1,799 research outputs found
Delayed Sampling and Automatic Rao-Blackwellization of Probabilistic Programs
We introduce a dynamic mechanism for the solution of analytically-tractable
substructure in probabilistic programs, using conjugate priors and affine
transformations to reduce variance in Monte Carlo estimators. For inference
with Sequential Monte Carlo, this automatically yields improvements such as
locally-optimal proposals and Rao-Blackwellization. The mechanism maintains a
directed graph alongside the running program that evolves dynamically as
operations are triggered upon it. Nodes of the graph represent random
variables, edges the analytically-tractable relationships between them. Random
variables remain in the graph for as long as possible, to be sampled only when
they are used by the program in a way that cannot be resolved analytically. In
the meantime, they are conditioned on as many observations as possible. We
demonstrate the mechanism with a few pedagogical examples, as well as a
linear-nonlinear state-space model with simulated data, and an epidemiological
model with real data of a dengue outbreak in Micronesia. In all cases one or
more variables are automatically marginalized out to significantly reduce
variance in estimates of the marginal likelihood, in the final case
facilitating a random-weight or pseudo-marginal-type importance sampler for
parameter estimation. We have implemented the approach in Anglican and a new
probabilistic programming language called Birch.Comment: 13 pages, 4 figure
A program for the Bayesian Neural Network in the ROOT framework
We present a Bayesian Neural Network algorithm implemented in the TMVA
package, within the ROOT framework. Comparing to the conventional utilization
of Neural Network as discriminator, this new implementation has more advantages
as a non-parametric regression tool, particularly for fitting probabilities. It
provides functionalities including cost function selection, complexity control
and uncertainty estimation. An example of such application in High Energy
Physics is shown. The algorithm is available with ROOT release later than 5.29.Comment: 12 pages, 6 figure
Sequential Gaussian Processes for Online Learning of Nonstationary Functions
Many machine learning problems can be framed in the context of estimating
functions, and often these are time-dependent functions that are estimated in
real-time as observations arrive. Gaussian processes (GPs) are an attractive
choice for modeling real-valued nonlinear functions due to their flexibility
and uncertainty quantification. However, the typical GP regression model
suffers from several drawbacks: i) Conventional GP inference scales
with respect to the number of observations; ii) updating a GP model
sequentially is not trivial; and iii) covariance kernels often enforce
stationarity constraints on the function, while GPs with non-stationary
covariance kernels are often intractable to use in practice. To overcome these
issues, we propose an online sequential Monte Carlo algorithm to fit mixtures
of GPs that capture non-stationary behavior while allowing for fast,
distributed inference. By formulating hyperparameter optimization as a
multi-armed bandit problem, we accelerate mixing for real time inference. Our
approach empirically improves performance over state-of-the-art methods for
online GP estimation in the context of prediction for simulated non-stationary
data and hospital time series data
Surrogate model for an aligned-spin effective one body waveform model of binary neutron star inspirals using Gaussian process regression
Fast and accurate waveform models are necessary for measuring the properties
of inspiraling binary neutron star systems such as GW170817. We present a
frequency-domain surrogate version of the aligned-spin binary neutron star
waveform model using the effective one body formalism known as SEOBNRv4T. This
model includes the quadrupolar and octopolar adiabatic and dynamical tides. The
version presented here is improved by the inclusion of the spin-induced
quadrupole moment effect, and completed by a prescription for tapering the end
of the waveform to qualitatively reproduce numerical relativity simulations.
The resulting model has 14 intrinsic parameters. We reduce its dimensionality
by using universal relations that approximate all matter effects in terms of
the leading quadrupolar tidal parameters. The implementation of the time-domain
model can take up to an hour to evaluate using a starting frequency of 20Hz,
and this is too slow for many parameter estimation codes that require
sequential waveform evaluations. We therefore construct a fast and faithful
frequency-domain surrogate of this model using Gaussian process regression. The
resulting surrogate has a maximum mismatch of for the
Advanced LIGO detector, and requires 0.13s to evaluate for a waveform with a
starting frequency of 20Hz. Finally, we perform an end-to-end test of the
surrogate with a set of parameter estimation runs, and find that the surrogate
accurately recovers the parameters of injected waveforms.Comment: 19 pages, 10 figures, submitted to PR
A unified approach to mortality modelling using state-space framework: characterisation, identification, estimation and forecasting
This paper explores and develops alternative statistical representations and
estimation approaches for dynamic mortality models. The framework we adopt is
to reinterpret popular mortality models such as the Lee-Carter class of models
in a general state-space modelling methodology, which allows modelling,
estimation and forecasting of mortality under a unified framework. Furthermore,
we propose an alternative class of model identification constraints which is
more suited to statistical inference in filtering and parameter estimation
settings based on maximization of the marginalized likelihood or in Bayesian
inference. We then develop a novel class of Bayesian state-space models which
incorporate apriori beliefs about the mortality model characteristics as well
as for more flexible and appropriate assumptions relating to heteroscedasticity
that present in observed mortality data. We show that multiple period and
cohort effect can be cast under a state-space structure. To study long term
mortality dynamics, we introduce stochastic volatility to the period effect.
The estimation of the resulting stochastic volatility model of mortality is
performed using a recent class of Monte Carlo procedure specifically designed
for state and parameter estimation in Bayesian state-space models, known as the
class of particle Markov chain Monte Carlo methods. We illustrate the framework
we have developed using Danish male mortality data, and show that incorporating
heteroscedasticity and stochastic volatility markedly improves model fit
despite an increase of model complexity. Forecasting properties of the enhanced
models are examined with long term and short term calibration periods on the
reconstruction of life tables.Comment: 46 page
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