# Mixture model where weights are dependent on covariates

**URL:** <https://discourse.edwardlib.org/t/mixture-model-where-weights-are-dependent-on-covariates/508>\
**Category:** General\
**Created:** [November 25, 2017, 2:02pm UTC](https://discourse.edwardlib.org/t/mixture-model-where-weights-are-dependent-on-covariates/508 "2017-11-25T14:02:06Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![mg11968](https://avatars.discourse-cdn.com/v4/letter/m/7993a0/32.png) [@mg11968](https://discourse.edwardlib.org/u/mg11968)\
**Post date:** [November 25, 2017, 2:02pm UTC](https://discourse.edwardlib.org/t/mixture-model-where-weights-are-dependent-on-covariates/508/1 "2017-11-25T14:02:07Z")

</div>

Hello all,

I am new to Edward, but I was wondering if anyone has had any success with a regression mixture model (with Gaussian errors) where the mixture weights are also determined by the covariates via a softmax function. I will try to explain it using some notation (forgive me if the typesetting is off).

y\_i ~ Sum[(w\_k | X[i, :]) \* Normal(alpha\_k + dot(beta\_k, X[i, :], sigma\_k) ]

where

1. i represents the index of the observation
2. k represents the index of the mixing cluster, and there are k = 1…K mixing classes where K is known in advance (i.e. this is a finite mixture)
3. the response variable, y, has i = 1…N elements
4. the predictors, X, have rows indexed by i (with N elements) and columns indexed by j = 1…M elements.

This is different than a conventional gaussian mixture in that the means are not constant, and the regression is heteroskedastic.

While I have run many of the Edward tutorial models, I get a little confused on the interchangeability of Tensorflow variables from Edward variables. If anyone could start a basic template model, I would be glad to run it and offer code review on how it works with data.

Any help would be appreciated.