8,104 research outputs found
A numerically efficient implementation of the expectation maximization algorithm for state space models
Peer reviewedPostprin
Maximum-likelihood estimation of delta-domain model parameters from noisy output signals
Fast sampling is desirable to describe signal transmission
through wide-bandwidth systems. The delta-operator provides an ideal discrete-time modeling description for such fast-sampled systems. However, the estimation of delta-domain model parameters is usually biased by directly applying the delta-transformations to a sampled signal corrupted by additive measurement noise. This problem is solved here by expectation-maximization, where the delta-transformations of the true signal are estimated and then used to obtain the model parameters. The method is
demonstrated on a numerical example to improve on the accuracy of using a shift operator approach when the sample rate is fast
Likelihood-Based Inference for Discretely Observed Birth-Death-Shift Processes, with Applications to Evolution of Mobile Genetic Elements
Continuous-time birth-death-shift (BDS) processes are frequently used in
stochastic modeling, with many applications in ecology and epidemiology. In
particular, such processes can model evolutionary dynamics of transposable
elements - important genetic markers in molecular epidemiology. Estimation of
the effects of individual covariates on the birth, death, and shift rates of
the process can be accomplished by analyzing patient data, but inferring these
rates in a discretely and unevenly observed setting presents computational
challenges. We propose a mutli-type branching process approximation to BDS
processes and develop a corresponding expectation maximization (EM) algorithm,
where we use spectral techniques to reduce calculation of expected sufficient
statistics to low dimensional integration. These techniques yield an efficient
and robust optimization routine for inferring the rates of the BDS process, and
apply more broadly to multi-type branching processes where rates can depend on
many covariates. After rigorously testing our methodology in simulation
studies, we apply our method to study intrapatient time evolution of IS6110
transposable element, a frequently used element during estimation of
epidemiological clusters of Mycobacterium tuberculosis infections.Comment: 31 pages, 7 figures, 1 tabl
Secrecy Energy Efficiency of MIMOME Wiretap Channels with Full-Duplex Jamming
Full-duplex (FD) jamming transceivers are recently shown to enhance the
information security of wireless communication systems by simultaneously
transmitting artificial noise (AN) while receiving information. In this work,
we investigate if FD jamming can also improve the systems secrecy energy
efficiency (SEE) in terms of securely communicated bits-per- Joule, when
considering the additional power used for jamming and self-interference (SI)
cancellation. Moreover, the degrading effect of the residual SI is also taken
into account. In this regard, we formulate a set of SEE maximization problems
for a FD multiple-input-multiple-output multiple-antenna eavesdropper (MIMOME)
wiretap channel, considering both cases where exact or statistical channel
state information (CSI) is available. Due to the intractable problem structure,
we propose iterative solutions in each case with a proven convergence to a
stationary point. Numerical simulations indicate only a marginal SEE gain,
through the utilization of FD jamming, for a wide range of system conditions.
However, when SI can efficiently be mitigated, the observed gain is
considerable for scenarios with a small distance between the FD node and the
eavesdropper, a high Signal-to-noise ratio (SNR), or for a bidirectional FD
communication setup.Comment: IEEE Transactions on Communication
Projected and Hidden Markov Models for calculating kinetics and metastable states of complex molecules
Markov state models (MSMs) have been successful in computing metastable
states, slow relaxation timescales and associated structural changes, and
stationary or kinetic experimental observables of complex molecules from large
amounts of molecular dynamics simulation data. However, MSMs approximate the
true dynamics by assuming a Markov chain on a clusters discretization of the
state space. This approximation is difficult to make for high-dimensional
biomolecular systems, and the quality and reproducibility of MSMs has therefore
been limited. Here, we discard the assumption that dynamics are Markovian on
the discrete clusters. Instead, we only assume that the full phase- space
molecular dynamics is Markovian, and a projection of this full dynamics is
observed on the discrete states, leading to the concept of Projected Markov
Models (PMMs). Robust estimation methods for PMMs are not yet available, but we
derive a practically feasible approximation via Hidden Markov Models (HMMs). It
is shown how various molecular observables of interest that are often computed
from MSMs can be computed from HMMs / PMMs. The new framework is applicable to
both, simulation and single-molecule experimental data. We demonstrate its
versatility by applications to educative model systems, an 1 ms Anton MD
simulation of the BPTI protein, and an optical tweezer force probe trajectory
of an RNA hairpin
Compressed sensing reconstruction using Expectation Propagation
Many interesting problems in fields ranging from telecommunications to
computational biology can be formalized in terms of large underdetermined
systems of linear equations with additional constraints or regularizers. One of
the most studied ones, the Compressed Sensing problem (CS), consists in finding
the solution with the smallest number of non-zero components of a given system
of linear equations for known
measurement vector and sensing matrix . Here, we
will address the compressed sensing problem within a Bayesian inference
framework where the sparsity constraint is remapped into a singular prior
distribution (called Spike-and-Slab or Bernoulli-Gauss). Solution to the
problem is attempted through the computation of marginal distributions via
Expectation Propagation (EP), an iterative computational scheme originally
developed in Statistical Physics. We will show that this strategy is
comparatively more accurate than the alternatives in solving instances of CS
generated from statistically correlated measurement matrices. For computational
strategies based on the Bayesian framework such as variants of Belief
Propagation, this is to be expected, as they implicitly rely on the hypothesis
of statistical independence among the entries of the sensing matrix. Perhaps
surprisingly, the method outperforms uniformly also all the other
state-of-the-art methods in our tests.Comment: 20 pages, 6 figure
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