3 research outputs found
A Workflow for Statistical Inference in Stochastic Gradient Descent
Stochastic gradient descent (SGD) is an estimation tool for large data
employed in machine learning and statistics. Due to the Markovian nature of the
SGD process, inference is a challenging problem. An underlying asymptotic
normality of the averaged SGD (ASGD) estimator allows for the construction of a
batch-means estimator of the asymptotic covariance matrix. Instead of the usual
increasing batch-size strategy employed in ASGD, we propose a memory efficient
equal batch-size strategy and show that under mild conditions, the estimator is
consistent. A key feature of the proposed batching technique is that it allows
for bias-correction of the variance, at no cost to memory. Since joint
inference for high dimensional problems may be undesirable, we present
marginal-friendly simultaneous confidence intervals, and show through an
example how covariance estimators of ASGD can be employed in improved
predictions.Comment: 43 pages, 8 figure
A Computationally Efficient algorithm to estimate the Parameters of a Two-Dimensional Chirp Model with the product term
Chirp signal models and their generalizations have been used to model many
natural and man-made phenomena in signal processing and time series literature.
In recent times, several methods have been proposed for parameter estimation of
these models. These methods however are either statistically sub-optimal or
computationally burdensome, specially for two dimensional (2D) chirp models. In
this paper, we consider the problem of parameter estimation of 2D chirp models
and propose a computationally efficient estimator and establish asymptotic
theoretical properties of the proposed estimators. And the proposed estimators
are observed to have the same rates of convergence as the least squares
estimators (LSEs). Furthermore, the proposed estimators of chirp rate
parameters are shown to be asymptotically optimal. Extensive and detailed
numerical simulations are conducted, which support theoretical results of the
proposed estimators
On estimating parameters of a multi-component Chirp Model with equal chirp rates
Multi-component chirp signal models with equal chirp rates appear in various
radar applications, e.g., synthetic aperture radar, echo signal of a rapid
mobile target, etc. Many sub-optimal estimators have been developed for such
models, however, these suffer from the problem of either identifiability or
error propagation effect. In this paper, we have developed theoretical
properties of the least squares estimators (LSEs) of the parameters of
multi-component chirp model with equal chirp rates, where the model is
contaminated with linear stationary errors. We also propose two computationally
efficient estimators as alternative to LSEs, namely sequential combined
estimators and sequential plugin estimators. Strong consistency and asymptotic
normality of these estimators have been derived. Interestingly, it is observed
that sequential combined estimator of the chirp rate parameter is
asymptotically efficient. Extensive numerical simulations have been performed,
which validate satisfactory computational and theoretical performance of all
three estimators. {We have also analysed a simulated radar data with the help
of our proposed estimators of multi-component chirp model with equal chirp
rates, which performs efficiently in recovery of inverse synthetic aperture
radar (ISAR) image of a target from a noisy data