21,627 research outputs found
High-Dimensional Undirected Graphical Models for Arbitrary Mixed Data
Graphical models are an important tool in exploring relationships between
variables in complex, multivariate data. Methods for learning such graphical
models are well developed in the case where all variables are either continuous
or discrete, including in high-dimensions. However, in many applications data
span variables of different types (e.g. continuous, count, binary, ordinal,
etc.), whose principled joint analysis is nontrivial. Latent Gaussian copula
models, in which all variables are modeled as transformations of underlying
jointly Gaussian variables, represent a useful approach. Recent advances have
shown how the binary-continuous case can be tackled, but the general mixed
variable type regime remains challenging. In this work, we make the simple yet
useful observation that classical ideas concerning polychoric and polyserial
correlations can be leveraged in a latent Gaussian copula framework. Building
on this observation we propose flexible and scalable methodology for data with
variables of entirely general mixed type. We study the key properties of the
approaches theoretically and empirically, via extensive simulations as well an
illustrative application to data from the UK Biobank concerning COVID-19 risk
factors.Comment: 17 pages, 2 Figure
Hidden Parameter Recurrent State Space Models For Changing Dynamics Scenarios
Recurrent State-space models (RSSMs) are highly expressive models for learning patterns in time series data and system identification. However, these models assume that the dynamics are fixed and unchanging, which is rarely the case in real-world scenarios. Many control applications often exhibit tasks with similar but not identical dynamics which can be modeled as a latent variable. We introduce the Hidden Parameter Recurrent State Space Models (HiP-RSSMs), a framework that parametrizes a family of related dynamical systems with a low-dimensional set of latent factors. We present a simple and effective way of learning and performing inference over this Gaussian graphical model that avoids approximations like variational inference. We show that HiP-RSSMs outperforms RSSMs and competing multi-task models on several challenging robotic benchmarks both on real-world systems and simulations
Hidden Parameter Recurrent State Space Models For Changing Dynamics Scenarios
Recurrent State-space models (RSSMs) are highly expressive models for
learning patterns in time series data and system identification. However, these
models assume that the dynamics are fixed and unchanging, which is rarely the
case in real-world scenarios. Many control applications often exhibit tasks
with similar but not identical dynamics which can be modeled as a latent
variable. We introduce the Hidden Parameter Recurrent State Space Models
(HiP-RSSMs), a framework that parametrizes a family of related dynamical
systems with a low-dimensional set of latent factors. We present a simple and
effective way of learning and performing inference over this Gaussian graphical
model that avoids approximations like variational inference. We show that
HiP-RSSMs outperforms RSSMs and competing multi-task models on several
challenging robotic benchmarks both on real-world systems and simulations.Comment: Published at the International Conference on Learning
Representations, ICLR 202
Hidden Parameter Recurrent State Space Models For Changing Dynamics Scenarios
Recurrent State-space models (RSSMs) are highly expressive models for
learning patterns in time series data and system identification. However, these
models assume that the dynamics are fixed and unchanging, which is rarely the
case in real-world scenarios. Many control applications often exhibit tasks
with similar but not identical dynamics which can be modeled as a latent
variable. We introduce the Hidden Parameter Recurrent State Space Models
(HiP-RSSMs), a framework that parametrizes a family of related dynamical
systems with a low-dimensional set of latent factors. We present a simple and
effective way of learning and performing inference over this Gaussian graphical
model that avoids approximations like variational inference. We show that
HiP-RSSMs outperforms RSSMs and competing multi-task models on several
challenging robotic benchmarks both on real-world systems and simulations.Comment: Published at the International Conference on Learning
Representations, ICLR 202
Learning Latent Tree Graphical Models
We study the problem of learning a latent tree graphical model where samples
are available only from a subset of variables. We propose two consistent and
computationally efficient algorithms for learning minimal latent trees, that
is, trees without any redundant hidden nodes. Unlike many existing methods, the
observed nodes (or variables) are not constrained to be leaf nodes. Our first
algorithm, recursive grouping, builds the latent tree recursively by
identifying sibling groups using so-called information distances. One of the
main contributions of this work is our second algorithm, which we refer to as
CLGrouping. CLGrouping starts with a pre-processing procedure in which a tree
over the observed variables is constructed. This global step groups the
observed nodes that are likely to be close to each other in the true latent
tree, thereby guiding subsequent recursive grouping (or equivalent procedures)
on much smaller subsets of variables. This results in more accurate and
efficient learning of latent trees. We also present regularized versions of our
algorithms that learn latent tree approximations of arbitrary distributions. We
compare the proposed algorithms to other methods by performing extensive
numerical experiments on various latent tree graphical models such as hidden
Markov models and star graphs. In addition, we demonstrate the applicability of
our methods on real-world datasets by modeling the dependency structure of
monthly stock returns in the S&P index and of the words in the 20 newsgroups
dataset
- …