13,384 research outputs found
Latent Autoregressive Source Separation
Autoregressive models have achieved impressive results over a wide range of
domains in terms of generation quality and downstream task performance. In the
continuous domain, a key factor behind this success is the usage of quantized
latent spaces (e.g., obtained via VQ-VAE autoencoders), which allow for
dimensionality reduction and faster inference times. However, using existing
pre-trained models to perform new non-trivial tasks is difficult since it
requires additional fine-tuning or extensive training to elicit prompting. This
paper introduces LASS as a way to perform vector-quantized Latent
Autoregressive Source Separation (i.e., de-mixing an input signal into its
constituent sources) without requiring additional gradient-based optimization
or modifications of existing models. Our separation method relies on the
Bayesian formulation in which the autoregressive models are the priors, and a
discrete (non-parametric) likelihood function is constructed by performing
frequency counts over latent sums of addend tokens. We test our method on
images and audio with several sampling strategies (e.g., ancestral, beam
search) showing competitive results with existing approaches in terms of
separation quality while offering at the same time significant speedups in
terms of inference time and scalability to higher dimensional data.Comment: Accepted to AAAI 202
Robust Bayesian inference via coarsening
The standard approach to Bayesian inference is based on the assumption that
the distribution of the data belongs to the chosen model class. However, even a
small violation of this assumption can have a large impact on the outcome of a
Bayesian procedure. We introduce a simple, coherent approach to Bayesian
inference that improves robustness to perturbations from the model: rather than
condition on the data exactly, one conditions on a neighborhood of the
empirical distribution. When using neighborhoods based on relative entropy
estimates, the resulting "coarsened" posterior can be approximated by simply
tempering the likelihood---that is, by raising it to a fractional power---thus,
inference is often easily implemented with standard methods, and one can even
obtain analytical solutions when using conjugate priors. Some theoretical
properties are derived, and we illustrate the approach with real and simulated
data, using mixture models, autoregressive models of unknown order, and
variable selection in linear regression
Bayesian Model Selection for Beta Autoregressive Processes
We deal with Bayesian inference for Beta autoregressive processes. We
restrict our attention to the class of conditionally linear processes. These
processes are particularly suitable for forecasting purposes, but are difficult
to estimate due to the constraints on the parameter space. We provide a full
Bayesian approach to the estimation and include the parameter restrictions in
the inference problem by a suitable specification of the prior distributions.
Moreover in a Bayesian framework parameter estimation and model choice can be
solved simultaneously. In particular we suggest a Markov-Chain Monte Carlo
(MCMC) procedure based on a Metropolis-Hastings within Gibbs algorithm and
solve the model selection problem following a reversible jump MCMC approach
A spliced Gamma-Generalized Pareto model for short-term extreme wind speed probabilistic forecasting
Renewable sources of energy such as wind power have become a sustainable
alternative to fossil fuel-based energy. However, the uncertainty and
fluctuation of the wind speed derived from its intermittent nature bring a
great threat to the wind power production stability, and to the wind turbines
themselves. Lately, much work has been done on developing models to forecast
average wind speed values, yet surprisingly little has focused on proposing
models to accurately forecast extreme wind speeds, which can damage the
turbines. In this work, we develop a flexible spliced Gamma-Generalized Pareto
model to forecast extreme and non-extreme wind speeds simultaneously. Our model
belongs to the class of latent Gaussian models, for which inference is
conveniently performed based on the integrated nested Laplace approximation
method. Considering a flexible additive regression structure, we propose two
models for the latent linear predictor to capture the spatio-temporal dynamics
of wind speeds. Our models are fast to fit and can describe both the bulk and
the tail of the wind speed distribution while producing short-term extreme and
non-extreme wind speed probabilistic forecasts.Comment: 25 page
A Simple Class of Bayesian Nonparametric Autoregression Models
We introduce a model for a time series of continuous outcomes, that can be expressed as fully nonparametric regression or density regression on lagged terms. The model is based on a dependent Dirichlet process prior on a family of random probability measures indexed by the lagged covariates. The approach is also extended to sequences of binary responses. We discuss implementation and applications of the models to a sequence of waiting times between eruptions of the Old Faithful Geyser, and to a dataset consisting of sequences of recurrence indicators for tumors in the bladder of several patients.MIUR 2008MK3AFZFONDECYT 1100010NIH/NCI R01CA075981Mathematic
Bayesian Nonparametric Calibration and Combination of Predictive Distributions
We introduce a Bayesian approach to predictive density calibration and
combination that accounts for parameter uncertainty and model set
incompleteness through the use of random calibration functionals and random
combination weights. Building on the work of Ranjan, R. and Gneiting, T. (2010)
and Gneiting, T. and Ranjan, R. (2013), we use infinite beta mixtures for the
calibration. The proposed Bayesian nonparametric approach takes advantage of
the flexibility of Dirichlet process mixtures to achieve any continuous
deformation of linearly combined predictive distributions. The inference
procedure is based on Gibbs sampling and allows accounting for uncertainty in
the number of mixture components, mixture weights, and calibration parameters.
The weak posterior consistency of the Bayesian nonparametric calibration is
provided under suitable conditions for unknown true density. We study the
methodology in simulation examples with fat tails and multimodal densities and
apply it to density forecasts of daily S&P returns and daily maximum wind speed
at the Frankfurt airport.Comment: arXiv admin note: text overlap with arXiv:1305.2026 by other author
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