4,747 research outputs found
Hierarchically-coupled hidden Markov models for learning kinetic rates from single-molecule data
We address the problem of analyzing sets of noisy time-varying signals that
all report on the same process but confound straightforward analyses due to
complex inter-signal heterogeneities and measurement artifacts. In particular
we consider single-molecule experiments which indirectly measure the distinct
steps in a biomolecular process via observations of noisy time-dependent
signals such as a fluorescence intensity or bead position. Straightforward
hidden Markov model (HMM) analyses attempt to characterize such processes in
terms of a set of conformational states, the transitions that can occur between
these states, and the associated rates at which those transitions occur; but
require ad-hoc post-processing steps to combine multiple signals. Here we
develop a hierarchically coupled HMM that allows experimentalists to deal with
inter-signal variability in a principled and automatic way. Our approach is a
generalized expectation maximization hyperparameter point estimation procedure
with variational Bayes at the level of individual time series that learns an
single interpretable representation of the overall data generating process.Comment: 9 pages, 5 figure
Variational Hamiltonian Monte Carlo via Score Matching
Traditionally, the field of computational Bayesian statistics has been
divided into two main subfields: variational methods and Markov chain Monte
Carlo (MCMC). In recent years, however, several methods have been proposed
based on combining variational Bayesian inference and MCMC simulation in order
to improve their overall accuracy and computational efficiency. This marriage
of fast evaluation and flexible approximation provides a promising means of
designing scalable Bayesian inference methods. In this paper, we explore the
possibility of incorporating variational approximation into a state-of-the-art
MCMC method, Hamiltonian Monte Carlo (HMC), to reduce the required gradient
computation in the simulation of Hamiltonian flow, which is the bottleneck for
many applications of HMC in big data problems. To this end, we use a {\it
free-form} approximation induced by a fast and flexible surrogate function
based on single-hidden layer feedforward neural networks. The surrogate
provides sufficiently accurate approximation while allowing for fast
exploration of parameter space, resulting in an efficient approximate inference
algorithm. We demonstrate the advantages of our method on both synthetic and
real data problems
Kinetic distance and kinetic maps from molecular dynamics simulation
Characterizing macromolecular kinetics from molecular dynamics (MD)
simulations requires a distance metric that can distinguish
slowly-interconverting states. Here we build upon diffusion map theory and
define a kinetic distance for irreducible Markov processes that quantifies how
slowly molecular conformations interconvert. The kinetic distance can be
computed given a model that approximates the eigenvalues and eigenvectors
(reaction coordinates) of the MD Markov operator. Here we employ the
time-lagged independent component analysis (TICA). The TICA components can be
scaled to provide a kinetic map in which the Euclidean distance corresponds to
the kinetic distance. As a result, the question of how many TICA dimensions
should be kept in a dimensionality reduction approach becomes obsolete, and one
parameter less needs to be specified in the kinetic model construction. We
demonstrate the approach using TICA and Markov state model (MSM) analyses for
illustrative models, protein conformation dynamics in bovine pancreatic trypsin
inhibitor and protein-inhibitor association in trypsin and benzamidine
Variational semi-blind sparse deconvolution with orthogonal kernel bases and its application to MRFM
We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior distributions are specified for the PSF and the 3D image. Joint image reconstruction and PSF estimation is then performed within a Bayesian framework, using a variational algorithm to estimate the posterior distribution. The image prior distribution imposes an explicit atomic measure that corresponds to image sparsity. Importantly, the proposed Bayesian deconvolution algorithm does not require hand tuning. Simulation results clearly demonstrate that the semi-blind deconvolution algorithm compares favorably with previous Markov chain Monte Carlo (MCMC) version of myopic sparse reconstruction. It significantly outperforms mismatched non-blind algorithms that rely on the assumption of the perfect knowledge of the PSF. The algorithm is illustrated on real data from magnetic resonance force microscopy (MRFM)
Variational semi-blind sparse deconvolution with orthogonal kernel bases and its application to MRFM
We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior distributions are specified for the PSF and the 3D image. Joint image reconstruction and PSF estimation is then performed within a Bayesian framework, using a variational algorithm to estimate the posterior distribution. The image prior distribution imposes an explicit atomic measure that corresponds to image sparsity. Importantly, the proposed Bayesian deconvolution algorithm does not require hand tuning. Simulation results clearly demonstrate that the semi-blind deconvolution algorithm compares favorably with previous Markov chain Monte Carlo (MCMC) version of myopic sparse reconstruction. It significantly outperforms mismatched non-blind algorithms that rely on the assumption of the perfect knowledge of the PSF. The algorithm is illustrated on real data from magnetic resonance force microscopy (MRFM)
A Nonparametric Bayesian Approach to Uncovering Rat Hippocampal Population Codes During Spatial Navigation
Rodent hippocampal population codes represent important spatial information
about the environment during navigation. Several computational methods have
been developed to uncover the neural representation of spatial topology
embedded in rodent hippocampal ensemble spike activity. Here we extend our
previous work and propose a nonparametric Bayesian approach to infer rat
hippocampal population codes during spatial navigation. To tackle the model
selection problem, we leverage a nonparametric Bayesian model. Specifically, to
analyze rat hippocampal ensemble spiking activity, we apply a hierarchical
Dirichlet process-hidden Markov model (HDP-HMM) using two Bayesian inference
methods, one based on Markov chain Monte Carlo (MCMC) and the other based on
variational Bayes (VB). We demonstrate the effectiveness of our Bayesian
approaches on recordings from a freely-behaving rat navigating in an open field
environment. We find that MCMC-based inference with Hamiltonian Monte Carlo
(HMC) hyperparameter sampling is flexible and efficient, and outperforms VB and
MCMC approaches with hyperparameters set by empirical Bayes
On Similarities between Inference in Game Theory and Machine Learning
In this paper, we elucidate the equivalence between inference in game theory and machine learning. Our aim in so doing is to establish an equivalent vocabulary between the two domains so as to facilitate developments at the intersection of both fields, and as proof of the usefulness of this approach, we use recent developments in each field to make useful improvements to the other. More specifically, we consider the analogies between smooth best responses in fictitious play and Bayesian inference methods. Initially, we use these insights to develop and demonstrate an improved algorithm for learning in games based on probabilistic moderation. That is, by integrating over the distribution of opponent strategies (a Bayesian approach within machine learning) rather than taking a simple empirical average (the approach used in standard fictitious play) we derive a novel moderated fictitious play algorithm and show that it is more likely than standard fictitious play to converge to a payoff-dominant but risk-dominated Nash equilibrium in a simple coordination game. Furthermore we consider the converse case, and show how insights from game theory can be used to derive two improved mean field variational learning algorithms. We first show that the standard update rule of mean field variational learning is analogous to a Cournot adjustment within game theory. By analogy with fictitious play, we then suggest an improved update rule, and show that this results in fictitious variational play, an improved mean field variational learning algorithm that exhibits better convergence in highly or strongly connected graphical models. Second, we use a recent advance in fictitious play, namely dynamic fictitious play, to derive a derivative action variational learning algorithm, that exhibits superior convergence properties on a canonical machine learning problem (clustering a mixture distribution)
Getting started in probabilistic graphical models
Probabilistic graphical models (PGMs) have become a popular tool for
computational analysis of biological data in a variety of domains. But, what
exactly are they and how do they work? How can we use PGMs to discover patterns
that are biologically relevant? And to what extent can PGMs help us formulate
new hypotheses that are testable at the bench? This note sketches out some
answers and illustrates the main ideas behind the statistical approach to
biological pattern discovery.Comment: 12 pages, 1 figur
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