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 $t$ to propose states at time $t$ 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

Bayesian Analysis of High Dimensional Vector Error Correction Model

Vector Error Correction Model (VECM) is a classic method to analyse cointegration relationships amongst multivariate non-stationary time series. In this paper, we focus on high dimensional setting and seek for sample-size-efficient methodology to determine the level of cointegration. Our investigation centres at a Bayesian approach to analyse the cointegration matrix, henceforth determining the cointegration rank. We design two algorithms and implement them on simulated examples, yielding promising results particularly when dealing with high number of variables and relatively low number of observations. Furthermore, we extend this methodology to empirically investigate the constituents of the S&P 500 index, where low-volatility portfolios can be found during both in-sample training and out-of-sample testing periods

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