Modeling Dependent Structure for Utterances in ASR Evaluation

The bootstrap resampling method has been popular for performing significance analysis on word error rate (WER) in automatic speech recognition (ASR) evaluation. To deal with dependent speech data, the blockwise bootstrap approach is also introduced. By dividing utterances into uncorrelated blocks, this approach resamples these blocks instead of original data. However, it is typically nontrivial to uncover the dependent structure among utterances and identify the blocks, which might lead to subjective conclusions in statistical testing. In this paper, we present graphical lasso based methods to explicitly model such dependency and estimate uncorrelated blocks of utterances in a rigorous way, after which blockwise bootstrap is applied on top of the inferred blocks. We show the resulting variance estimator of WER in ASR evaluation is statistically consistent under mild conditions. We also demonstrate the validity of proposed approach on LibriSpeech dataset

Statistical Inference for the Haezendonck-Goovaerts Risk Measure

Recently the Haezendonck-Goovaerts (H-G) risk measure is receiving much attention in actuarial science with applications to optimal portfolios and optimal reinsurance because of its advantage in well quantifying the tail behavior of losses. This thesis systematically studies statistical inferences of the H-G risk measure under various settings including heavy-tailed losses, fixed and intermediate risk levels. The thesis starts by proposing an empirical likelihood inference for the H-G risk measure for two different risk levels---fixed risk level and intermediate risk level. More specifically, Chapter 2 considers the case of fixed risk level, and the derived asymptotic limit of a nonparametric inference is employed to construct an interval for the H-G risk measure. Chapter 3 considers the case of intermediate risk level, i.e., the level is treated as a function of the sample size and goes to one as the sample size tends to infinity. The proposed maximum empirical likelihood estimator for the H-G risk measure has a different limit from that for the case of a fixed level. But the proposed empirical likelihood method indeed gives a unified interval estimation for both cases. Chapter 4 proposes a two-part estimation for the H-G risk measure and the proposed estimators always have an asymptotic normal distribution regardless of the moment conditions. To achieve this, we separately estimate the tail part by extreme value theory and the middle part non-parametrically. The above chapters focus on independent data. In Chapter 5, we extend our methodology from independent data to dependent data and conduct the sensitivity analysis of a portfolio under the H-G risk measure. We first derive an expression for computing the sensitivity of the H-G risk measure, which enables us to estimate the sensitivity non-parametrically via the H-G risk measure. Second, we derive the asymptotic distributions of the nonparametric estimators for the H-G risk measure and its sensitivity by assuming that loss variables in the portfolio follow from a strictly stationary alpha-mixing sequence. Finally, this estimation combining with a bootstrap method is applied to a real dataset. Besides the study of the H-G risk measure, we investigate the estimation of the finite endpoint of a distribution function when normally distributed measurement errors contaminate the observations. Under the framework of extreme value theory, we propose a class of estimators for the standard deviation of the measurement errors as well as for the endpoint. Asymptotic properties of the proposed estimators are established and simulations demonstrate their good finite sample performance

Sparse reduced-rank regression for imaging genetics studies: models and applications

We present a novel statistical technique; the sparse reduced rank regression (sRRR) model which is a strategy for multivariate modelling of high-dimensional imaging responses and genetic predictors. By adopting penalisation techniques, the model is able to enforce sparsity in the regression coefficients, identifying subsets of genetic markers that best explain the variability observed in subsets of the phenotypes. To properly exploit the rich structure present in each of the imaging and genetics domains, we additionally propose the use of several structured penalties within the sRRR model. Using simulation procedures that accurately reflect realistic imaging genetics data, we present detailed evaluations of the sRRR method in comparison with the more traditional univariate linear modelling approach. In all settings considered, we show that sRRR possesses better power to detect the deleterious genetic variants. Moreover, using a simple genetic model, we demonstrate the potential benefits, in terms of statistical power, of carrying out voxel-wise searches as opposed to extracting averages over regions of interest in the brain. Since this entails the use of phenotypic vectors of enormous dimensionality, we suggest the use of a sparse classification model as a de-noising step, prior to the imaging genetics study. Finally, we present the application of a data re-sampling technique within the sRRR model for model selection. Using this approach we are able to rank the genetic markers in order of importance of association to the phenotypes, and similarly rank the phenotypes in order of importance to the genetic markers. In the very end, we illustrate the application perspective of the proposed statistical models in three real imaging genetics datasets and highlight some potential associations

Sparse Predictive Modeling : A Cost-Effective Perspective

Many real life problems encountered in industry, economics or engineering are complex and difficult to model by conventional mathematical methods. Machine learning provides a wide variety of methods and tools for solving such problems by learning mathematical models from data. Methods from the field have found their way to applications such as medical diagnosis, financial forecasting, and web-search engines. The predictions made by a learned model are based on a vector of feature values describing the input to the model. However, predictions do not come for free in real world applications, since the feature values of the input have to be bought, measured or produced before the model can be used. Feature selection is a process of eliminating irrelevant and redundant features from the model. Traditionally, it has been applied for achieving interpretable and more accurate models, while the possibility of lowering prediction costs has received much less attention in the literature. In this thesis we consider novel feature selection techniques for reducing prediction costs. The contributions of this thesis are as follows. First, we propose several cost types characterizing the cost of performing prediction with a trained model. Particularly, we consider costs emerging from multitarget prediction problems as well as a number of cost types arising when the feature extraction process is structured. Second, we develop greedy regularized least-squares methods to maximize the predictive performance of the models under given budget constraints. Empirical evaluations are performed on numerous benchmark data sets as well as on a novel water quality analysis application. The results demonstrate that in settings where the considered cost types apply, the proposed methods lead to substantial cost savings compared to conventional methods

Linearization Methods in Time Series Analysis

In this dissertation, we propose a set of computationally efficient methods based on approximating/representing nonlinear processes by linear ones, so-called linearization. Firstly, a linearization method is introduced for estimating the multiple frequencies in sinusoidal processes. It utilizes a regularized autoregressive (AR) approximation, which can be regarded as a "large p - small n" approach in a time series context. An appealing property of regularized AR is that it avoids a model selection step and allows for an efficient updating of the frequency estimates whenever new observations are obtained. The theoretical analysis shows that the regularized AR frequency estimates are consistent and asymptotically normally distributed. Secondly, a sieve bootstrap scheme is proposed using the linear representation of generalized autoregressive conditional heteroscedastic (GARCH) models to construct prediction intervals (PIs) for the returns and volatilities. Our method is simple, fast and distribution-free, while providing sharp and well-calibrated PIs. A similar linear bootstrap scheme can also be used for diagnostic testing. Thirdly, we introduce a robust lagrange multiplier (LM) test, which utilizes either the bootstrap or permutation procedure to obtain critical values, for detecting GARCH effects. We justify that both bootstrap and permutation LM tests are consistent. Intensive numerical studies indicate that the proposed resampling algorithms significantly improve the size and power of the LM test in both skewed and heavy-tailed processes. Moreover, fourthly, we introduce a nonparametric trend test in the presence of GARCH effects (NT-GARCH) based on heteroscedastic ANOVA. Our empirical evidence show that NT-GARCH can effectively detect non-monotonic trends under GARCH, especially in the presence of irregular seasonal components. We suggest to apply the bootstrap procedure for both selecting the window length and finding critical values. The newly proposed methods are illustrated by applications to astronomical data, to foreign currency exchange rates as well as to water and air pollution data. Finally, the dissertation is concluded by an outlook on further extensions of linearization methods, e.g., in model order selection and change point detection

Proceedings of the 1st Doctoral Consortium at the European Conference on Artificial Intelligence (DC-ECAI 2020)

1st Doctoral Consortium at the European Conference on Artificial Intelligence (DC-ECAI 2020), 29-30 August, 2020 Santiago de Compostela, SpainThe DC-ECAI 2020 provides a unique opportunity for PhD students, who are close to finishing their doctorate research, to interact with experienced researchers in the field. Senior members of the community are assigned as mentors for each group of students based on the student’s research or similarity of research interests. The DC-ECAI 2020, which is held virtually this year, allows students from all over the world to present their research and discuss their ongoing research and career plans with their mentor, to do networking with other participants, and to receive training and mentoring about career planning and career option

Analysis and Modeling of Passive Stereo and Time-of-Flight Imaging

This thesis is concerned with the analysis and modeling of effects which cause errors in passive stereo and Time-of-Flight imaging systems. The main topics are covered in four chapters: I commence with a treatment of a system combining Time-of-Flight imaging with passive stereo and show how commonly used fusion models relate to the measurements of the individual modalities. In addition, I present novel fusion techniques capable of improving the depth reconstruction over those obtained separately by either modality. Next, I present a pipeline and uncertainty analysis for the generation of large amounts of reference data for quantitative stereo evaluation. The resulting datasets not only contain reference geometry, but also per pixel measures of reference data uncertainty. The next two parts deal with individual effects observed: Time-of-Flight cameras suffer from range ambiguity if the scene extends beyond a certain distance. I show that it is possible to extend the valid range by changing design parameters of the underlying measurement system. Finally, I present methods that make it possible to amend model violation errors in stereo due to reflections. This is done by means of modeling a limited level of light transport and material properties in the scene