27,805 research outputs found
Probabilistic Successor Representations with Kalman Temporal Differences
The effectiveness of Reinforcement Learning (RL) depends on an animal's
ability to assign credit for rewards to the appropriate preceding stimuli. One
aspect of understanding the neural underpinnings of this process involves
understanding what sorts of stimulus representations support generalisation.
The Successor Representation (SR), which enforces generalisation over states
that predict similar outcomes, has become an increasingly popular model in this
space of inquiries. Another dimension of credit assignment involves
understanding how animals handle uncertainty about learned associations, using
probabilistic methods such as Kalman Temporal Differences (KTD). Combining
these approaches, we propose using KTD to estimate a distribution over the SR.
KTD-SR captures uncertainty about the estimated SR as well as covariances
between different long-term predictions. We show that because of this, KTD-SR
exhibits partial transition revaluation as humans do in this experiment without
additional replay, unlike the standard TD-SR algorithm. We conclude by
discussing future applications of the KTD-SR as a model of the interaction
between predictive and probabilistic animal reasoning.Comment: Conference on Cognitive Computational Neuroscienc
State-space solutions to the dynamic magnetoencephalography inverse problem using high performance computing
Determining the magnitude and location of neural sources within the brain
that are responsible for generating magnetoencephalography (MEG) signals
measured on the surface of the head is a challenging problem in functional
neuroimaging. The number of potential sources within the brain exceeds by an
order of magnitude the number of recording sites. As a consequence, the
estimates for the magnitude and location of the neural sources will be
ill-conditioned because of the underdetermined nature of the problem. One
well-known technique designed to address this imbalance is the minimum norm
estimator (MNE). This approach imposes an regularization constraint that
serves to stabilize and condition the source parameter estimates. However,
these classes of regularizer are static in time and do not consider the
temporal constraints inherent to the biophysics of the MEG experiment. In this
paper we propose a dynamic state-space model that accounts for both spatial and
temporal correlations within and across candidate intracortical sources. In our
model, the observation model is derived from the steady-state solution to
Maxwell's equations while the latent model representing neural dynamics is
given by a random walk process.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS483 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Stochastic partial differential equation based modelling of large space-time data sets
Increasingly larger data sets of processes in space and time ask for
statistical models and methods that can cope with such data. We show that the
solution of a stochastic advection-diffusion partial differential equation
provides a flexible model class for spatio-temporal processes which is
computationally feasible also for large data sets. The Gaussian process defined
through the stochastic partial differential equation has in general a
nonseparable covariance structure. Furthermore, its parameters can be
physically interpreted as explicitly modeling phenomena such as transport and
diffusion that occur in many natural processes in diverse fields ranging from
environmental sciences to ecology. In order to obtain computationally efficient
statistical algorithms we use spectral methods to solve the stochastic partial
differential equation. This has the advantage that approximation errors do not
accumulate over time, and that in the spectral space the computational cost
grows linearly with the dimension, the total computational costs of Bayesian or
frequentist inference being dominated by the fast Fourier transform. The
proposed model is applied to postprocessing of precipitation forecasts from a
numerical weather prediction model for northern Switzerland. In contrast to the
raw forecasts from the numerical model, the postprocessed forecasts are
calibrated and quantify prediction uncertainty. Moreover, they outperform the
raw forecasts, in the sense that they have a lower mean absolute error
When and Where: Predicting Human Movements Based on Social Spatial-Temporal Events
Predicting both the time and the location of human movements is valuable but
challenging for a variety of applications. To address this problem, we propose
an approach considering both the periodicity and the sociality of human
movements. We first define a new concept, Social Spatial-Temporal Event (SSTE),
to represent social interactions among people. For the time prediction, we
characterise the temporal dynamics of SSTEs with an ARMA (AutoRegressive Moving
Average) model. To dynamically capture the SSTE kinetics, we propose a Kalman
Filter based learning algorithm to learn and incrementally update the ARMA
model as a new observation becomes available. For the location prediction, we
propose a ranking model where the periodicity and the sociality of human
movements are simultaneously taken into consideration for improving the
prediction accuracy. Extensive experiments conducted on real data sets validate
our proposed approach
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