4,214 research outputs found
Boosting Monte Carlo simulations of spin glasses using autoregressive neural networks
The autoregressive neural networks are emerging as a powerful computational
tool to solve relevant problems in classical and quantum mechanics. One of
their appealing functionalities is that, after they have learned a probability
distribution from a dataset, they allow exact and efficient sampling of typical
system configurations. Here we employ a neural autoregressive distribution
estimator (NADE) to boost Markov chain Monte Carlo (MCMC) simulations of a
paradigmatic classical model of spin-glass theory, namely the two-dimensional
Edwards-Anderson Hamiltonian. We show that a NADE can be trained to accurately
mimic the Boltzmann distribution using unsupervised learning from system
configurations generated using standard MCMC algorithms. The trained NADE is
then employed as smart proposal distribution for the Metropolis-Hastings
algorithm. This allows us to perform efficient MCMC simulations, which provide
unbiased results even if the expectation value corresponding to the probability
distribution learned by the NADE is not exact. Notably, we implement a
sequential tempering procedure, whereby a NADE trained at a higher temperature
is iteratively employed as proposal distribution in a MCMC simulation run at a
slightly lower temperature. This allows one to efficiently simulate the
spin-glass model even in the low-temperature regime, avoiding the divergent
correlation times that plague MCMC simulations driven by local-update
algorithms. Furthermore, we show that the NADE-driven simulations quickly
sample ground-state configurations, paving the way to their future utilization
to tackle binary optimization problems.Comment: 13 pages, 14 figure
Herding as a Learning System with Edge-of-Chaos Dynamics
Herding defines a deterministic dynamical system at the edge of chaos. It
generates a sequence of model states and parameters by alternating parameter
perturbations with state maximizations, where the sequence of states can be
interpreted as "samples" from an associated MRF model. Herding differs from
maximum likelihood estimation in that the sequence of parameters does not
converge to a fixed point and differs from an MCMC posterior sampling approach
in that the sequence of states is generated deterministically. Herding may be
interpreted as a"perturb and map" method where the parameter perturbations are
generated using a deterministic nonlinear dynamical system rather than randomly
from a Gumbel distribution. This chapter studies the distinct statistical
characteristics of the herding algorithm and shows that the fast convergence
rate of the controlled moments may be attributed to edge of chaos dynamics. The
herding algorithm can also be generalized to models with latent variables and
to a discriminative learning setting. The perceptron cycling theorem ensures
that the fast moment matching property is preserved in the more general
framework
Psychophysical identity and free energy
An approach to implementing variational Bayesian inference in biological
systems is considered, under which the thermodynamic free energy of a system
directly encodes its variational free energy. In the case of the brain, this
assumption places constraints on the neuronal encoding of generative and
recognition densities, in particular requiring a stochastic population code.
The resulting relationship between thermodynamic and variational free energies
is prefigured in mind-brain identity theses in philosophy and in the Gestalt
hypothesis of psychophysical isomorphism.Comment: 22 pages; published as a research article on 8/5/2020 in Journal of
the Royal Society Interfac
Some applications of higher-order hidden Markov models in the exotic commodity markets
The liberalisation of regional and global commodity markets over the last several decades resulted in certain commodity price behaviours that require new modelling and estimation approaches. Such new approaches have important implications to the valuation and utilisation of commodity derivatives. Derivatives are becoming increasingly crucial for market participants in hedging their exposure to volatile price swings and in managing risks associated with derivative trading. The modelling of commodity-based variables is an integral part of risk management and optimal-investment strategies for commodity-linked portfolios. The characteristics of commodity price evolution cannot be captured sufficiently by one-state driven models even with the inclusion of multiple factors. This inspires the adoption of regime-switching methods to rectify the one-state multi-factor modelling inadequacies. In this research, we aim to employ higher-order hidden Markov models (HOHMMs) in order to take advantage of the latent information in the observed process recorded in the past. This hugely enhances and complements the regime-switching features of our approach in describing certain variables that virtually determine the value of some commodity derivatives such as contracts dependent on temperature, electricity spot price, and fish-price dynamics. Our push for the utility of the change-of-probability-measure technique facilitates the derivation of recursive filtering algorithms. This then establishes a self-tuning dynamic estimation procedure. Both the data-fitting and forecasting performances of various model settings are investigated.
This research work emerged from four related projects detailed as follows. (i) We start with an HMM to model the behaviour of daily average temperatures (DATs) geared towards the analysis of weather derivatives. (ii) The model in (i) is extended naturally by showcasing the capacity of an HOHMM-based approach to simultaneously describe the DATs’ salient properties of mean reversion, seasonality, memory and stochasticity. (iii) An HOHMM-driven jump process augments the HOHMM-based de-seasonalised temperature process to capture price spikes, and the ensuing filtering algorithms under this modelling framework are constructed to provide optimal parameter estimates. (iv) Finally, a multi-dimensional HOHMM-modulated set up is built for futures price-curve dynamics pertinent to financial product valuation and risk management in the aquaculture sector. We examine the performance of this new modelling set up by considering goodness-of-fit and out-of-sample forecasting metrics with a detailed numerical demonstration using a multivariate dataset compiled by the Fish Pool ASA.
This research offers a collection of more flexible stochastic modelling approaches for pricing and risk analysis of certain commodity derivatives on weather, electricity and fish prices. The novelty of our techniques is the powerful capability to automate the parameter estimation. Consequently, we contribute to the development of financial tools that aid in selecting the appropriate and optimal model on the basis of some information criteria and within current technological advancements in which continuous flow of observed data are now readily accessible in real time
Many Roads to Synchrony: Natural Time Scales and Their Algorithms
We consider two important time scales---the Markov and cryptic orders---that
monitor how an observer synchronizes to a finitary stochastic process. We show
how to compute these orders exactly and that they are most efficiently
calculated from the epsilon-machine, a process's minimal unifilar model.
Surprisingly, though the Markov order is a basic concept from stochastic
process theory, it is not a probabilistic property of a process. Rather, it is
a topological property and, moreover, it is not computable from any
finite-state model other than the epsilon-machine. Via an exhaustive survey, we
close by demonstrating that infinite Markov and infinite cryptic orders are a
dominant feature in the space of finite-memory processes. We draw out the roles
played in statistical mechanical spin systems by these two complementary length
scales.Comment: 17 pages, 16 figures:
http://cse.ucdavis.edu/~cmg/compmech/pubs/kro.htm. Santa Fe Institute Working
Paper 10-11-02
Decoding Single Molecule Time Traces with Dynamic Disorder
Single molecule time trajectories of biomolecules provide glimpses into
complex folding landscapes that are difficult to visualize using conventional
ensemble measurements. Recent experiments and theoretical analyses have
highlighted dynamic disorder in certain classes of biomolecules, whose dynamic
pattern of conformational transitions is affected by slower transition dynamics
of internal state hidden in a low dimensional projection. A systematic means to
analyze such data is, however, currently not well developed. Here we report a
new algorithm - Variational Bayes-double chain Markov model (VB-DCMM) - to
analyze single molecule time trajectories that display dynamic disorder. The
proposed analysis employing VB-DCMM allows us to detect the presence of dynamic
disorder, if any, in each trajectory, identify the number of internal states,
and estimate transition rates between the internal states as well as the rates
of conformational transition within each internal state. Applying VB-DCMM
algorithm to single molecule FRET data of H-DNA in 100 mM-Na solution,
followed by data clustering, we show that at least 6 kinetic paths linking 4
distinct internal states are required to correctly interpret the duplex-triplex
transitions of H-DNA
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