881 research outputs found
The effective temperature
This review presents the effective temperature notion as defined from the
deviations from the equilibrium fluctuation-dissipation theorem in out of
equilibrium systems with slow dynamics. The thermodynamic meaning of this
quantity is discussed in detail. Analytic, numeric and experimental
measurements are surveyed. Open issues are mentioned.Comment: 58 page
Bayesian Inference for partially observed SDEs Driven by Fractional Brownian Motion
We consider continuous-time diffusion models driven by fractional Brownian
motion. Observations are assumed to possess a non-trivial likelihood given the
latent path. Due to the non-Markovianity and high-dimensionality of the latent
paths, estimating posterior expectations is a computationally challenging
undertaking. We present a reparameterization framework based on the Davies and
Harte method for sampling stationary Gaussian processes and use this framework
to construct a Markov chain Monte Carlo algorithm that allows computationally
efficient Bayesian inference. The Markov chain Monte Carlo algorithm is based
on a version of hybrid Monte Carlo that delivers increased efficiency when
applied on the high-dimensional latent variables arising in this context. We
specify the methodology on a stochastic volatility model allowing for memory in
the volatility increments through a fractional specification. The methodology
is illustrated on simulated data and on the S&P500/VIX time series and is shown
to be effective. Contrary to a long range dependence attribute of such models
often assumed in the literature, with Hurst parameter larger than 1/2, the
posterior distribution favours values smaller than 1/2, pointing towards medium
range dependence
Energy Discrepancies: A Score-Independent Loss for Energy-Based Models
Energy-based models are a simple yet powerful class of probabilistic models,
but their widespread adoption has been limited by the computational burden of
training them. We propose a novel loss function called Energy Discrepancy (ED)
which does not rely on the computation of scores or expensive Markov chain
Monte Carlo. We show that ED approaches the explicit score matching and
negative log-likelihood loss under different limits, effectively interpolating
between both. Consequently, minimum ED estimation overcomes the problem of
nearsightedness encountered in score-based estimation methods, while also
enjoying theoretical guarantees. Through numerical experiments, we demonstrate
that ED learns low-dimensional data distributions faster and more accurately
than explicit score matching or contrastive divergence. For high-dimensional
image data, we describe how the manifold hypothesis puts limitations on our
approach and demonstrate the effectiveness of energy discrepancy by training
the energy-based model as a prior of a variational decoder model
A Survey on Generative Diffusion Model
Deep learning shows excellent potential in generation tasks thanks to deep
latent representation. Generative models are classes of models that can
generate observations randomly concerning certain implied parameters. Recently,
the diffusion Model has become a rising class of generative models by its
power-generating ability. Nowadays, great achievements have been reached. More
applications except for computer vision, speech generation, bioinformatics, and
natural language processing are to be explored in this field. However, the
diffusion model has its genuine drawback of a slow generation process, single
data types, low likelihood, and the inability for dimension reduction. They are
leading to many enhanced works. This survey makes a summary of the field of the
diffusion model. We first state the main problem with two landmark works --
DDPM and DSM, and a unified landmark work -- Score SDE. Then, we present
improved techniques for existing problems in the diffusion-based model field,
including speed-up improvement For model speed-up improvement, data structure
diversification, likelihood optimization, and dimension reduction. Regarding
existing models, we also provide a benchmark of FID score, IS, and NLL
according to specific NFE. Moreover, applications with diffusion models are
introduced including computer vision, sequence modeling, audio, and AI for
science. Finally, there is a summarization of this field together with
limitations \& further directions. The summation of existing well-classified
methods is in our
Github:https://github.com/chq1155/A-Survey-on-Generative-Diffusion-Model
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