4,018 research outputs found
Learning Hybrid System Models for Supervisory Decoding of Discrete State, with applications to the Parietal Reach Region
Based on Gibbs sampling, a novel method to identify mathematical models of neural activity in response to temporal changes of behavioral or cognitive state is presented. This work is motivated by the developing field of neural prosthetics, where a supervisory controller is required to classify activity of a brain region into suitable discrete modes. Here, neural activity in each discrete mode is modeled with nonstationary point processes, and transitions between modes are modeled as hidden Markov models. The effectiveness of this framework is first demonstrated on a simulated example. The identification algorithm is then applied to extracellular neural activity recorded from multi-electrode arrays in the parietal reach region of a rhesus monkey, and the results demonstrate the ability to decode discrete changes even from small data sets
Capacity and Complexity of HMM Duration Modeling Techniques
The ability of a standard hidden Markov model (HMM) or expanded state HMM (ESHMM) to accurately model duration distributions of phonemes is compared with specific duration-focused approaches such as semi-Markov models or variable transition probabilities. It is demonstrated that either a three-state ESHMM or a standard HMM with an increased number of states is capable of closely matching both Gamma distributions and duration distributions of phonemes from the TIMIT corpus, as measured by Bhattacharyya distance to the true distributions. Standard HMMs are easily implemented with off-the-shelf tools, whereas duration models require substantial algorithmic development and have higher computational costs when implemented, suggesting that a simple adjustment to HMM topologies is perhaps a more efficient solution to the problem of duration than more complex approaches
Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime
An autoregressive process with Markov regime is an autoregressive process for
which the regression function at each time point is given by a nonobservable
Markov chain. In this paper we consider the asymptotic properties of the
maximum likelihood estimator in a possibly nonstationary process of this kind
for which the hidden state space is compact but not necessarily finite.
Consistency and asymptotic normality are shown to follow from uniform
exponential forgetting of the initial distribution for the hidden Markov chain
conditional on the observations.Comment: Published at http://dx.doi.org/10.1214/009053604000000021 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Emergence of event cascades in inhomogeneous networks
There is a commonality among contagious diseases, tweets, urban crimes,
nuclear reactions, and neuronal firings that past events facilitate the future
occurrence of events. The spread of events has been extensively studied such
that the systems exhibit catastrophic chain reactions if the interaction
represented by the ratio of reproduction exceeds unity; however, their
subthreshold states for the case of the weaker interaction are not fully
understood. Here, we report that these systems are possessed by nonstationary
cascades of event-occurrences already in the subthreshold regime. Event
cascades can be harmful in some contexts, when the peak-demand causes vaccine
shortages, heavy traffic on communication lines, frequent crimes, or large
fluctuations in nuclear reactions, but may be beneficial in other contexts,
such that spontaneous activity in neural networks may be used to generate
motion or store memory. Thus it is important to comprehend the mechanism by
which such cascades appear, and consider controlling a system to tame or
facilitate fluctuations in the event-occurrences. The critical interaction for
the emergence of cascades depends greatly on the network structure in which
individuals are connected. We demonstrate that we can predict whether cascades
may emerge in a network, given information about the interactions between
individuals. Furthermore, we develop a method of reallocating connections among
individuals so that event cascades may be either impeded or impelled in a
network.Comment: 16 pages, 5 figure
A Bayesian Nonparametric Markovian Model for Nonstationary Time Series
Stationary time series models built from parametric distributions are, in
general, limited in scope due to the assumptions imposed on the residual
distribution and autoregression relationship. We present a modeling approach
for univariate time series data, which makes no assumptions of stationarity,
and can accommodate complex dynamics and capture nonstandard distributions. The
model for the transition density arises from the conditional distribution
implied by a Bayesian nonparametric mixture of bivariate normals. This implies
a flexible autoregressive form for the conditional transition density, defining
a time-homogeneous, nonstationary, Markovian model for real-valued data indexed
in discrete-time. To obtain a more computationally tractable algorithm for
posterior inference, we utilize a square-root-free Cholesky decomposition of
the mixture kernel covariance matrix. Results from simulated data suggest the
model is able to recover challenging transition and predictive densities. We
also illustrate the model on time intervals between eruptions of the Old
Faithful geyser. Extensions to accommodate higher order structure and to
develop a state-space model are also discussed
A New MCMC Sampling Based Segment Model for Radar Target Recognition
One of the main tools in radar target recognition is high resolution range profile (HRRP)â. âHoweverâ, âit is very sensitive to the aspect angleâ. âOne solution to this problem is to assume the consecutive samples of HRRP identically independently distributed (IID) in small frames of aspect anglesâ, âan assumption which is not true in realityâ. âHowever, bââased on this assumptionâ, âsome models have been developed to characterize the sequential information contained in the multi-aspect radar echoesâ. âThereforeâ, âthey only consider the short dependency between consecutive samplesâ. âHereâ, âwe propose an alternative modelâ, âthe segment modelâ, âto address the shortcomings of these assumptionsâ. âIn additionâ, âusing a Markov chain Monte-Carlo (MCMC) based Gibbs sampler as an iterative approach to estimate the parameters of the segment modelâ, âwe will show that the proposed method is able to estimate the parameters with quite satisfying accuracy and computational loadâ
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