65,418 research outputs found
A Tractable State-Space Model for Symmetric Positive-Definite Matrices
Bayesian analysis of state-space models includes computing the posterior
distribution of the system's parameters as well as filtering, smoothing, and
predicting the system's latent states. When the latent states wander around
there are several well-known modeling components and
computational tools that may be profitably combined to achieve these tasks.
However, there are scenarios, like tracking an object in a video or tracking a
covariance matrix of financial assets returns, when the latent states are
restricted to a curve within and these models and tools do not
immediately apply. Within this constrained setting, most work has focused on
filtering and less attention has been paid to the other aspects of Bayesian
state-space inference, which tend to be more challenging. To that end, we
present a state-space model whose latent states take values on the manifold of
symmetric positive-definite matrices and for which one may easily compute the
posterior distribution of the latent states and the system's parameters, in
addition to filtered distributions and one-step ahead predictions. Deploying
the model within the context of finance, we show how one can use realized
covariance matrices as data to predict latent time-varying covariance matrices.
This approach out-performs factor stochastic volatility.Comment: 22 pages: 16 pages main manuscript, 4 pages appendix, 2 pages
reference
Dynamic Clustering via Asymptotics of the Dependent Dirichlet Process Mixture
This paper presents a novel algorithm, based upon the dependent Dirichlet
process mixture model (DDPMM), for clustering batch-sequential data containing
an unknown number of evolving clusters. The algorithm is derived via a
low-variance asymptotic analysis of the Gibbs sampling algorithm for the DDPMM,
and provides a hard clustering with convergence guarantees similar to those of
the k-means algorithm. Empirical results from a synthetic test with moving
Gaussian clusters and a test with real ADS-B aircraft trajectory data
demonstrate that the algorithm requires orders of magnitude less computational
time than contemporary probabilistic and hard clustering algorithms, while
providing higher accuracy on the examined datasets.Comment: This paper is from NIPS 2013. Please use the following BibTeX
citation: @inproceedings{Campbell13_NIPS, Author = {Trevor Campbell and Miao
Liu and Brian Kulis and Jonathan P. How and Lawrence Carin}, Title = {Dynamic
Clustering via Asymptotics of the Dependent Dirichlet Process}, Booktitle =
{Advances in Neural Information Processing Systems (NIPS)}, Year = {2013}
Bayesian forecasting and scalable multivariate volatility analysis using simultaneous graphical dynamic models
The recently introduced class of simultaneous graphical dynamic linear models
(SGDLMs) defines an ability to scale on-line Bayesian analysis and forecasting
to higher-dimensional time series. This paper advances the methodology of
SGDLMs, developing and embedding a novel, adaptive method of simultaneous
predictor selection in forward filtering for on-line learning and forecasting.
The advances include developments in Bayesian computation for scalability, and
a case study in exploring the resulting potential for improved short-term
forecasting of large-scale volatility matrices. A case study concerns financial
forecasting and portfolio optimization with a 400-dimensional series of daily
stock prices. Analysis shows that the SGDLM forecasts volatilities and
co-volatilities well, making it ideally suited to contributing to quantitative
investment strategies to improve portfolio returns. We also identify
performance metrics linked to the sequential Bayesian filtering analysis that
turn out to define a leading indicator of increased financial market stresses,
comparable to but leading the standard St. Louis Fed Financial Stress Index
(STLFSI) measure. Parallel computation using GPU implementations substantially
advance the ability to fit and use these models.Comment: 28 pages, 9 figures, 7 table
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A Mixed-Effects Location Scale Model for Dyadic Interactions.
We present a mixed-effects location scale model (MELSM) for examining the daily dynamics of affect in dyads. The MELSM includes person and time-varying variables to predict the location, or individual means, and the scale, or within-person variances. It also incorporates a submodel to account for between-person variances. The dyadic specification can accommodate individual and partner effects in both the location and the scale components, and allows random effects for all location and scale parameters. All covariances among the random effects, within and across the location and the scale are also estimated. These covariances offer new insights into the interplay of individual mean structures, intra-individual variability, and the influence of partner effects on such factors. To illustrate the model, we use data from 274 couples who provided daily ratings on their positive and negative emotions toward their relationship - up to 90 consecutive days. The model is fit using Hamiltonian Monte Carlo methods, and includes subsets of predictors in order to demonstrate the flexibility of this approach. We conclude with a discussion on the usefulness and the limitations of the MELSM for dyadic research
A Spatio-Temporal Point Process Model for Ambulance Demand
Ambulance demand estimation at fine time and location scales is critical for
fleet management and dynamic deployment. We are motivated by the problem of
estimating the spatial distribution of ambulance demand in Toronto, Canada, as
it changes over discrete 2-hour intervals. This large-scale dataset is sparse
at the desired temporal resolutions and exhibits location-specific serial
dependence, daily and weekly seasonality. We address these challenges by
introducing a novel characterization of time-varying Gaussian mixture models.
We fix the mixture component distributions across all time periods to overcome
data sparsity and accurately describe Toronto's spatial structure, while
representing the complex spatio-temporal dynamics through time-varying mixture
weights. We constrain the mixture weights to capture weekly seasonality, and
apply a conditionally autoregressive prior on the mixture weights of each
component to represent location-specific short-term serial dependence and daily
seasonality. While estimation may be performed using a fixed number of mixture
components, we also extend to estimate the number of components using
birth-and-death Markov chain Monte Carlo. The proposed model is shown to give
higher statistical predictive accuracy and to reduce the error in predicting
EMS operational performance by as much as two-thirds compared to a typical
industry practice
Predictive information in Gaussian processes with application to music analysis
This is the author's accepted manuscript of this article. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-40020-9.Lecture Notes in Computer ScienceLecture Notes in Computer ScienceWe describe an information-theoretic approach to the analysis of sequential data, which emphasises the predictive aspects of perception, and the dynamic process of forming and modifying expectations about an unfolding stream of data, characterising these using a set of process information measures. After reviewing the theoretical foundations and the definition of the predictive information rate, we describe how this can be computed for Gaussian processes, including how the approach can be adpated to non-stationary processes, using an online Bayesian spectral estimation method to compute the Bayesian surprise. We finish with a sample analysis of a recording of Steve Reich’s Drummin
Bayesian Nonstationary Spatial Modeling for Very Large Datasets
With the proliferation of modern high-resolution measuring instruments
mounted on satellites, planes, ground-based vehicles and monitoring stations, a
need has arisen for statistical methods suitable for the analysis of large
spatial datasets observed on large spatial domains. Statistical analyses of
such datasets provide two main challenges: First, traditional
spatial-statistical techniques are often unable to handle large numbers of
observations in a computationally feasible way. Second, for large and
heterogeneous spatial domains, it is often not appropriate to assume that a
process of interest is stationary over the entire domain.
We address the first challenge by using a model combining a low-rank
component, which allows for flexible modeling of medium-to-long-range
dependence via a set of spatial basis functions, with a tapered remainder
component, which allows for modeling of local dependence using a compactly
supported covariance function. Addressing the second challenge, we propose two
extensions to this model that result in increased flexibility: First, the model
is parameterized based on a nonstationary Matern covariance, where the
parameters vary smoothly across space. Second, in our fully Bayesian model, all
components and parameters are considered random, including the number,
locations, and shapes of the basis functions used in the low-rank component.
Using simulated data and a real-world dataset of high-resolution soil
measurements, we show that both extensions can result in substantial
improvements over the current state-of-the-art.Comment: 16 pages, 2 color figure
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