Statistical properties of linear prediction analysis underlying the challenge of formant bandwidth estimation.

Formant bandwidth estimation is often observed to be more challenging than the estimation of formant center frequencies due to the presence of multiple glottal pulses within a period and short closed-phase durations. This study explores inherently different statistical properties between linear prediction (LP)-based estimates of formant frequencies and their corresponding bandwidths that may be explained in part by the statistical bounds on the variances of estimated LP coefficients. A theoretical analysis of the Cramér-Rao bounds on LP estimator variance indicates that the accuracy of bandwidth estimation is approximately twice as low as that of center frequency estimation.

Network histograms and universality of blockmodel approximation.

In this paper we introduce the network histogram, a statistical summary of network interactions to be used as a tool for exploratory data analysis. A network histogram is obtained by fitting a stochastic blockmodel to a single observation of a network dataset. Blocks of edges play the role of histogram bins and community sizes that of histogram bandwidths or bin sizes.

Kalman-based autoregressive moving average modeling and inference for formant and antiformant tracking.

Vocal tract resonance characteristics in acoustic speech signals are classically tracked using frame-by-frame point estimates of formant frequencies followed by candidate selection and smoothing using dynamic programming methods that minimize ad hoc cost functions. The goal of the current work is to provide both point estimates and associated uncertainties of center frequencies and bandwidths in a statistically principled state-space framework. Extended Kalman (K) algorithms take advantage of a linearized mapping to infer formant and antiformant parameters from frame-based estimates of autoregressive moving average (ARMA) cepstral coefficients.

A CURE for noisy magnetic resonance images: chi-square unbiased risk estimation.

n this article we derive an unbiased expression for the expected mean-squared error associated with continuously differentiable estimators of the noncentrality parameter of a chisquare random variable. We then consider the task of denoising squared-magnitude magnetic resonance image data, which are well modeled as independent noncentral chi-square random variables on two degrees of freedom. We consider two broad classes of linearly parameterized shrinkage estimators that can be optimized using our risk estimate, one in the general context of undecimated filterbank transforms, and another in the specific case of the unnormalized Haar wavelet transform.

On landmark selection and sampling in high-dimensional data analysis.

In recent years, the spectral analysis of appropriately defined kernel matrices has emerged as a principled way to extract the low-dimensional structure often prevalent in high-dimensional data. Here, we provide an introduction to spectral methods for linear and nonlinear dimension reduction, emphasizing ways to overcome the computational limitations currently faced by practitioners with massive datasets. In particular, a data subsampling or landmark selection process is often employed to construct a kernel based on partial information, followed by an approximate spectral analysis termed the Nyström extension.

Spectral methods in machine learning and new strategies for very large datasets.

Spectral methods are of fundamental importance in statistics and machine learning, because they underlie algorithms from classical principal components analysis to more recent approaches that exploit manifold structure. In most cases, the core technical problem can be reduced to computing a low-rank approximation to a positive-definite kernel. For the growing number of applications dealing with very large or high-dimensional datasets, however, the optimal approximation afforded by an exact spectral decomposition is too costly, because its complexity scales as the cube of either the number of training examples or their dimensionality.

Spatio-spectral color filter array design for optimal image recovery.

In digital imaging applications, data are typically obtained via a spatial subsampling procedure implemented as a color filter array-a physical construction whereby only a single color value is measured at each pixel location. Owing to the growing ubiquity of color imaging and display devices, much recent work has focused on the implications of such arrays for subsequent digital processing, including in particular the canonical demosaicking task of reconstructing a full color image from spatially subsampled and incomplete color data acquired under a particular choice of array pattern. In contrast to the majority of the demosaicking literature, we consider here the problem of color filter array design and its implications for spatial reconstruction quality.