12 research outputs found
Replica Conditional Sequential Monte Carlo
We propose a Markov chain Monte Carlo (MCMC) scheme to perform state
inference in non-linear non-Gaussian state-space models. Current
state-of-the-art methods to address this problem rely on particle MCMC
techniques and its variants, such as the iterated conditional Sequential Monte
Carlo (cSMC) scheme, which uses a Sequential Monte Carlo (SMC) type proposal
within MCMC. A deficiency of standard SMC proposals is that they only use
observations up to time to propose states at time when an entire
observation sequence is available. More sophisticated SMC based on lookahead
techniques could be used but they can be difficult to put in practice. We
propose here replica cSMC where we build SMC proposals for one replica using
information from the entire observation sequence by conditioning on the states
of the other replicas. This approach is easily parallelizable and we
demonstrate its excellent empirical performance when compared to the standard
iterated cSMC scheme at fixed computational complexity.Comment: To appear in Proceedings of ICML '1
Efficient Bayesian inference for stochastic volatility models with ensemble MCMC methods
In this paper, we introduce efficient ensemble Markov Chain Monte Carlo
(MCMC) sampling methods for Bayesian computations in the univariate stochastic
volatility model. We compare the performance of our ensemble MCMC methods with
an improved version of a recent sampler of Kastner and Fruwirth-Schnatter
(2014). We show that ensemble samplers are more efficient than this state of
the art sampler by a factor of about 3.1, on a data set simulated from the
stochastic volatility model. This performance gain is achieved without the
ensemble MCMC sampler relying on the assumption that the latent process is
linear and Gaussian, unlike the sampler of Kastner and Fruwirth-Schnatter
Dynamic Time Warping for Lead-Lag Relationships in Lagged Multi-Factor Models
In multivariate time series systems, lead-lag relationships reveal
dependencies between time series when they are shifted in time relative to each
other. Uncovering such relationships is valuable in downstream tasks, such as
control, forecasting, and clustering. By understanding the temporal
dependencies between different time series, one can better comprehend the
complex interactions and patterns within the system. We develop a
cluster-driven methodology based on dynamic time warping for robust detection
of lead-lag relationships in lagged multi-factor models. We establish
connections to the multireference alignment problem for both the homogeneous
and heterogeneous settings. Since multivariate time series are ubiquitous in a
wide range of domains, we demonstrate that our algorithm is able to robustly
detect lead-lag relationships in financial markets, which can be subsequently
leveraged in trading strategies with significant economic benefits.Comment: arXiv admin note: substantial text overlap with arXiv:2305.0670
Uncertainty Quantification in Bayesian Reduced-Rank Sparse Regressions
Reduced-rank regression recognises the possibility of a rank-deficient matrix
of coefficients, which is particularly useful when the data is
high-dimensional. We propose a novel Bayesian model for estimating the rank of
the rank of the coefficient matrix, which obviates the need of post-processing
steps, and allows for uncertainty quantification. Our method employs a mixture
prior on the regression coefficient matrix along with a global-local shrinkage
prior on its low-rank decomposition. Then, we rely on the Signal Adaptive
Variable Selector to perform sparsification, and define two novel tools, the
Posterior Inclusion Probability uncertainty index and the Relevance Index. The
validity of the method is assessed in a simulation study, then its advantages
and usefulness are shown in real-data applications on the chemical composition
of tobacco and on the photometry of galaxies
Low-rank extended Kalman filtering for online learning of neural networks from streaming data
We propose an efficient online approximate Bayesian inference algorithm for
estimating the parameters of a nonlinear function from a potentially
non-stationary data stream. The method is based on the extended Kalman filter
(EKF), but uses a novel low-rank plus diagonal decomposition of the posterior
precision matrix, which gives a cost per step which is linear in the number of
model parameters. In contrast to methods based on stochastic variational
inference, our method is fully deterministic, and does not require step-size
tuning. We show experimentally that this results in much faster (more sample
efficient) learning, which results in more rapid adaptation to changing
distributions, and faster accumulation of reward when used as part of a
contextual bandit algorithm
On Bayesian inference for the M/G/1 queue with efficient MCMC sampling
We introduce an efficient MCMC sampling scheme to perform Bayesian inference in the M/G/1 queueing model given only observations of interdeparture times. Our MCMC scheme uses a combination of Gibbs sampling and simple Metropolis updates together with three novel âshift â and âscale â updates. We show that our novel updates improve the speed of sampling considerably, by factors of about 60 to about 180 on a variety of simulated data sets. This paper proposes a new approach to computation for Bayesian inference for the M/G/1 queue (Markovian arrival process/General service time distribution/1 server). Inference for this model using ABC (Approximate Bayesian Computation) was previously considered by Bonassi (2013), Fearnhead and Prangle (2012), and Blum and Francois (2010). ABC, in general, does not yield samples from the exact posterior distribution. We use the strategy of considering certain unobserved quantities as latent variables, allowing us to use Markov Chain Monte Carlo (MCMC), which converges to the exact posterior distribution. 1 The mode