Sum-Product Networks for Hybrid Domains

10/09/2017
by   Alejandro Molina, et al.
0

While all kinds of mixed data -from personal data, over panel and scientific data, to public and commercial data- are collected and stored, building probabilistic graphical models for these hybrid domains becomes more difficult. Users spend significant amounts of time in identifying the parametric form of the random variables (Gaussian, Poisson, Logit, etc.) involved and learning the mixed models. To make this difficult task easier, we propose the first trainable probabilistic deep architecture for hybrid domains that features tractable queries. It is based on Sum-Product Networks (SPNs) with piecewise polynomial leave distributions together with novel nonparametric decomposition and conditioning steps using the Hirschfeld-Gebelein-Rényi Maximum Correlation Coefficient. This relieves the user from deciding a-priori the parametric form of the random variables but is still expressive enough to effectively approximate any continuous distribution and permits efficient learning and inference. Our empirical evidence shows that the architecture, called Mixed SPNs, can indeed capture complex distributions across a wide range of hybrid domains.

READ FULL TEXT
research
07/14/2018

Tractable Querying and Learning in Hybrid Domains via Sum-Product Networks

Probabilistic representations, such as Bayesian and Markov networks, are...
research
07/09/2020

Adversarially-learned Inference via an Ensemble of Discrete Undirected Graphical Models

Undirected graphical models are compact representations of joint probabi...
research
05/21/2019

Conditional Sum-Product Networks: Imposing Structure on Deep Probabilistic Architectures

Bayesian networks are a central tool in machine learning and artificial ...
research
03/03/2021

Continuous scaled phase-type distributions

We study random variables arising as the product of phase-type distribut...
research
10/07/2020

SPPL: Probabilistic Programming with Fast Exact Symbolic Inference

We present the Sum-Product Probabilistic Language (SPPL), a new probabil...
research
10/14/2021

On Efficient Range-Summability of IID Random Variables in Two or Higher Dimensions

d-dimensional efficient range-summability (dD-ERS) of a long list of ran...
research
08/29/2016

Visualizing and Understanding Sum-Product Networks

Sum-Product Networks (SPNs) are recently introduced deep tractable proba...

Please sign up or login with your details

Forgot password? Click here to reset