Estimation of Stokes vector components from an interferometric fringe encoded image is a novel way of measuring the State Of Polarization (SOP) distribution across a scene. Imaging polarimeters employing interferometric techniques encode SOP information in a single image in the form of fringes. The lack of moving parts and the use of a single image eliminates the problems of conventional polarimetry - vibration, spurious signal generation due to artifacts, beam wander and the need for registration routines. However, interferometric polarimeters are limited by narrow band pass operation and short exposure time operations which decrease the Signal to Noise Ratio (SNR) in the detected image.A simulation environment for designing an Interferometric Stokes Imaging polarimeter (ISIP) and a detector with noise effects is created and presented. A user is capable of imaging an object with defined SOP through an ISIP on to a detector producing a digitized image output. The simulation also includes band pass imaging capabilities, control of detector noise, and object brightness levels.The Stokes images are estimated from a fringe encoded image of a scene by means of a reconstructor algorithm. A spatial domain methodology involving the idea of a unit cell and slide approach is applied to the reconstructor model developed using Mueller calculus. The validation of this methodology and effectiveness compared to a discrete approach is demonstrated with suitable examples. The pixel size required to sample the fringes and the minimum unit cell size required for reconstruction are investigated using condition numbers. The importance of the PSF of fore-optics (telescope) used in imaging the object is investigated and analyzed using a point source imaging example and a Nyquist criteria is presented.Reconstruction of fringe modulated images in the presence of noise involves choosing an optimal sized unitcell. The choice of the unit cell based on the size of the polarization domain and illumination level is analyzed using a bias-variance tradeoff to obtain the minimum root mean square error. A similar tradeoff study is used to analyze the choice of the band pass filters under various illumination levels. Finally, a sensitivity analysis of the ISIP is presented to explore the applicability of this device to detect low degrees of polarization in areas like remote sensing.

Modern scientific technology such as microarrays, imaging devices, genome-wide association studies or social science surveys provide statisticians with hundreds or even thousands of tests to consider simultaneously. Testing many thousands of null hypotheses may increase the number of Type $I$ errors. In large-scale hypothesis testing, researchers can use different statistical techniques such as family-wise error rates, false discovery rates, permutation methods, local false discovery rate, where all available data usually should be analyzed together. In applications, the thousands of tests are related by a scientifically meaningful structure. Ignoring that structure can be misleading as it may increase the number of false positives and false negatives. As an example, in genome-wide association studies each test corresponds to a specific genetic marker. In such a case, the scientific structure for each genetic marker can be its minor allele frequency. In this research, the local false discovery rate as a relevant statistical approach is considered to analyze the thousands of tests together. We present a model for multiple hypothesis testing when the scientific structure of each test is incorporated as a co-variate. The purpose of this model is to incorporate the co-variate to improve the performance of testing procedures. The method we consider has different estimates depending on the tuning parameter. We would like to estimate the optimal value of that parameter by considering observed statistics. Thus, among those estimators, the one which minimizes the estimated errors due to bias and to variance is chosen by applying the bootstrap approach. Such an estimation method is called an adaptive reference class method. Under the combined reference class method, the effect of the co-variates is ignored and all null hypotheses should be analyzed together. In this research, under some assumptions for the co-variates and the prior probabilities, the proposed adaptive reference class method shows smaller error than the combined reference class method in estimating the local false discovery rate, when the number of tests gets large. We describe the adaptive reference class method to the coronary artery disease data, and we use simulation data to evaluate the performance of the estimator associated with the adaptive reference class method.

Relevance is an essential concept in information retrieval (IR) and relevance estimation is a fundamental IR task. It involves not only document relevance estimation, but also estimation of user's information need. Relevance-based language model aims to estimate a relevance model (i.e., a relevant query term distribution) from relevance feedback documents. The true relevance model should be generated from truly relevant documents. The ideal estimation of the true relevance model is expected to be not only effective in terms of mean retrieval performance (e.g., Mean Average Precision) over all the queries, but also stable in the sense that the performance is stable across different individual queries. In practice, however, in approximating/estimating the true relevance model, the improvement of retrieval effectiveness often sacrifices the retrieval stability, and vice versa. In this thesis, we propose to explore and analyze such effectiveness-stability tradeoff from a new perspective, i.e., the bias-variance tradeoff that is a fundamental theory in statistical estimation. We first formulate the bias, variance and the trade-off between them for retrieval performance as well as for query model estimation. We then analytically and empirically study a number of factors (e.g., query model complexity, query model combination, document weight smoothness and irrelevant documents removal) that can affect the bias and variance. Our study shows that the proposed bias-variance trade-off analysis can serve as an analytical framework for query model estimation. We then investigate in depth on two particular key factors: document weight smoothness and removal of irrelevant documents, in query model estimation, by proposing novel methods for document weight smoothing and irrelevance distribution separation, respectively. Systematic experimental evaluation on TREC collections shows that the proposed methods can improve both retrieval effectiveness and retrieval stability of query model estimation. In addition to the above main contributions, we also carry out initial exploration on two further directions: the formulation of bias-variance in personalization and looking at the query model estimation via a novel theoretical angle (i.e., Quantum theory) that has partially inspired our research.

In terms of the Bias/Variance decomposition, very flexible (i.e., complex) Supervised Machine Learning systems may lead to unbiased estimators but with high variance. A rigid model, in contrast, may lead to small variance but high bias. There is a trade-off between the bias and variance contributions to the error, where the optimal performance is achieved.In this work we present three schemes related to the control of the Bias/Variance decomposition for Feed-forward Neural Networks (FNNs) with the (sometimes modified) quadratic loss function:1. An algorithm for sequential approximation with FNNs, named Sequential Approximation with Optimal Coefficients and Interacting Frequencies (SAOCIF). Most of the sequential approximations proposed in the literature select the new frequencies (the non-linear weights) guided by the approximation of the residue of the partial approximation. We propose a sequential algorithm where the new frequency is selected taking into account its interactions with the previously selected ones. The interactions are discovered by means of their optimal coefficients (the linear weights). A number of heuristics can be used to select the new frequencies. The aim is that the same level of approximation may be achieved with less hidden units than if we only try to match the residue as best as possible. In terms of the Bias/Variance decomposition, it will be possible to obtain simpler models with the same bias. The idea behind SAOCIF can be extended to approximation in Hilbert spaces, maintaining orthogonal-like properties. In this case, the importance of the interacting frequencies lies in the expectation of increasing the rate of approximation. Experimental results show that the idea of interacting frequencies allows to construct better approximations than matching the residue.2. A study and comparison of different criteria to perform Feature Selection (FS) with Multi-Layer Perceptrons (MLPs) and the Sequential Backward Selection (SBS) procedure within the wrapper approach. FS procedures control the Bias/Variance decomposition by means of the input dimension, establishing a clear connection with the curse of dimensionality. Several critical decision points are studied and compared. First, the stopping criterion. Second, the data set where the value of the loss function is measured. Finally, we also compare two ways of computing the saliency (i.e., the relative importance) of a feature: either first train a network and then remove temporarily every feature or train a different network with every feature temporarily removed. The experiments are performed for linear and non-linear models. Experimental results suggest that the increase in the computational cost associated with retraining a different network with every feature temporarily removed previous to computing the saliency can be rewarded with a significant performance improvement, specially if non-linear models are used. Although this idea could be thought as very intuitive, it has been hardly used in practice. Regarding the data set where the value of the loss function is measured, it seems clear that the SBS procedure for MLPs takes profit from measuring the loss function in a validation set. A somewhat non-intuitive conclusion is drawn looking at the stopping criterion, where it can be seen that forcing overtraining may be as useful as early stopping.3. A modification of the quadratic loss function for classification problems, inspired in Support Vector Machines (SVMs) and the AdaBoost algorithm, named Weighted Quadratic Loss (WQL) function. The modification consists in weighting the contribution of every example to the total error. In the linearly separable case, the solution of the hard margin SVM also minimizes the proposed loss function. The hardness of the resulting solution can be controlled, as in SVMs, so that this scheme may also be used for the non-linearly separable case. The error weighting proposed in WQL forces the training procedure to pay more attention to the points with a smaller margin. Therefore, variance tries to be controlled by not attempting to overfit the points that are already well classified. The model shares several properties with the SVMs framework, with some additional advantages. On the one hand, the final solution is neither restricted to have an architecture with so many hidden units as points (or support vectors) in the data set nor to use kernel functions. The frequencies are not restricted to be a subset of the data set. On the other hand, it allows to deal with multiclass and multilabel problems in a natural way. Experimental results are shown confirming these claims.A wide experimental work has been done with the proposed schemes, including artificial data sets, well-known benchmark data sets and two real-world problems from the Natural Language Processing domain. In addition to widely used activation functions, such as the hyperbolic tangent or the Gaussian function, other activation functions have been tested. In particular, sinusoidal MLPs showed a very good behavior. The experimental results can be considered as very satisfactory. The schemes presented in this work have been found to be very competitive when compared to other existing schemes described in the literature. In addition, they can be combined among them, since they deal with complementary aspects of the whole learning process.

L’objectif principal de cette thèse est de souligner que le compromis biais-variance n’est pas toujours vrai (p. ex. dans les réseaux neuronaux). Nous plaidons pour que ce manque d’universalité soit reconnu dans les manuels scolaires et enseigné dans les cours d’introduction qui couvrent le compromis. Nous passons d’abord en revue l’historique du compromis entre les biais et les variances, sa prévalence dans les manuels scolaires et certaines des principales affirmations faites au sujet du compromis entre les biais et les variances. Au moyen d’expériences et d’analyses approfondies, nous montrons qu’il n’y a pas de compromis entre la variance et le biais dans les réseaux de neurones lorsque la largeur du réseau augmente. Nos conclusions semblent contredire les affirmations de l’oeuvre historique de Geman et al. (1992). Motivés par cette contradiction, nous revisitons les mesures expérimentales dans Geman et al. (1992). Nous discutons du fait qu’il n’y a jamais eu de preuves solides d’un compromis dans les réseaux neuronaux lorsque le nombre de paramètres variait. Nous observons un phénomène similaire au-delà de l’apprentissage supervisé, avec un ensemble d’expériences d’apprentissage de renforcement profond. Nous soutenons que les révisions des manuels et des cours magistraux ont pour but de transmettre cette compréhension moderne nuancée de l’arbitrage entre les biais et les variances. / The main goal of this thesis is to point out that the bias-variance tradeoff is not always true (e.g. in neural networks). We advocate for this lack of universality to be acknowledged in textbooks and taught in introductory courses that cover the tradeoff. We first review the history of the bias-variance tradeoff, its prevalence in textbooks, and some of the main claims made about the bias-variance tradeoff. Through extensive experiments and analysis, we show a lack of a bias-variance tradeoff in neural networks when increasing network width. Our findings seem to contradict the claims of the landmark work by Geman et al. (1992). Motivated by this contradiction, we revisit the experimental measurements in Geman et al. (1992). We discuss that there was never strong evidence for a tradeoff in neural networks when varying the number of parameters. We observe a similar phenomenon beyond supervised learning, with a set of deep reinforcement learning experiments. We argue that textbook and lecture revisions are in order to convey this nuanced modern understanding of the bias-variance tradeoff.

<p>The capacity of deep reinforcement learning policy networks has been found to affect the performance of trained agents. It has been observed that policy networks with more parameters have better training performance and generalization ability than smaller networks. In this work, we find cases where this does not hold true. We observe unimodal variance in the zero-shot test return of varying width policies, which accompanies a drop in both train and test return. Empirically, we demonstrate mostly monotonically increasing performance or mostly optimal performance as the width of deep policy networks increase, except near the variance mode. Finally, we find a scenario where larger networks have increasing performance up to a point, then decreasing performance. We hypothesize that these observations align with the theory of double descent in supervised learning, although with specific differences.</p>

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In this work, new methods of feature extraction, feature selection, stochastic data characterization/modeling, variance reduction and measures for parametric discrimination are proposed. These methods have implications for data mining, machine learning, and information theory. A novel decision-support system is developed in order to guide intervention during cardiac arrest. The models are built upon knowledge extracted with signal-processing, non-linear dynamic and machine-learning methods. The proposed ECG characterization, combined with information extracted from PetCO2 signals, shows viability for decision-support in clinical settings. The approach, which focuses on integration of multiple features through machine learning techniques, suits well to inclusion of multiple physiologic signals. Ventricular Fibrillation (VF) is a common presenting dysrhythmia in the setting of cardiac arrest whose main treatment is defibrillation through direct current countershock to achieve return of spontaneous circulation. However, often defibrillation is unsuccessful and may even lead to the transition of VF to more nefarious rhythms such as asystole or pulseless electrical activity. Multiple methods have been proposed for predicting defibrillation success based on examination of the VF waveform. To date, however, no analytical technique has been widely accepted. For a given desired sensitivity, the proposed model provides a significantly higher accuracy and specificity as compared to the state-of-the-art. Notably, within the range of 80-90% of sensitivity, the method provides about 40% higher specificity. This means that when trained to have the same level of sensitivity, the model will yield far fewer false positives (unnecessary shocks). Also introduced is a new model that predicts recurrence of arrest after a successful countershock is delivered. To date, no other work has sought to build such a model. I validate the method by reporting multiple performance metrics calculated on (blind) test sets.