On the Stochastic Stability of Deep Markov Models

11/08/2021
by   Jan Drgona, et al.
0

Deep Markov models (DMM) are generative models that are scalable and expressive generalization of Markov models for representation, learning, and inference problems. However, the fundamental stochastic stability guarantees of such models have not been thoroughly investigated. In this paper, we provide sufficient conditions of DMM's stochastic stability as defined in the context of dynamical systems and propose a stability analysis method based on the contraction of probabilistic maps modeled by deep neural networks. We make connections between the spectral properties of neural network's weights and different types of used activation functions on the stability and overall dynamic behavior of DMMs with Gaussian distributions. Based on the theory, we propose a few practical methods for designing constrained DMMs with guaranteed stability. We empirically substantiate our theoretical results via intuitive numerical experiments using the proposed stability constraints.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 8

11/26/2020

Spectral Analysis and Stability of Deep Neural Dynamics

Our modern history of deep learning follows the arc of famous emergent d...
04/23/2015

Stability of Stochastic Approximations with `Controlled Markov' Noise and Temporal Difference Learning

In this paper we present a `stability theorem' for stochastic approximat...
04/11/2020

Convex Sets of Robust Recurrent Neural Networks

Recurrent neural networks (RNNs) are a class of nonlinear dynamical syst...
03/26/2021

Almost Surely Stable Deep Dynamics

We introduce a method for learning provably stable deep neural network b...
11/13/2020

On the stability properties of Gated Recurrent Units neural networks

The goal of this paper is to provide sufficient conditions for guarantee...
03/31/2021

Linear systems with neural network nonlinearities: Improved stability analysis via acausal Zames-Falb multipliers

In this paper, we analyze the stability of feedback interconnections of ...
12/26/2020

Stability-Certified Reinforcement Learning via Spectral Normalization

In this article, two types of methods from different perspectives based ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.