Simulation and Robust Modifications of Estimates in Branching Processes

This study is focused on the comparison and modification of different estimates arising in the branching processes. Simulations of models with or without migration are put through. Due to the complexity of the computations the algorithms are designed with the language of technical computing MATLAB. Using the simulations, estimates of the o spring mean of the generated processes are calculated. It is well known in the literature that under certain conditions the asymptotic distribution of the estimates is proved to be normal. Using the asymptotic normality a modified method of maximum likelihood is proposed. The aim is to obtain trimmed maximum likelihood estimates based on several sample paths with the same number of generations. Thus in a natural way the observations, inconsistent with the aprior information about the asymptotic normality are excluded from the model. The computation of the standard error allows the comparison of different types of estimates.

Robust estimation of tear film surface quality in lateral shearing interferometry

Interferometry is a sensitive technique for recording tear film surface irregularities in a noninvasive manner. At the same time, the technique is hindered by natural eye movements resulting in measurement noise. Estimating tear film surface quality from interferograms can be reduced to a spatial-average-localized weighted estimate of the first harmonic of the interference fringes. However, previously reported estimation techniques proved to perform poorly in cases where the pattern fringes were significantly disturbed. This can occur in cases of measuring tear film surface quality on a contact lens on the eye or in a dry eye. We present a new estimation technique for extracting the first harmonic from the interference fringes that combines the traditional spectral estimation techniques with morphological image processing techniques. The proposed technique proves to be more robust to changes in interference fringes caused by natural eye movements and the degree of dryness of the contact lens and corneal surfaces than its predecessors, resulting in tear film surface quality estimates that are less noisy

Robust speech recognition using speech enhancement

Automatic Speech Recognition (ASR) has matured into a technology which is becoming more common in our everyday lives, and is emerging as a necessity to minimise driver distraction when operating in-car systems such as navigation and infotainment. In “noise-free” environments, word recognition performance of these systems has been shown to approach 100%, however this performance degrades rapidly as the level of background noise is increased. Speech enhancement is a popular method for making ASR systems more ro- bust. Single-channel spectral subtraction was originally designed to improve hu- man speech intelligibility and many attempts have been made to optimise this algorithm in terms of signal-based metrics such as maximised Signal-to-Noise Ratio (SNR) or minimised speech distortion. Such metrics are used to assess en- hancement performance for intelligibility not speech recognition, therefore mak- ing them sub-optimal ASR applications. This research investigates two methods for closely coupling subtractive-type enhancement algorithms with ASR: (a) a computationally-efficient Mel-filterbank noise subtraction technique based on likelihood-maximisation (LIMA), and (b) in- troducing phase spectrum information to enable spectral subtraction in the com- plex frequency domain. Likelihood-maximisation uses gradient-descent to optimise parameters of the enhancement algorithm to best fit the acoustic speech model given a word se- quence known a priori. Whilst this technique is shown to improve the ASR word accuracy performance, it is also identified to be particularly sensitive to non-noise mismatches between the training and testing data. Phase information has long been ignored in spectral subtraction as it is deemed to have little effect on human intelligibility. In this work it is shown that phase information is important in obtaining highly accurate estimates of clean speech magnitudes which are typically used in ASR feature extraction. Phase Estimation via Delay Projection is proposed based on the stationarity of sinusoidal signals, and demonstrates the potential to produce improvements in ASR word accuracy in a wide range of SNR. Throughout the dissertation, consideration is given to practical implemen- tation in vehicular environments which resulted in two novel contributions – a LIMA framework which takes advantage of the grounding procedure common to speech dialogue systems, and a resource-saving formulation of frequency-domain spectral subtraction for realisation in field-programmable gate array hardware. The techniques proposed in this dissertation were evaluated using the Aus- tralian English In-Car Speech Corpus which was collected as part of this work. This database is the first of its kind within Australia and captures real in-car speech of 50 native Australian speakers in seven driving conditions common to Australian environments.

The use of phase in complex spectrum subtraction for robust speech recognition

In this paper we propose a new method for utilising phase information by complementing it with traditional magnitude-only spectral subtraction speech enhancement through Complex Spectrum Subtraction (CSS). The proposed approach has the following advantages over traditional magnitude-only spectral subtraction: (a) it introduces complementary information to the enhancement algorithm; (b) it reduces the total number of algorithmic parameters, and; (c) is designed for improving clean speech magnitude spectra and is therefore suitable for both automatic speech recognition (ASR) and speech perception applications. Oracle-based ASR experiments verify this approach, showing an average of 20% relative word accuracy improvements when accurate estimates of the phase spectrum are available. Based on sinusoidal analysis and assuming stationarity between observations (which is shown to be better approximated as the frame rate is increased), this paper also proposes a novel method for acquiring the phase information called Phase Estimation via Delay Projection (PEDEP). Further oracle ASR experiments validate the potential for the proposed PEDEP technique in ideal conditions. Realistic implementation of CSS with PEDEP shows performance comparable to state of the art spectral subtraction techniques in a range of 15-20 dB signal-to-noise ratio environments. These results clearly demonstrate the potential for using phase spectra in spectral subtractive enhancement applications, and at the same time highlight the need for deriving more accurate phase estimates in a wider range of noise conditions.

Robust designs for Poisson regression models

We consider the problem of how to construct robust designs for Poisson regression models. An analytical expression is derived for robust designs for first-order Poisson regression models where uncertainty exists in the prior parameter estimates. Given certain constraints in the methodology, it may be necessary to extend the robust designs for implementation in practical experiments. With these extensions, our methodology constructs designs which perform similarly, in terms of estimation, to current techniques, and offers the solution in a more timely manner. We further apply this analytic result to cases where uncertainty exists in the linear predictor. The application of this methodology to practical design problems such as screening experiments is explored. Given the minimal prior knowledge that is usually available when conducting such experiments, it is recommended to derive designs robust across a variety of systems. However, incorporating such uncertainty into the design process can be a computationally intense exercise. Hence, our analytic approach is explored as an alternative.

Robust designs for Poisson regression models

We consider the problem of how to construct robust designs for Poisson regression models. An analytical expression is derived for robust designs for first-order Poisson regression models where uncertainty exists in the prior parameter estimates. Given certain constraints in the methodology, it may be necessary to extend the robust designs for implementation in practical experiments. With these extensions, our methodology constructs designs which perform similarly, in terms of estimation, to current techniques, and offers the solution in a more timely manner. We further apply this analytic result to cases where uncertainty exists in the linear predictor. The application of this methodology to practical design problems such as screening experiments is explored. Given the minimal prior knowledge that is usually available when conducting such experiments, it is recommended to derive designs robust across a variety of systems. However, incorporating such uncertainty into the design process can be a computationally intense exercise. Hence, our analytic approach is explored as an alternative.

Deformable face ensemble alignment with robust grouped-L1 anchors

Many methods exist at the moment for deformable face fitting. A drawback to nearly all these approaches is that they are (i) noisy in terms of landmark positions, and (ii) the noise is biased across frames (i.e. the misalignment is toward common directions across all frames). In this paper we propose a grouped $\mathcal{L}1$-norm anchored method for simultaneously aligning an ensemble of deformable face images stemming from the same subject, given noisy heterogeneous landmark estimates. Impressive alignment performance improvement and refinement is obtained using very weak initialization as "anchors".

Systematic and Day-to-Day Effects of Chemical-Derived Population Estimates on Wastewater-Based Drug Epidemiology

Population size is crucial when estimating population-normalized drug consumption (PNDC) from wastewater-based drug epidemiology (WBDE). Three conceptually different population estimates can be used: de jure (common census, residence), de facto (all persons within a sewer catchment), and chemical loads (contributors to the sampled wastewater). De facto and chemical loads will be the same where all households contribute to a central sewer system without wastewater loss. This study explored the feasibility of determining a de facto population and its effect on estimating PNDC in an urban community over an extended period. Drugs and other chemicals were analyzed in 311 daily composite wastewater samples. The daily estimated de facto population (using chemical loads) was on average 32% higher than the de jure population. Consequently, using the latter would systemically overestimate PNDC by 22%. However, the relative day-to-day pattern of drug consumption was similar regardless of the type of normalization as daily illicit drug loads appeared to vary substantially more than the population. Using chemical loads population, we objectively quantified the total methodological uncertainty of PNDC and reduced it by a factor of 2. Our study illustrated the potential benefits of using chemical loads population for obtaining more robust PNDC data in WBDE.

Identifying Robust Plans through Plan Diagram Reduction

Estimates of predicate selectivities by database query optimizers often differ significantly from those actually encountered during query execution, leading to poor plan choices and inflated response times. In this paper, we investigate mitigating this problem by replacing selectivity error-sensitive plan choices with alternative plans that provide robust performance. Our approach is based on the recent observation that even the complex and dense "plan diagrams" associated with industrial-strength optimizers can be efficiently reduced to "anorexic" equivalents featuring only a few plans, without materially impacting query processing quality. Extensive experimentation with a rich set of TPC-H and TPC-DS-based query templates in a variety of database environments indicate that plan diagram reduction typically retains plans that are substantially resistant to selectivity errors on the base relations. However, it can sometimes also be severely counter-productive, with the replacements performing much worse. We address this problem through a generalized mathematical characterization of plan cost behavior over the parameter space, which lends itself to efficient criteria of when it is safe to reduce. Our strategies are fully non-invasive and have been implemented in the Picasso optimizer visualization tool.

Mathematical Model of Viral Kinetics In Vitro Estimates the Number of E2-CD81 Complexes Necessary for Hepatitis C Virus Entry

Interaction between the hepatitis C virus (HCV) envelope protein E2 and the host receptor CD81 is essential for HCV entry into target cells. The number of E2-CD81 complexes necessary for HCV entry has remained difficult to estimate experimentally. Using the recently developed cell culture systems that allow persistent HCV infection in vitro, the dependence of HCV entry and kinetics on CD81 expression has been measured. We reasoned that analysis of the latter experiments using a mathematical model of viral kinetics may yield estimates of the number of E2-CD81 complexes necessary for HCV entry. Here, we constructed a mathematical model of HCV viral kinetics in vitro, in which we accounted explicitly for the dependence of HCV entry on CD81 expression. Model predictions of viral kinetics are in quantitative agreement with experimental observations. Specifically, our model predicts triphasic viral kinetics in vitro, where the first phase is characterized by cell proliferation, the second by the infection of susceptible cells and the third by the growth of cells refractory to infection. By fitting model predictions to the above data, we were able to estimate the threshold number of E2-CD81 complexes necessary for HCV entry into human hepatoma-derived cells. We found that depending on the E2-CD81 binding affinity, between 1 and 13 E2-CD81 complexes are necessary for HCV entry. With this estimate, our model captured data from independent experiments that employed different HCV clones and cells with distinct CD81 expression levels, indicating that the estimate is robust. Our study thus quantifies the molecular requirements of HCV entry and suggests guidelines for intervention strategies that target the E2-CD81 interaction. Further, our model presents a framework for quantitative analyses of cell culture studies now extensively employed to investigate HCV infection.

Robust formulations for clustering-based large-scale classification

Chebyshev-inequality-based convex relaxations of Chance-Constrained Programs (CCPs) are shown to be useful for learning classifiers on massive datasets. In particular, an algorithm that integrates efficient clustering procedures and CCP approaches for computing classifiers on large datasets is proposed. The key idea is to identify high density regions or clusters from individual class conditional densities and then use a CCP formulation to learn a classifier on the clusters. The CCP formulation ensures that most of the data points in a cluster are correctly classified by employing a Chebyshev-inequality-based convex relaxation. This relaxation is heavily dependent on the second-order statistics. However, this formulation and in general such relaxations that depend on the second-order moments are susceptible to moment estimation errors. One of the contributions of the paper is to propose several formulations that are robust to such errors. In particular a generic way of making such formulations robust to moment estimation errors is illustrated using two novel confidence sets. An important contribution is to show that when either of the confidence sets is employed, for the special case of a spherical normal distribution of clusters, the robust variant of the formulation can be posed as a second-order cone program. Empirical results show that the robust formulations achieve accuracies comparable to that with true moments, even when moment estimates are erroneous. Results also illustrate the benefits of employing the proposed methodology for robust classification of large-scale datasets.

Design and Evaluation of a Robust Optical Beam-Interruption-Based Vehicle Classifier System

This paper presents the design and development of a novel optical vehicle classifier system, which is based on interruption of laser beams, that is suitable for use in places with poor transportation infrastructure. The system can estimate the speed, axle count, wheelbase, tire diameter, and the lane of motion of a vehicle. The design of the system eliminates the need for careful optical alignment, whereas the proposed estimation strategies render the estimates insensitive to angular mounting errors and to unevenness of the road. Strategies to estimate vehicular parameters are described along with the optimization of the geometry of the system to minimize estimation errors due to quantization. The system is subsequently fabricated, and the proposed features of the system are experimentally demonstrated. The relative errors in the estimation of velocity and tire diameter are shown to be within 0.5% and to change by less than 17% for angular mounting errors up to 30 degrees. In the field, the classifier demonstrates accuracy better than 97.5% and 94%, respectively, in the estimation of the wheelbase and lane of motion and can classify vehicles with an average accuracy of over 89.5%.

A robust layer adapted difference method for singularly perturbed two-parameter parabolic problems

A finite difference method for a time-dependent singularly perturbed convection-diffusion-reaction problem involving two small parameters in one space dimension is considered. We use the classical implicit Euler method for time discretization and upwind scheme on the Shishkin-Bakhvalov mesh for spatial discretization. The method is analysed for convergence and is shown to be uniform with respect to both the perturbation parameters. The use of the Shishkin-Bakhvalov mesh gives first-order convergence unlike the Shishkin mesh where convergence is deteriorated due to the presence of a logarithmic factor. Numerical results are presented to validate the theoretical estimates obtained.

Tracking Pacific bluefin tuna (Thunnus thynnus orientalis) in the northeastern Pacific with an automated algorithm that estimates latitude by matching sea-surface-temperature data from satellites with temperature data from tags on fish

Data recovered from 11 popup satellite archival tags and 3 surgically implanted archival tags were used to analyze the movement patterns of juvenile northern bluefin tuna (Thunnus thynnus orientalis) in the eastern Pacific. The light sensors on archival and pop-up satellite transmitting archival tags (PSATs) provide data on the time of sunrise and sunset, allowing the calculation of an approximate geographic position of the animal. Light-based estimates of longitude are relatively robust but latitude estimates are prone to large degrees of error, particularly near the times of the equinoxes and when the tag is at low latitudes. Estimating latitude remains a problem for researchers using light-based geolocation algorithms and it has been suggested that sea surface temperature data from satellites may be a useful tool for refining latitude estimates. Tag data from bluefin tuna were subjected to a newly developed algorithm, called “PSAT Tracker,” which automatically matches sea surface temperature data from the tags with sea surface temperatures recorded by satellites. The results of this algorithm compared favorably to the estimates of latitude calculated with the lightbased algorithms and allowed for estimation of fish positions during times of the year when the lightbased algorithms failed. Three near one-year tracks produced by PSAT tracker showed that the fish range from the California−Oregon border to southern Baja California, Mexico, and that the majority of time is spent off the coast of central Baja Mexico. A seasonal movement pattern was evident; the fish spend winter and spring off central Baja California, and summer through fall is spent moving northward to Oregon and returning to Baja California.

Robust filtering and smoothing with gaussian processes

We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP) models. GPs are gaining increasing importance in signal processing, machine learning, robotics, and control for representing unknown system functions by posterior probability distributions. This modern way of system identification is more robust than finding point estimates of a parametric function representation. Our principled filtering/smoothing approach for GP dynamic systems is based on analytic moment matching in the context of the forward-backward algorithm. Our numerical evaluations demonstrate the robustness of the proposed approach in situations where other state-of-the-art Gaussian filters and smoothers can fail. © 2011 IEEE.