confused and frustrated that nobody could clearly explain this old Max Ent business, and whether it was still worth studying.
All N-grams up to the specified order in the training data will be used as features.
Currently, it's not possible to use feature cutoff. Note that lattices rescored with Max Ent models tend to be much bigger than the lattices created with N-gram models and you can even run out of memory during rescoring.
invariance under relabelling of the hypotheses), but the point remains: Maximum Entropy updates probabilities from a previous distribution, it doesn’t generate them from scratch (I will use the term `ME’ to refer to Max Ent applied in this updating fashion).
This puts the principle on the same turf as another, much more well-accepted method for updating probabilities: Bayes’s theorem.
Furthermore, including the in-domain data with full weight when building the background model often produces slightly better adapted models. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
My updated advice for building the background model is to use a simple approach like this: The default values alpha=0.5 and \sigma^2=6 were empirically found to be globally optimal by Chen (2009), but of course you can try other values. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.7.1.2 Mapping ME N-gram Model Parameters to ARPA Back-off Model Parameters, available here). My title is taken from a similarly titled article by the physicist Ed Jaynes, whose work influenced me greatly.We have found that for adaptation, smaller values for \sigma^2 work better, so the default for adaptation is 0.5. Gao, ``Scalable training of L1-regularized log-linear models,'' in Proceedings of the 24th International Conference on Machine Learning. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.Max Ent models can be converted directly to ARPA format without any loss in accuracy (see Jun Wu's thesis, chap. Khudanpur, ``Building a topic-dependent maximum entropy model for very large corpora,'' in Proceedings of ICASSP, Orlando, Florida, USA, 2002. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.With no constraints apart from normalisation, you get a uniform distribution, which is lurking in the background as a “prior” that is assumed by Max Ent.