11,271 research outputs found
Empirical Bayes conditional density estimation
The problem of nonparametric estimation of the conditional density of a
response, given a vector of explanatory variables, is classical and of
prominent importance in many prediction problems since the conditional density
provides a more comprehensive description of the association between the
response and the predictor than, for instance, does the regression function.
The problem has applications across different fields like economy, actuarial
sciences and medicine. We investigate empirical Bayes estimation of conditional
densities establishing that an automatic data-driven selection of the prior
hyper-parameters in infinite mixtures of Gaussian kernels, with
predictor-dependent mixing weights, can lead to estimators whose performance is
on par with that of frequentist estimators in being minimax-optimal (up to
logarithmic factors) rate adaptive over classes of locally H\"older smooth
conditional densities and in performing an adaptive dimension reduction if the
response is independent of (some of) the explanatory variables which,
containing no information about the response, are irrelevant to the purpose of
estimating its conditional density
Outlier robust system identification: a Bayesian kernel-based approach
In this paper, we propose an outlier-robust regularized kernel-based method
for linear system identification. The unknown impulse response is modeled as a
zero-mean Gaussian process whose covariance (kernel) is given by the recently
proposed stable spline kernel, which encodes information on regularity and
exponential stability. To build robustness to outliers, we model the
measurement noise as realizations of independent Laplacian random variables.
The identification problem is cast in a Bayesian framework, and solved by a new
Markov Chain Monte Carlo (MCMC) scheme. In particular, exploiting the
representation of the Laplacian random variables as scale mixtures of
Gaussians, we design a Gibbs sampler which quickly converges to the target
distribution. Numerical simulations show a substantial improvement in the
accuracy of the estimates over state-of-the-art kernel-based methods.Comment: 5 figure
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