On the BRST Quantization of the Massless Bosonic Particle in Twistor-Like Formulation

We study some features of bosonic particle path-integral quantization in a twistor-like approach by use of the BRST-BFV quantization prescription. In the course of the Hamiltonian analysis we observe links between various formulations of the twistor-like particle by performing a conversion of the Hamiltonian constraints of one formulation to another. A particular feature of the conversion procedure applied to turn the second-class constraints into the first-class constraints is that the simplest Lorentz-covariant way to do this is to convert a full mixed set of the initial first- and second-class constraints rather than explicitly extracting and converting only the second-class constraints. Another novel feature of the conversion procedure applied below is that in the case of the D=4 and D=6 twistor-like particle the number of new auxiliary Lorentz-covariant coordinates, which one introduces to get a system of first-class constraints in an extended phase space, exceeds the number of independent second-class constraints of the original dynamical system. We calculate the twistor-like particle propagator in D=3, 4 and 6 space-time dimensions and show, that it coincides with that of a conventional massless bosonic particle.Comment: LaTeX file, 17 page

Modeling and Analysis of Software Product Line Variability in Clafer

Both feature and class modeling are used in Software Product Line (SPL) engineering to model variability. Feature models are used primarily to represent user-visible characteristics (i.e., features) of products; whereas class models are often used to model types of components and connectors in a product-line architecture. Previous works have explored the approach of using a single language to express both configurations of features and components. Their goal was to simplify the definition and analysis of feature-to-component mappings and to allow modeling component options as features. A prominent example of this approach is cardinality-based feature modeling, which extends feature models with multiple instantiation and references to express component-like, replicated features. Another example is to support feature modeling in a class modeling language, such as UML or MOF, using their profiling mechanisms and a stylized use of composition. Both examples have notable drawbacks: cardinality-based feature modeling lacks a constraint language and a well-defined semantics; encoding feature models as class models and their evolution bring extra complexity. This dissertation presents Clafer (class, feature, reference), a class modeling language with first-class support for feature modeling. Clafer can express rich structural models augmented with complex constraints, i.e., domain, variability, component models, and meta-models. Clafer supports: (i) class-based meta-models, (ii) object models (with uncertainty, if needed), (iii) feature models with attributes and multiple instantiation, (iv) configurations of feature models, (v) mixtures of meta- and feature models and model templates, and (vi) first-order logic constraints. Clafer also makes it possible to arrange models into multiple specialization and extension layers via constraints and inheritance. On the other hand, in designing Clafer we wanted to create a language that builds upon as few concepts as possible, and is easy to learn. The language is supported by tools for SPL verification and optimization. We propose to unify basic modeling constructs into a single concept, called clafer. In other words, Clafer is not a hybrid language. We identify several key mechanisms allowing a class modeling language to express feature models concisely. We provide Clafer with a formal semantics built in a novel, structurally explicit way. As Clafer subsumes cardinality-based feature modeling with attributes, references, and constraints, we are the first to precisely define semantics of such models. We also explore the notion of partial instantiation that allows for modeling with uncertainty and variability. We show that Object-Oriented Modeling (OOM) languages with no direct support for partial instances can support them via class modeling, using subclassing and strengthening multiplicity constraints. We make the encoding of partial instances via subclassing precise and general. Clafer uses this encoding and pushes the idea even further: it provides a syntactic unification of types and (partial) instances via subclassing and redefinition. We evaluate Clafer analytically and experimentally. The analytical evaluation shows that Clafer can concisely express feature and meta-models via a uniform syntax and unified semantics. The experimental evaluation shows that: 1) Clafer can express a variety of realistic rich structural models with complex constraints, such as variability models, meta-models, model templates, and domain models; and 2) that useful analyses can be performed within seconds

Convex and non-convex optimization using centroid-encoding for visualization, classification, and feature selection

Includes bibliographical references.2022 Fall.Classification, visualization, and feature selection are the three essential tasks of machine learning. This Ph.D. dissertation presents convex and non-convex models suitable for these three tasks. We propose Centroid-Encoder (CE), an autoencoder-based supervised tool for visualizing complex and potentially large, e.g., SUSY with 5 million samples and high-dimensional datasets, e.g., GSE73072 clinical challenge data. Unlike an autoencoder, which maps a point to itself, a centroid-encoder has a modified target, i.e., the class centroid in the ambient space. We present a detailed comparative analysis of the method using various data sets and state-of-the-art techniques. We have proposed a variation of the centroid-encoder, Bottleneck Centroid-Encoder (BCE), where additional constraints are imposed at the bottleneck layer to improve generalization performance in the reduced space. We further developed a sparse optimization problem for the non-linear mapping of the centroid-encoder called Sparse Centroid-Encoder (SCE) to determine the set of discriminate features between two or more classes. The sparse model selects variables using the 1-norm applied to the input feature space. SCE extracts discriminative features from multi-modal data sets, i.e., data whose classes appear to have multiple clusters, by using several centers per class. This approach seems to have advantages over models which use a one-hot-encoding vector. We also provide a feature selection framework that first ranks each feature by its occurrence, and the optimal number of features is chosen using a validation set. CE and SCE are models based on neural network architectures and require the solution of non-convex optimization problems. Motivated by the CE algorithm, we have developed a convex optimization for the supervised dimensionality reduction technique called Centroid Component Retrieval (CCR). The CCR model optimizes a multi-objective cost by balancing two complementary terms. The first term pulls the samples of a class towards its centroid by minimizing a sample's distance from its class centroid in low dimensional space. The second term pushes the classes by maximizing the scattering volume of the ellipsoid formed by the class-centroids in embedded space. Although the design principle of CCR is similar to LDA, our experimental results show that CCR exhibits performance advantages over LDA, especially on high-dimensional data sets, e.g., Yale Faces, ORL, and COIL20. Finally, we present a linear formulation of Centroid-Encoder with orthogonality constraints, called Principal Centroid Component Analysis (PCCA). This formulation is similar to PCA, except the class labels are used to formulate the objective, resulting in the form of supervised PCA. We show the classification and visualization experiments results with this new linear tool

Receptive fields optimization in deep learning for enhanced interpretability, diversity, and resource efficiency.

In both supervised and unsupervised learning settings, deep neural networks (DNNs) are known to perform hierarchical and discriminative representation of data. They are capable of automatically extracting excellent hierarchy of features from raw data without the need for manual feature engineering. Over the past few years, the general trend has been that DNNs have grown deeper and larger, amounting to huge number of final parameters and highly nonlinear cascade of features, thus improving the flexibility and accuracy of resulting models. In order to account for the scale, diversity and the difficulty of data DNNs learn from, the architectural complexity and the excessive number of weights are often deliberately built in into their design. This flexibility and performance usually come with high computational and memory demands both during training and inference. In addition, insight into the mappings DNN models perform and human ability to understand them still remain very limited. This dissertation addresses some of these limitations by balancing three conflicting objectives: computational/ memory demands, interpretability, and accuracy. This dissertation first introduces some unsupervised feature learning methods in a broader context of dictionary learning. It also sets the tone for deep autoencoder learning and constraints for data representations in light of removing some of the aforementioned bottlenecks such as the feature interpretability of deep learning models with nonnegativity constraints on receptive fields. In addition, the two main classes of solution to the drawbacks associated with overparameterization/ over-complete representation in deep learning models are also presented. Subsequently, two novel methods, one for each solution class, are presented to address the problems resulting from over-complete representation exhibited by most deep learning models. The first method is developed to achieve inference-cost-efficient models via elimination of redundant features with negligible deterioration of prediction accuracy. This is important especially for deploying deep learning models into resource-limited portable devices. The second method aims at diversifying the features of DNNs in the learning phase to improve their performance without undermining their size and capacity. Lastly, feature diversification is considered to stabilize adversarial learning and extensive experimental outcomes show that these methods have the potential of advancing the current state-of-the-art on different learning tasks and benchmark datasets

The Hitchin Image in Type-D

Motivated by their appearance as Coulomb branch geometries of Class S theories, we study the image of the local Hitchin map in tame Hitchin systems of type-D with residue in a special nilpotent orbit $\mathcal{O}_H$. We describe two important features which distinguish it from the type A case studied in arXiv:2008.01020. The first feature, which we term even type constraints, arise iff the partition label $[\mathcal{O}_H]$ has even parts. In this case, our Hitchin image is non-singular and thus different from the one studied by Baraglia and Kamgarpour. We argue that our Hitchin image always globalizes to being the Hitchin base of an integrable system. The second feature, which we term odd type constraints, is related to a particular finite group $\overline{A}_b(\mathcal{O}_H)$ being non-trivial. When this finite group is non-trivial, we have $\mid \overline{A}_b \mid$ choices for the local Hitchin base. Additionally, we also show that the finite group $\overline{A}_b(\mathcal{O}_H)$ encodes the size of the dual special piece.Comment: 37 pages + references, 3 figure

Sequence-Based Classification Using Discriminatory Motif Feature Selection

Most existing methods for sequence-based classification use exhaustive feature generation, employing, for example, all -mer patterns. The motivation behind such (enumerative) approaches is to minimize the potential for overlooking important features. However, there are shortcomings to this strategy. First, practical constraints limit the scope of exhaustive feature generation to patterns of length , such that potentially important, longer () predictors are not considered. Second, features so generated exhibit strong dependencies, which can complicate understanding of derived classification rules. Third, and most importantly, numerous irrelevant features are created. These concerns can compromise prediction and interpretation. While remedies have been proposed, they tend to be problem-specific and not broadly applicable. Here, we develop a generally applicable methodology, and an attendant software pipeline, that is predicated on discriminatory motif finding. In addition to the traditional training and validation partitions, our framework entails a third level of data partitioning, a discovery partition. A discriminatory motif finder is used on sequences and associated class labels in the discovery partition to yield a (small) set of features. These features are then used as inputs to a classifier in the training partition. Finally, performance assessment occurs on the validation partition. Important attributes of our approach are its modularity (any discriminatory motif finder and any classifier can be deployed) and its universality (all data, including sequences that are unaligned and/or of unequal length, can be accommodated). We illustrate our approach on two nucleosome occupancy datasets and a protein solubility dataset, previously analyzed using enumerative feature generation. Our method achieves excellent performance results, with and without optimization of classifier tuning parameters. A Python pipeline implementing the approach is available at http://www.epibiostat.ucsf.edu/biostat/sen/dmfs/

New models and methods for classification and feature selection. a mathematical optimization perspective

The objective of this PhD dissertation is the development of new models for Supervised Classification and Benchmarking, making use of Mathematical Optimization and Statistical tools. Particularly, we address the fusion of instruments from both disciplines, with the aim of extracting knowledge from data. In such a way, we obtain innovative methodologies that overcome to those existing ones, bridging theoretical Mathematics with real-life problems. The developed works along this thesis have focused on two fundamental methodologies in Data Science: support vector machines (SVM) and Benchmarking. Regarding the first one, the SVM classifier is based on the search for the separating hyperplane of maximum margin and it is written as a quadratic convex problem. In the Benchmarking context, the goal is to calculate the different efficiencies through a non-parametric deterministic approach. In this thesis we will focus on Data Envelopment Analysis (DEA), which consists on a Linear Programming formulation. This dissertation is structured as follows. In Chapter 1 we briefly present the different challenges this thesis faces on, as well as their state-of-the-art. In the same vein, the different formulations used as base models are exposed, together with the notation used along the chapters in this thesis. In Chapter 2, we tackle the problem of the construction of a version of the SVM that considers misclassification errors. To do this, we incorporate new performance constraints in the SVM formulation, imposing upper bounds on the misclassification errors. The resulting formulation is a quadratic convex problem with linear constraints. Chapter 3 continues with the SVM as the basis, and sets out the problem of providing not only a hard-labeling for each of the individuals belonging to the dataset, but a class probability estimation. Furthermore, confidence intervals for both the score values and the posterior class probabilities will be provided. In addition, as in the previous chapter, we will carry the obtained results to the field in which misclassified errors are considered. With such a purpose, we have to solve either a quadratic convex problem or a quadratic convex problem with linear constraints and integer variables, and always taking advantage of the parameter tuning of the SVM, that is usually wasted. Based on the results in Chapter 2, in Chapter 4 we handle the problem of feature selection, taking again into account the misclassification errors. In order to build this technique, the feature selection is embedded in the classifier model. Such a process is divided in two different steps. In the first step, feature selection is performed while at the same time data is separated via an hyperplane or linear classifier, considering the performance constraints. In the second step, we build the maximum margin classifier (SVM) using the selected features from the first step, and again taking into account the same performance constraints. In Chapter 5, we move to the problem of Benchmarking, where the practices of different entities are compared through the products or services they provide. This is done with the aim of make some changes or improvements in each of them. Concretely, in this chapter we propose a Mixed Integer Linear Programming formulation based in Data Envelopment Analysis (DEA), with the aim of perform feature selection, improving the interpretability and comprehension of the obtained model and efficiencies. Finally, in Chapter 6 we collect the conclusions of this thesis as well as future lines of research

DeSTSeg: Segmentation Guided Denoising Student-Teacher for Anomaly Detection

Visual anomaly detection, an important problem in computer vision, is usually formulated as a one-class classification and segmentation task. The student-teacher (S-T) framework has proved to be effective in solving this challenge. However, previous works based on S-T only empirically applied constraints on normal data and fused multi-level information. In this study, we propose an improved model called DeSTSeg, which integrates a pre-trained teacher network, a denoising student encoder-decoder, and a segmentation network into one framework. First, to strengthen the constraints on anomalous data, we introduce a denoising procedure that allows the student network to learn more robust representations. From synthetically corrupted normal images, we train the student network to match the teacher network feature of the same images without corruption. Second, to fuse the multi-level S-T features adaptively, we train a segmentation network with rich supervision from synthetic anomaly masks, achieving a substantial performance improvement. Experiments on the industrial inspection benchmark dataset demonstrate that our method achieves state-of-the-art performance, 98.6% on image-level ROC, 75.8% on pixel-level average precision, and 76.4% on instance-level average precision

Feature selection for chemical sensor arrays using mutual information

We address the problem of feature selection for classifying a diverse set of chemicals using an array of metal oxide sensors. Our aim is to evaluate a filter approach to feature selection with reference to previous work, which used a wrapper approach on the same data set, and established best features and upper bounds on classification performance. We selected feature sets that exhibit the maximal mutual information with the identity of the chemicals. The selected features closely match those found to perform well in the previous study using a wrapper approach to conduct an exhaustive search of all permitted feature combinations. By comparing the classification performance of support vector machines (using features selected by mutual information) with the performance observed in the previous study, we found that while our approach does not always give the maximum possible classification performance, it always selects features that achieve classification performance approaching the optimum obtained by exhaustive search. We performed further classification using the selected feature set with some common classifiers and found that, for the selected features, Bayesian Networks gave the best performance. Finally, we compared the observed classification performances with the performance of classifiers using randomly selected features. We found that the selected features consistently outperformed randomly selected features for all tested classifiers. The mutual information filter approach is therefore a computationally efficient method for selecting near optimal features for chemical sensor arrays