Learning and Inference in Sparse Coding Models with Langevin Dynamics
- URL: http://arxiv.org/abs/2204.11150v1
- Date: Sat, 23 Apr 2022 23:16:47 GMT
- Title: Learning and Inference in Sparse Coding Models with Langevin Dynamics
- Authors: Michael Y.-S. Fang, Mayur Mudigonda, Ryan Zarcone, Amir Khosrowshahi,
Bruno A. Olshausen
- Abstract summary: We describe a system capable of inference and learning in a probabilistic latent variable model.
We demonstrate this idea for a sparse coding model by deriving a continuous-time equation for inferring its latent variables via Langevin dynamics.
We show that Langevin dynamics lead to an efficient procedure for sampling from the posterior distribution in the 'L0 sparse' regime, where latent variables are encouraged to be set to zero as opposed to having a small L1 norm.
- Score: 3.0600309122672726
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We describe a stochastic, dynamical system capable of inference and learning
in a probabilistic latent variable model. The most challenging problem in such
models - sampling the posterior distribution over latent variables - is
proposed to be solved by harnessing natural sources of stochasticity inherent
in electronic and neural systems. We demonstrate this idea for a sparse coding
model by deriving a continuous-time equation for inferring its latent variables
via Langevin dynamics. The model parameters are learned by simultaneously
evolving according to another continuous-time equation, thus bypassing the need
for digital accumulators or a global clock. Moreover we show that Langevin
dynamics lead to an efficient procedure for sampling from the posterior
distribution in the 'L0 sparse' regime, where latent variables are encouraged
to be set to zero as opposed to having a small L1 norm. This allows the model
to properly incorporate the notion of sparsity rather than having to resort to
a relaxed version of sparsity to make optimization tractable. Simulations of
the proposed dynamical system on both synthetic and natural image datasets
demonstrate that the model is capable of probabilistically correct inference,
enabling learning of the dictionary as well as parameters of the prior.
Related papers
- Path-minimizing Latent ODEs for improved extrapolation and inference [0.0]
Latent ODE models provide flexible descriptions of dynamic systems, but they can struggle with extrapolation and predicting complicated non-linear dynamics.
In this paper we exploit this dichotomy by encouraging time-independent latent representations.
By replacing the common variational penalty in latent space with an $ell$ penalty on the path length of each system, the models learn data representations that can easily be distinguished from those of systems with different configurations.
This results in faster training, smaller models, more accurate and long-time extrapolation compared to the baseline ODE models with GRU, RNN, and LSTM/decoders on tests with
arXiv Detail & Related papers (2024-10-11T15:50:01Z) - Latent Space Energy-based Neural ODEs [73.01344439786524]
This paper introduces a novel family of deep dynamical models designed to represent continuous-time sequence data.
We train the model using maximum likelihood estimation with Markov chain Monte Carlo.
Experiments on oscillating systems, videos and real-world state sequences (MuJoCo) illustrate that ODEs with the learnable energy-based prior outperform existing counterparts.
arXiv Detail & Related papers (2024-09-05T18:14:22Z) - On the Trajectory Regularity of ODE-based Diffusion Sampling [79.17334230868693]
Diffusion-based generative models use differential equations to establish a smooth connection between a complex data distribution and a tractable prior distribution.
In this paper, we identify several intriguing trajectory properties in the ODE-based sampling process of diffusion models.
arXiv Detail & Related papers (2024-05-18T15:59:41Z) - Capturing dynamical correlations using implicit neural representations [85.66456606776552]
We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data.
In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
arXiv Detail & Related papers (2023-04-08T07:55:36Z) - Anamnesic Neural Differential Equations with Orthogonal Polynomial
Projections [6.345523830122166]
We propose PolyODE, a formulation that enforces long-range memory and preserves a global representation of the underlying dynamical system.
Our construction is backed by favourable theoretical guarantees and we demonstrate that it outperforms previous works in the reconstruction of past and future data.
arXiv Detail & Related papers (2023-03-03T10:49:09Z) - Capturing Actionable Dynamics with Structured Latent Ordinary
Differential Equations [68.62843292346813]
We propose a structured latent ODE model that captures system input variations within its latent representation.
Building on a static variable specification, our model learns factors of variation for each input to the system, thus separating the effects of the system inputs in the latent space.
arXiv Detail & Related papers (2022-02-25T20:00:56Z) - Anomaly Detection of Time Series with Smoothness-Inducing Sequential
Variational Auto-Encoder [59.69303945834122]
We present a Smoothness-Inducing Sequential Variational Auto-Encoder (SISVAE) model for robust estimation and anomaly detection of time series.
Our model parameterizes mean and variance for each time-stamp with flexible neural networks.
We show the effectiveness of our model on both synthetic datasets and public real-world benchmarks.
arXiv Detail & Related papers (2021-02-02T06:15:15Z) - ImitationFlow: Learning Deep Stable Stochastic Dynamic Systems by
Normalizing Flows [29.310742141970394]
We introduce ImitationFlow, a novel Deep generative model that allows learning complex globally stable, nonlinear dynamics.
We show the effectiveness of our method with both standard datasets and a real robot experiment.
arXiv Detail & Related papers (2020-10-25T14:49:46Z) - Variational inference formulation for a model-free simulation of a
dynamical system with unknown parameters by a recurrent neural network [8.616180927172548]
We propose a "model-free" simulation of a dynamical system with unknown parameters without prior knowledge.
The deep learning model aims to jointly learn the nonlinear time marching operator and the effects of the unknown parameters from a time series dataset.
It is found that the proposed deep learning model is capable of correctly identifying the dimensions of the random parameters and learning a representation of complex time series data.
arXiv Detail & Related papers (2020-03-02T20:57:02Z) - Variational Hyper RNN for Sequence Modeling [69.0659591456772]
We propose a novel probabilistic sequence model that excels at capturing high variability in time series data.
Our method uses temporal latent variables to capture information about the underlying data pattern.
The efficacy of the proposed method is demonstrated on a range of synthetic and real-world sequential data.
arXiv Detail & Related papers (2020-02-24T19:30:32Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.