16,033 research outputs found
Graphical Normalizing Flows
Normalizing flows model complex probability distributions by combining a base
distribution with a series of bijective neural networks. State-of-the-art
architectures rely on coupling and autoregressive transformations to lift up
invertible functions from scalars to vectors. In this work, we revisit these
transformations as probabilistic graphical models, showing they reduce to
Bayesian networks with a pre-defined topology and a learnable density at each
node. From this new perspective, we propose the graphical normalizing flow, a
new invertible transformation with either a prescribed or a learnable graphical
structure. This model provides a promising way to inject domain knowledge into
normalizing flows while preserving both the interpretability of Bayesian
networks and the representation capacity of normalizing flows. We show that
graphical conditioners discover relevant graph structure when we cannot
hypothesize it. In addition, we analyze the effect of -penalization on
the recovered structure and on the quality of the resulting density estimation.
Finally, we show that graphical conditioners lead to competitive white box
density estimators. Our implementation is available at
https://github.com/AWehenkel/DAG-NF
Causal normalizing flows: from theory to practice
In this work, we deepen on the use of normalizing flows for causal reasoning.
Specifically, we first leverage recent results on non-linear ICA to show that
causal models are identifiable from observational data given a causal ordering,
and thus can be recovered using autoregressive normalizing flows (NFs). Second,
we analyze different design and learning choices for causal normalizing flows
to capture the underlying causal data-generating process. Third, we describe
how to implement the do-operator in causal NFs, and thus, how to answer
interventional and counterfactual questions. Finally, in our experiments, we
validate our design and training choices through a comprehensive ablation
study; compare causal NFs to other approaches for approximating causal models;
and empirically demonstrate that causal NFs can be used to address real-world
problems, where the presence of mixed discrete-continuous data and partial
knowledge on the causal graph is the norm. The code for this work can be found
at https://github.com/psanch21/causal-flows.Comment: 32 pages, 15 figures. Accepted as an Oral presentation at NeurIPS
202
The Convolution Exponential and Generalized Sylvester Flows
This paper introduces a new method to build linear flows, by taking the
exponential of a linear transformation. This linear transformation does not
need to be invertible itself, and the exponential has the following desirable
properties: it is guaranteed to be invertible, its inverse is straightforward
to compute and the log Jacobian determinant is equal to the trace of the linear
transformation. An important insight is that the exponential can be computed
implicitly, which allows the use of convolutional layers. Using this insight,
we develop new invertible transformations named convolution exponentials and
graph convolution exponentials, which retain the equivariance of their
underlying transformations. In addition, we generalize Sylvester Flows and
propose Convolutional Sylvester Flows which are based on the generalization and
the convolution exponential as basis change. Empirically, we show that the
convolution exponential outperforms other linear transformations in generative
flows on CIFAR10 and the graph convolution exponential improves the performance
of graph normalizing flows. In addition, we show that Convolutional Sylvester
Flows improve performance over residual flows as a generative flow model
measured in log-likelihood
Normalizing Flows for Human Pose Anomaly Detection
Video anomaly detection is an ill-posed problem because it relies on many
parameters such as appearance, pose, camera angle, background, and more. We
distill the problem to anomaly detection of human pose, thus reducing the risk
of nuisance parameters such as appearance affecting the result. Focusing on
pose alone also has the side benefit of reducing bias against distinct minority
groups. Our model works directly on human pose graph sequences and is
exceptionally lightweight ( parameters), capable of running on any
machine able to run the pose estimation with negligible additional resources.
We leverage the highly compact pose representation in a normalizing flows
framework, which we extend to tackle the unique characteristics of
spatio-temporal pose data and show its advantages in this use case. Our
algorithm uses normalizing flows to learn a bijective mapping between the pose
data distribution and a Gaussian distribution, using spatio-temporal graph
convolution blocks. The algorithm is quite general and can handle training data
of only normal examples, as well as a supervised dataset that consists of
labeled normal and abnormal examples. We report state-of-the-art results on two
anomaly detection benchmarks - the unsupervised ShanghaiTech dataset and the
recent supervised UBnormal dataset
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