4 research outputs found
The Poisson transform for unnormalised statistical models
Contrary to standard statistical models, unnormalised statistical models only
specify the likelihood function up to a constant. While such models are natural
and popular, the lack of normalisation makes inference much more difficult.
Here we show that inferring the parameters of a unnormalised model on a space
can be mapped onto an equivalent problem of estimating the intensity
of a Poisson point process on . The unnormalised statistical model now
specifies an intensity function that does not need to be normalised.
Effectively, the normalisation constant may now be inferred as just another
parameter, at no loss of information. The result can be extended to cover
non-IID models, which includes for example unnormalised models for sequences of
graphs (dynamical graphs), or for sequences of binary vectors. As a
consequence, we prove that unnormalised parameteric inference in non-IID models
can be turned into a semi-parametric estimation problem. Moreover, we show that
the noise-contrastive divergence of Gutmann & Hyv\"arinen (2012) can be
understood as an approximation of the Poisson transform, and extended to
non-IID settings. We use our results to fit spatial Markov chain models of eye
movements, where the Poisson transform allows us to turn a highly non-standard
model into vanilla semi-parametric logistic regression
Stochastic Wasserstein Barycenters
We present a stochastic algorithm to compute the barycenter of a set of
probability distributions under the Wasserstein metric from optimal transport.
Unlike previous approaches, our method extends to continuous input
distributions and allows the support of the barycenter to be adjusted in each
iteration. We tackle the problem without regularization, allowing us to recover
a sharp output whose support is contained within the support of the true
barycenter. We give examples where our algorithm recovers a more meaningful
barycenter than previous work. Our method is versatile and can be extended to
applications such as generating super samples from a given distribution and
recovering blue noise approximations.Comment: ICML 201