27,655 research outputs found
Statistical inference in mechanistic models: time warping for improved gradient matching
Inference in mechanistic models of non-linear differential equations is a challenging problem in current computational statistics. Due to the high computational costs of numerically solving the differential equations in every step of an iterative parameter adaptation scheme, approximate methods based on gradient matching have become popular. However, these methods critically depend on the smoothing scheme for function interpolation. The present article adapts an idea from manifold learning and demonstrates that a time warping approach aiming to homogenize intrinsic length scales can lead to a significant improvement in parameter estimation accuracy. We demonstrate the effectiveness of this scheme on noisy data from two dynamical systems with periodic limit cycle, a biopathway, and an application from soft-tissue mechanics. Our study also provides a comparative evaluation on a wide range of signal-to-noise ratios
Second-Order Inference for the Mean of a Variable Missing at Random
We present a second-order estimator of the mean of a variable subject to
missingness, under the missing at random assumption. The estimator improves
upon existing methods by using an approximate second-order expansion of the
parameter functional, in addition to the first-order expansion employed by
standard doubly robust methods. This results in weaker assumptions about the
convergence rates necessary to establish consistency, local efficiency, and
asymptotic linearity. The general estimation strategy is developed under the
targeted minimum loss-based estimation (TMLE) framework. We present a
simulation comparing the sensitivity of the first and second order estimators
to the convergence rate of the initial estimators of the outcome regression and
missingness score. In our simulation, the second-order TMLE improved the
coverage probability of a confidence interval by up to 85%. In addition, we
present a first-order estimator inspired by a second-order expansion of the
parameter functional. This estimator only requires one-dimensional smoothing,
whereas implementation of the second-order TMLE generally requires kernel
smoothing on the covariate space. The first-order estimator proposed is
expected to have improved finite sample performance compared to existing
first-order estimators. In our simulations, the proposed first-order estimator
improved the coverage probability by up to 90%. We provide an illustration of
our methods using a publicly available dataset to determine the effect of an
anticoagulant on health outcomes of patients undergoing percutaneous coronary
intervention. We provide R code implementing the proposed estimator
Clustering via kernel decomposition
Spectral clustering methods were proposed recently which rely on the eigenvalue decomposition of an affinity matrix. In this letter, the affinity matrix is created from the elements of a nonparametric density estimator and then decomposed to obtain posterior probabilities of class membership. Hyperparameters are selected using standard cross-validation methods
Dynamic texture recognition using time-causal and time-recursive spatio-temporal receptive fields
This work presents a first evaluation of using spatio-temporal receptive
fields from a recently proposed time-causal spatio-temporal scale-space
framework as primitives for video analysis. We propose a new family of video
descriptors based on regional statistics of spatio-temporal receptive field
responses and evaluate this approach on the problem of dynamic texture
recognition. Our approach generalises a previously used method, based on joint
histograms of receptive field responses, from the spatial to the
spatio-temporal domain and from object recognition to dynamic texture
recognition. The time-recursive formulation enables computationally efficient
time-causal recognition. The experimental evaluation demonstrates competitive
performance compared to state-of-the-art. Especially, it is shown that binary
versions of our dynamic texture descriptors achieve improved performance
compared to a large range of similar methods using different primitives either
handcrafted or learned from data. Further, our qualitative and quantitative
investigation into parameter choices and the use of different sets of receptive
fields highlights the robustness and flexibility of our approach. Together,
these results support the descriptive power of this family of time-causal
spatio-temporal receptive fields, validate our approach for dynamic texture
recognition and point towards the possibility of designing a range of video
analysis methods based on these new time-causal spatio-temporal primitives.Comment: 29 pages, 16 figure
Smoothing and mean-covariance estimation of functional data with a Bayesian hierarchical model
Functional data, with basic observational units being functions (e.g.,
curves, surfaces) varying over a continuum, are frequently encountered in
various applications. While many statistical tools have been developed for
functional data analysis, the issue of smoothing all functional observations
simultaneously is less studied. Existing methods often focus on smoothing each
individual function separately, at the risk of removing important systematic
patterns common across functions. We propose a nonparametric Bayesian approach
to smooth all functional observations simultaneously and nonparametrically. In
the proposed approach, we assume that the functional observations are
independent Gaussian processes subject to a common level of measurement errors,
enabling the borrowing of strength across all observations. Unlike most
Gaussian process regression models that rely on pre-specified structures for
the covariance kernel, we adopt a hierarchical framework by assuming a Gaussian
process prior for the mean function and an Inverse-Wishart process prior for
the covariance function. These prior assumptions induce an automatic
mean-covariance estimation in the posterior inference in addition to the
simultaneous smoothing of all observations. Such a hierarchical framework is
flexible enough to incorporate functional data with different characteristics,
including data measured on either common or uncommon grids, and data with
either stationary or nonstationary covariance structures. Simulations and real
data analysis demonstrate that, in comparison with alternative methods, the
proposed Bayesian approach achieves better smoothing accuracy and comparable
mean-covariance estimation results. Furthermore, it can successfully retain the
systematic patterns in the functional observations that are usually neglected
by the existing functional data analyses based on individual-curve smoothing.Comment: Submitted to Bayesian Analysi
Kernel density classification and boosting: an L2 sub analysis
Kernel density estimation is a commonly used approach to classification. However, most of the theoretical results for kernel methods apply to estimation per se and not necessarily to classification. In this paper we show that when estimating the difference between two densities, the optimal smoothing parameters are increasing functions of the sample size of the complementary group, and we provide a small simluation study which examines the relative performance of kernel density methods when the final goal is classification. A relative newcomer to the classification portfolio is “boosting”, and this paper proposes an algorithm for boosting kernel density classifiers. We note that boosting is closely linked to a previously proposed method of bias reduction in kernel density estimation and indicate how it will enjoy similar properties for classification. We show that boosting kernel classifiers reduces the bias whilst only slightly increasing the variance, with an overall reduction in error. Numerical examples and simulations are used to illustrate the findings, and we also suggest further areas of research
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