Hierarchical State Space Research Articles

TREE GROWTH INFERENCE AND PREDICTION FROM DIAMETER CENSUSES AND RING WIDTHS

Estimation of tree growth is based on sparse observations of tree diameter, ring widths, or increments read from a dendrometer. From annual measurements on a few trees (e.g., increment cores) or sporadic measurements from many trees (e.g., diameter censuses on mapped plots), relationships with resources, tree size, and climate are extrapolated to whole stands. There has been no way to formally integrate different types of data and problems of estimation that result from (1) multiple sources of observation error, which frequently result in impossible estimates of negative growth, (2) the fact that data are typically sparse (a few trees or a few years), whereas inference is needed broadly (many trees over many years), (3) the fact that some unknown fraction of the variance is shared across the population, and (4) the fact that growth rates of trees within competing stands are not independent. We develop a hierarchical Bayes state space model for tree growth that addresses all of these challenges, allowing for formal inference that is consistent with the available data and the assumption that growth is nonnegative. Prediction follows directly, incorporating the full uncertainty from inference with scenarios for "filling the gaps" for past growth rates and for future conditions affecting growth. An example involving multiple species and multiple stands with tree-ring data and up to 14 years of tree census data illustrates how different levels of information at the tree and stand level contribute to inference and prediction.

A neurologically plausible implementation of statistical inference applied to random dot motion

We propose a model of basic motion perception consisting of a hierarchical non-linear state space model (NSSM) developed within a variational Bayesian (VB) framework. Each level of the hierarchy is a `cause' that generates a prior distribution on the level below via a generative function. The temporal dynamics and generative functions between layers of the hierarchy are implemented as neural networks with non-linear activation functions. Optimization of model parameters and causes proceed concurrently as a combination of fixed-point rules and gradient decent schemes. To make the optimization problem tractable, the standard mean-field and Laplace approximations are employed. The precise factoring used in the mean-field approximation is designed to meet a balance between tractability, neurological plausibility and modeling power. In this approach inference and learning proceed concurrently, in an online and unsupervised fashion. Other work has produced similar implementations of NSSMs that have been successful in predicting low-dimensional temporal signals, but with highly restrictive assumptions on the form of the posterior distributions and with learning done in batches instead of online [1]. Competing work has relaxed many of these implementation assumptions and achieved prediction of high dimensional input but at the cost of discarding VB techniques in favor of inefficient discrete state-space methods [2]. Moreover, such techniques have been demonstrated only with pre-learned weights and simplistic statistical models. Our model is primarily tested on realistic high-dimensional input generated by randomly moving dots over a detection grid. The results from a spiking neuron implementation of the model based on the Neural Engineering Framework (NEF) are compared directly to single cell recordings in random dot motion perception and decision-making tasks.

Robust hierarchical state–space models reveal diel variation in travel rates of migrating leatherback turtles

1. Biological and statistical complexity are features common to most ecological data that hinder our ability to extract meaningful patterns using conventional tools. Recent work on implementing modern statistical methods for analysis of such ecological data has focused primarily on population dynamics but other types of data, such as animal movement pathways obtained from satellite telemetry, can also benefit from the application of modern statistical tools. 2. We develop a robust hierarchical state-space approach for analysis of multiple satellite telemetry pathways obtained via the Argos system. State-space models are time-series methods that allow unobserved states and biological parameters to be estimated from data observed with error. We show that the approach can reveal important patterns in complex, noisy data where conventional methods cannot. 3. Using the largest Atlantic satellite telemetry data set for critically endangered leatherback turtles, we show that the diel pattern in travel rates of these turtles changes over different phases of their migratory cycle. While foraging in northern waters the turtles show similar travel rates during day and night, but on their southward migration to tropical waters travel rates are markedly faster during the day. These patterns are generally consistent with diving data, and may be related to changes in foraging behaviour. Interestingly, individuals that migrate southward to breed generally show higher daytime travel rates than individuals that migrate southward in a non-breeding year. 4. Our approach is extremely flexible and can be applied to many ecological analyses that use complex, sequential data.

State hierarchy induced by correlated spin domains in short-range spin glasses

We generate equilibrium configurations for the three and four dimensional Ising spin glass with Gaussian distributed couplings at temperatures well below the transition temperature T_c. These states are analyzed by a recently proposed method using clustering. The analysis reveals a hierarchical state space structure. At each level of the hierarchy states are labeled by the orientations of a set of correlated macroscopic spin domains. Our picture of the low temperature phase of short range spin glasses is that of a State Hierarchy Induced by Correlated Spin domains (SHICS). The complexity of the low temperature phase is manifest in the fact that the composition of such a spin domain (i.e. its constituent spins), as well as its identifying label, are defined and determined by the ``location'' in the state hierarchy at which it appears. Mapping out the phase space structure by means of the orientations assumed by these domains enhances our ability to investigate the overlap distribution, which we find to be non-trivial. Evidence is also presented that these states may have a non-ultrametric structure.

Hierarchical state space partitioning with a network self-organising map for the recognition of ST-T segment changes.

The problem of maximising the performance of ST-T segment automatic recognition for ischaemia detection is a difficult pattern classification problem. The paper proposes the network self-organising map (NetSOM) model as an enhancement to the Kohonen self-organised map (SOM) model. This model is capable of effectively decomposing complex large-scale pattern classification problems into a number of partitions, each of which is more manageable with a local classification device. The NetSOM attempts to generalize the regularization and ordering potential of the basic SOM from the space of vectors to the space of approximating functions. It becomes a device for the ordering of local experts (i.e. independent neural networks) over its lattice of neurons and for their selection and co-ordination. Each local expert is an independent neural network that is trained and activated under the control of the NetSOM. This method is evaluated with examples from the European ST-T database. The first results obtained after the application of NetSOM to ST-T segment change recognition show a significant improvement in the performance compared with that obtained with monolithic approaches, i.e. with single network types. The basic SOM model has attained an average ischaemic beat sensitivity of 73.6% and an average ischaemic beat predictivity of 68.3%. The work reports and discusses the improvements that have been obtained from the implementation of a NetSOM classification system with both multilayer perceptrons and radial basis function (RBF) networks as local experts for the ST-T segment change problem. Specifically, the NetSOM with multilayer perceptrons (radial basis functions) as local experts has improved the results over the basic SOM to an average ischaemic beat sensitivity of 75.9% (77.7%) and an average ischaemic beat predictivity of 72.5% (74.1%).

Task analysis for error identification: a methodology for designing error-tolerant consumer products

Abstract This paper presents an approach to the assessment of ‘intelligent’ consumer products. We assume that a primary reason for the difficulties people encounter in their use of intelligent consumer products is the lack of clear, consistent, and logical task sequences. The approach we have developed aims to illustrate the task sequences required for the purposeful use of ‘intelligent’ products, in order to indicate points at which errors, problems or confusions may occur. The approach combines two well proven methodologies (hierarchical task analysis and state space diagrams) to provide a description of human product interaction.