Mixed models are powerful tools for the analysis of clustered data and many extensions of the classical linear mixed model with normally distributed response have been established. As with all parametric models, correctness of the assumed model is critical for the validity of the ensuing inference. Model robust regression techniques predict mean response as a convex combination of a parametric and a nonparametric model fit to the data. It is a semiparametric method by which incompletely or incorrectly specified parametric models can be improved through adding an appropriate amount of a nonparametric fit. We apply this idea of model robustness in the framework of the linear mixed model. The mixed model robust regression (MMRR) predictions we propose are convex combinations of predictions obtained from a standard normal-theory linear mixed model, which serves as the parametric model component, and a locally weighted maximum likelihood fit which serves as the nonparametric component. An application of this technique with real data is provided. / Ph. D.

In this thesis, we study robust combinatorial problems with interval data. We introduce several new measures of robustness in response to the drawbacks of existing measures of robustness. The idea of these new measures is to ensure that the solutions are satisfactory for the decision maker in all scenarios, including the worst case scenario. Therefore, we have introduced a threshold over the worst case costs, in which above this threshold, solutions are no longer satisfactory for the decision maker. It is, however, important to consider other criteria than just the worst case. Therefore, in each of these new measures, a second criteria is used to evaluate the performance of the solution in other scenarios such as the best case one. We also study the robust deviation p-elements problem. In fact, we study when this solution is equal to the optimal solution in the scenario where the cost of each element is the midpoint of its corresponding interval. Then, we finally formulate the robust combinatorial problem with interval data as a bicriteria problem. We also integrate the decision maker's preferences over certain types of solutions into the model. We propose a method that uses these preferences to find the set of solutions that are never preferred by any other solution. We call this set the final set. We study the properties of the final sets from a coherence point of view and from a robust point of view. From a coherence point of view, we study necessary and sufficient conditions for the final set to be monotonic, for the corresponding preferences to be without cycles, and for the set to be stable. Those that do not satisfy these properties are eliminated since we believe these properties to be essential. We also study other properties such as the transitivity of the preference and indifference relations and more. We note that many of our final sets are included in one another and some are even intersections of other final sets. From a robust point of view, we compare our final sets with different measures of robustness and with the first- and second-degree stochastic dominance. We show which sets contain all of these solutions and which only contain these types of solutions. Therefore, when the decision maker chooses his preferences to find the final set, he knows what types of solutions may or may not be in the set. Lastly, we implement this method and apply it to the Robust Shortest Path Problem. We look at how this method performs using different types of randomly generated instances.

The goal of robust speech recognition is to maintain satisfactory recognition accuracy under mismatched operating conditions. This dissertation addresses the robustness issue from two directions. In the first part of the dissertation, we propose the Gauss-Newton method as a unified approach to estimating noise parameters for use in prevalent nonlinear compensation models, such as vector Taylor series (VTS), data-driven parallel model combination (DPMC), and unscented transform (UT), for noise-robust speech recognition. While iterative estimation of noise means in a generalized EM framework has been widely known, we demonstrate that such approaches are variants of the Gauss-Newton method. Furthermore, we propose a novel noise variance estimation algorithm that is consistent with the Gauss-Newton principle. The formulation of the Gauss-Newton method reduces the noise estimation problem to determining the Jacobians of the corrupted speech parameters. For sampling-based compensations, we present two methods, sample Jacobian average (SJA) and cross-covariance (XCOV), to evaluate these Jacobians. The Gauss-Newton method is closely related to another noise estimation approach, which views the model compensation from a generative perspective, giving rise to an EM-based algorithm analogous to the ML estimation for factor analysis (EM-FA). We demonstrate a close connection between these two approaches: they belong to the family of gradient-based methods except with different convergence rates. Note that the convergence property can be crucial to the noise estimation in many applications where model compensation may have to be frequently carried out in changing noisy environments to retain desired performance. Furthermore, several techniques are explored to further improve the nonlinear compensation approaches. To overcome the demand of the clean speech data for training acoustic models, we integrate nonlinear compensation with adaptive training. We also investigate the fast VTS compensation to improve the noise estimation efficiency, and combine the VTS compensation with acoustic echo cancellation (AEC) to mitigate issues due to interfering background speech. The proposed noise estimation algorithm is evaluated for various compensation models on two tasks. The first is to fit a GMM model to artificially corrupted samples, the second is to perform speech recognition on the Aurora 2 database, and the third is on a speech corpus simulating the meeting of multiple competing speakers. The significant performance improvements confirm the efficacy of the Gauss-Newton method to estimating the noise parameters of the nonlinear compensation models. The second research work is devoted to developing more effective models to take full advantage of heterogeneous speech data, which are typically collected from thousands of speakers in various environments via different transducers. The proposed synchronous HMM, in contrast to the conventional HMMs, introduces an additional layer of substates between the HMM state and the Gaussian component variables. The substates have the capability to register long-span non-phonetic attributes, such as gender, speaker identity, and environmental condition, which are integrally called speech scenes in this study. The hierarchical modeling scheme allows an accurate description of probability distribution of speech units in different speech scenes. To address the data sparsity problem in estimating parameters of multiple speech scene sub-models, a decision-based clustering algorithm is presented to determine the set of speech scenes and to tie the substate parameters, allowing us to achieve an excellent balance between modeling accuracy and robustness. In addition, by exploiting the synchronous relationship among the speech scene sub-models, we propose the multiplex Viterbi algorithm to efficiently decode the synchronous HMM within a search space of the same size as for the standard HMM. The multiplex Viterbi can also be generalized to decode an ensemble of isomorphic HMM sets, a problem often arising in the multi-model systems. The experiments on the Aurora 2 task show that the synchronous HMMs produce a significant improvement in recognition performance over the HMM baseline at the expense of a moderate increase in the memory requirement and computational complexity.

L’objectif de cette thèse est de proposer des solutions efficaces à des problèmes de décision qui ont un impact sur la vie des citoyens, et qui reposent sur des données incertaines. Au niveau des applications, nous nous intéressons à deux problèmes de localisation qui ont un impact sur l’espace public, notamment la localisation de nouveaux logements, et la localisation de vendeurs mobiles dans l’espace urbain. Les problèmes de localisation ne sont pas un sujet récent dans la littérature, toutefois, pour ces deux problèmes qui reposent sur des modèles de choix pour le comportement d’achat des consommateurs, l’incertitude dans le modèle génère un cas spécial qui permet d’étendre la littérature sur l’Optimisation Robuste. Les contributions de cette thèse peuvent s’appliquer à divers problèmes génériques d’optimisation. / We address decision problems under uncertain information with non-linear structures of parameter variation, and devise solution methods in the spirit of Bertsimas and Sim’s Γ-Robustness approach. Furthermore, although the non-linear impact of uncertainty often introduces discrete structures to the problem, for tractability, we provide the conditions under which the complexity class of the nominal model is preserved for the robust counterpart. We extend the Γ-Robustness approach in three avenues. First, we propose a generic case of non-linear impact of parameter variation, and model it with a piecewise linear approximation of the impact function. We show that the subproblem of determining the worst-case variation can be dualized despite the discrete structure of the piece-wise function. Next, we built a robust model for the location of new housing where the non-linearity is introduced by a choice model, and propose a solution combining Γ-Robustness with a scenario-based approach. We show that the subproblem is tractable and leads to a linear formulation of the robust problem. Finally, we model the demand in a Location Problem through a Poisson Process inducing, when demands are uncertain, non-linear structures of parameter variation. We propose the concept of Nested Uncertainty Budgets to manage uncertainty in a tractable way through a hierarchical structure and, under this framework, obtain a subproblem that includes both continuous and discrete deviation variables.

Path selection and generating tests for small delay faults is an important issue in the delay fault area. A novel technique for generating effective vectors for delay defects is the first issue that we have presented in the thesis. The test set achieves high path delay fault coverage to capture small-distributed delay defects and high transition fault coverage to capture gross delay defects. Furthermore, non-robust paths for ATPG are filtered (selected) carefully so that there is a minimum overlap with the already tested robust paths. A relationship between path delay fault model and transition fault model has been observed which helps us reduce the number of non-robust paths considered for test generation. To generate tests for robust and non-robust paths, a deterministic ATPG engine is developed. To deal with small delay faults, we have proposed a new transition fault model called As late As Possible Transition Fault (ALAPTF) Model. The model aims at detecting smaller delays, which will be missed by both the traditional transition fault model and the path delay model. The model makes sure that each transition is launched as late as possible at the fault site, accumulating the small delay defects along its way. Because some transition faults may require multiple paths to be launched, simple path-delay model will miss such faults. The algorithm proposed also detects robust and non-robust paths along with the transition faults and the execution time is linear to the circuit size. Results on ISCAS'85 and ISCAS'89 benchmark circuits shows that for all the cases, the new model is capable of detecting smaller gate delays and produces better results in case of process variations. Results also show that the filtered non-robust path set can be reduced to 40% smaller than the conventional path set without losing delay defect coverage. / Master of Science

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by Man-Cheung Hau. / Bibliography: leaves 110-112 / Thesis (M.Ph.)--Chinese University of Hong Kong, 1984

Telecommunication networks become major parts in modern complex control systems recently. They provide many advantages over conventional point-to-point connections, such as the simplification on installation and maintenance with comparatively low cost and the nature requirement of wireless communication in remote control systems. In practice, limited resource networks are shared by multiple controllers, sensors and actuators, and they may need to serve some other information unrelated to control purpose. Consequently, the control system design in networked control systems should be revised by taking communication constraints, for example, finite precision data, time delay and noise in transmission, into account. This thesis studies the robust control and state estimation of uncertain systems, when feedback information is sent via limited capacity communication channels. It focuses on the problem of finite precision data due to the communication constraints. The proposed schemes are based on the robust set-valued state estimation and the optimal control techniques. A state estimation problem of linear uncertain system is studied first. In this problem, we propose an algorithm called coder-decoder for uncertain systems. The coder encodes the observed output into a finite-length codeword and sends it to the decoder that generates the estimated state based on the received codeword. As an illustration, we apply the results in state estimation problem to a precision missile guidance problem using sensor fusion. In this problem, the information obtained from remote sensors is transmitted through limited capacity communication networks to the guided missile. Next, we study a stabilization problem of linear uncertain systems with state feedback. In this problem, the coder-controller scheme is developed to asymptotically stabilize the uncertain systems via limited capacity communication channels. The coder encodes the full state variable into a finite-length codeword and sends it to the controller that drives the system state to the origin. To achieve the asymptotic stability, we use a dynamic quantizer so that quantization noise converges to zero. The results in both state estimation and stabilization problems can handle the problem of finite data rate communication networks in control systems.

Telecommunication networks become major parts in modern complex control systems recently. They provide many advantages over conventional point-to-point connections, such as the simplification on installation and maintenance with comparatively low cost and the nature requirement of wireless communication in remote control systems. In practice, limited resource networks are shared by multiple controllers, sensors and actuators, and they may need to serve some other information unrelated to control purpose. Consequently, the control system design in networked control systems should be revised by taking communication constraints, for example, finite precision data, time delay and noise in transmission, into account. This thesis studies the robust control and state estimation of uncertain systems, when feedback information is sent via limited capacity communication channels. It focuses on the problem of finite precision data due to the communication constraints. The proposed schemes are based on the robust set-valued state estimation and the optimal control techniques. A state estimation problem of linear uncertain system is studied first. In this problem, we propose an algorithm called coder-decoder for uncertain systems. The coder encodes the observed output into a finite-length codeword and sends it to the decoder that generates the estimated state based on the received codeword. As an illustration, we apply the results in state estimation problem to a precision missile guidance problem using sensor fusion. In this problem, the information obtained from remote sensors is transmitted through limited capacity communication networks to the guided missile. Next, we study a stabilization problem of linear uncertain systems with state feedback. In this problem, the coder-controller scheme is developed to asymptotically stabilize the uncertain systems via limited capacity communication channels. The coder encodes the full state variable into a finite-length codeword and sends it to the controller that drives the system state to the origin. To achieve the asymptotic stability, we use a dynamic quantizer so that quantization noise converges to zero. The results in both state estimation and stabilization problems can handle the problem of finite data rate communication networks in control systems.