1,874 research outputs found
The Parameter Houlihan: a solution to high-throughput identifiability indeterminacy for brutally ill-posed problems
One way to interject knowledge into clinically impactful forecasting is to
use data assimilation, a nonlinear regression that projects data onto a
mechanistic physiologic model, instead of a set of functions, such as neural
networks. Such regressions have an advantage of being useful with particularly
sparse, non-stationary clinical data. However, physiological models are often
nonlinear and can have many parameters, leading to potential problems with
parameter identifiability, or the ability to find a unique set of parameters
that minimize forecasting error. The identifiability problems can be minimized
or eliminated by reducing the number of parameters estimated, but reducing the
number of estimated parameters also reduces the flexibility of the model and
hence increases forecasting error. We propose a method, the parameter Houlihan,
that combines traditional machine learning techniques with data assimilation,
to select the right set of model parameters to minimize forecasting error while
reducing identifiability problems. The method worked well: the data
assimilation-based glucose forecasts and estimates for our cohort using the
Houlihan-selected parameter sets generally also minimize forecasting errors
compared to other parameter selection methods such as by-hand parameter
selection. Nevertheless, the forecast with the lowest forecast error does not
always accurately represent physiology, but further advancements of the
algorithm provide a path for improving physiologic fidelity as well. Our hope
is that this methodology represents a first step toward combining machine
learning with data assimilation and provides a lower-threshold entry point for
using data assimilation with clinical data by helping select the right
parameters to estimate
A study of parameter identification
A set of definitions for deterministic parameter identification ability were proposed. Deterministic parameter identificability properties are presented based on four system characteristics: direct parameter recoverability, properties of the system transfer function, properties of output distinguishability, and uniqueness properties of a quadratic cost functional. Stochastic parameter identifiability was defined in terms of the existence of an estimation sequence for the unknown parameters which is consistent in probability. Stochastic parameter identifiability properties are presented based on the following characteristics: convergence properties of the maximum likelihood estimate, properties of the joint probability density functions of the observations, and properties of the information matrix
Asymptotic normality of maximum likelihood and its variational approximation for stochastic blockmodels
Variational methods for parameter estimation are an active research area,
potentially offering computationally tractable heuristics with theoretical
performance bounds. We build on recent work that applies such methods to
network data, and establish asymptotic normality rates for parameter estimates
of stochastic blockmodel data, by either maximum likelihood or variational
estimation. The result also applies to various sub-models of the stochastic
blockmodel found in the literature.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1124 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
The identifiability of tree topology for phylogenetic models, including covarion and mixture models
For a model of molecular evolution to be useful for phylogenetic inference,
the topology of evolutionary trees must be identifiable. That is, from a joint
distribution the model predicts, it must be possible to recover the tree
parameter. We establish tree identifiability for a number of phylogenetic
models, including a covarion model and a variety of mixture models with a
limited number of classes. The proof is based on the introduction of a more
general model, allowing more states at internal nodes of the tree than at
leaves, and the study of the algebraic variety formed by the joint
distributions to which it gives rise. Tree identifiability is first established
for this general model through the use of certain phylogenetic invariants.Comment: 20 pages, 1 figur
Bayesian Updating, Model Class Selection and Robust Stochastic Predictions of Structural Response
A fundamental issue when predicting structural response by using mathematical models is how to treat both modeling and excitation uncertainty. A general framework for this is presented which uses probability as a multi-valued
conditional logic for quantitative plausible reasoning in the presence of uncertainty due to incomplete information. The
fundamental probability models that represent the structure’s uncertain behavior are specified by the choice of a stochastic
system model class: a set of input-output probability models for the structure and a prior probability distribution over this set
that quantifies the relative plausibility of each model. A model class can be constructed from a parameterized deterministic
structural model by stochastic embedding utilizing Jaynes’ Principle of Maximum Information Entropy. Robust predictive
analyses use the entire model class with the probabilistic predictions of each model being weighted by its prior probability, or if
structural response data is available, by its posterior probability from Bayes’ Theorem for the model class. Additional robustness
to modeling uncertainty comes from combining the robust predictions of each model class in a set of competing candidates
weighted by the prior or posterior probability of the model class, the latter being computed from Bayes’ Theorem. This higherlevel application of Bayes’ Theorem automatically applies a quantitative Ockham razor that penalizes the data-fit of more
complex model classes that extract more information from the data. Robust predictive analyses involve integrals over highdimensional spaces that usually must be evaluated numerically. Published applications have used Laplace's method of
asymptotic approximation or Markov Chain Monte Carlo algorithms
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