We study the problem of robust distribution estimation under the Wasserstein metric, a popular discrepancy measure between probability distributions rooted in optimal transport (OT) theory. We introduce a new outlier-robust Wasserstein distance $\mathsf{W}_p^\varepsilon$ which allows for $\varepsilon$ outlier mass to be removed from its input distributions, and show that minimum distance estimation under $\mathsf{W}_p^\varepsilon$ achieves minimax optimal robust estimation risk. Our analysis is rooted in several new results for partial OT, including an approximate triangle inequality, which may be of independent interest. To address computational tractability, we derive a dual formulation for $\mathsf{W}_p^\varepsilon$ that adds a simple penalty term to the classic Kantorovich dual objective. As such, $\mathsf{W}_p^\varepsilon$ can be implemented via an elementary modification to standard, duality-based OT solvers. Our results are extended to sliced OT, where distributions are projected onto low-dimensional subspaces, and applications to homogeneity and independence testing are explored. We illustrate the virtues of our framework via applications to generative modeling with contaminated datasets.

While Fourier Transform has seen many applications in data compression and signal processing, it's applications in Deep Neural Networks are limited. They are often only used for Medical Imaging based applications. Here, I discuss three approaches of scaling up Neural Networks for computer vision using Fast Fourier Transform (FFT). Note: python libraries were used for FFT as they provide extremely efficient cuda-based approaches for FFT on the GPU. The report only contains part of the code; the entire code-base is very large and includes the dataloaders, hyperparameter configurations, scripts to test fps, datasets, training and validation engines, and the model implementations themselves.

We propose $\mathcal{T}$ruth $\mathcal{T}$able net ($\mathcal{TT}$net), a novel Convolutional Neural Network (CNN) architecture that addresses, by design, the open challenges of interpretability, formal verification, and logic gate conversion. $\mathcal{TT}$net is built using CNNs' filters that are equivalent to tractable truth tables and that we call Learning Truth Table (LTT) blocks. The dual form of LTT blocks allows the truth tables to be easily trained with gradient descent and makes these CNNs easy to interpret, verify and infer. Specifically, $\mathcal{TT}$net is a deep CNN model that can be automatically represented, after post-training transformation, as a sum of Boolean decision trees, or as a sum of Disjunctive/Conjunctive Normal Form (DNF/CNF) formulas, or as a compact Boolean logic circuit. We demonstrate the effectiveness and scalability of $\mathcal{TT}$net on multiple datasets, showing comparable interpretability to decision trees, fast complete/sound formal verification, and scalable logic gate representation, all compared to state-of-the-art methods. We believe this work represents a step towards making CNNs more transparent and trustworthy for real-world critical applications.

This preprint specifies and defines all the Terms, Properties, and Relationships of NFRsTDO (Non-Functional Requirements Top-Domain Ontology). NFRsTDO v1.2, whose UML conceptualization is shown in Figure 1 is a slightly updated version of its predecessor, namely NFRsTDO v1.1. NFRsTDO is an ontology mainly devoted to quality (non-functional) requirements and quality/cost views, which is placed at the top-domain level in the context of a multilayer ontological architecture called FCD-OntoArch (Foundational, Core, Domain, and instance Ontological Architecture for sciences). Figure 2 depicts its five tiers, which entail Foundational, Core, Top-Domain, Low-Domain, and Instance. Each level is populated with ontological components or, in other words, ontologies. Ontologies at the same level can be related to each other, except at the foundational level, where only ThingFO (Thing Foundational Ontology) is found. In addition, ontologies' terms and relationships at lower levels can be semantically enriched by ontologies' terms and relationships from the higher levels. NFRsTDO's terms and relationships are mainly extended/reused from ThingFO, SituationCO (Situation Core Ontology), ProcessCO (Process Core Ontology), and FRsTDO (Functional Requirements Top-Domain Ontology). Stereotypes are the used mechanism for enriching NFRsTDO terms. Note that annotations of updates from the previous version (NFRsTDO v1.1) to the current one (v1.2) can be found in Appendix A.

The Computer-aided Diagnosis or Detection (CAD) approach for skin lesion analysis is an emerging field of research that has the potential to alleviate the burden and cost of skin cancer screening. Researchers have recently indicated increasing interest in developing such CAD systems, with the intention of providing a user-friendly tool to dermatologists to reduce the challenges encountered or associated with manual inspection. This article aims to provide a comprehensive literature survey and review of a total of 594 publications (356 for skin lesion segmentation and 238 for skin lesion classification) published between 2011 and 2022. These articles are analyzed and summarized in a number of different ways to contribute vital information regarding the methods for the development of CAD systems. These ways include relevant and essential definitions and theories, input data (dataset utilization, preprocessing, augmentations, and fixing imbalance problems), method configuration (techniques, architectures, module frameworks, and losses), training tactics (hyperparameter settings), and evaluation criteria. We intend to investigate a variety of performance-enhancing approaches, including ensemble and post-processing. We also discuss these dimensions to reveal their current trends based on utilization frequencies. In addition, we highlight the primary difficulties associated with evaluating skin lesion segmentation and classification systems using minimal datasets, as well as the potential solutions to these difficulties. Findings, recommendations, and trends are disclosed to inform future research on developing an automated and robust CAD system for skin lesion analysis.

Fair machine learning methods seek to train models that balance model performance across demographic subgroups defined over sensitive attributes like race and gender. Although sensitive attributes are typically assumed to be known during training, they may not be available in practice due to privacy and other logistical concerns. Recent work has sought to train fair models without sensitive attributes on training data. However, these methods need extensive hyper-parameter tuning to achieve good results, and hence assume that sensitive attributes are known on validation data. However, this assumption too might not be practical. Here, we propose Antigone, a framework to train fair classifiers without access to sensitive attributes on either training or validation data. Instead, we generate pseudo sensitive attributes on the validation data by training a biased classifier and using the classifier's incorrectly (correctly) labeled examples as proxies for minority (majority) groups. Since fairness metrics like demographic parity, equal opportunity and subgroup accuracy can be estimated to within a proportionality constant even with noisy sensitive attribute information, we show theoretically and empirically that these proxy labels can be used to maximize fairness under average accuracy constraints. Key to our results is a principled approach to select the hyper-parameters of the biased classifier in a completely unsupervised fashion (meaning without access to ground truth sensitive attributes) that minimizes the gap between fairness estimated using noisy versus ground-truth sensitive labels.

Nonlinear dynamics is ubiquitous in nature and commonly seen in various science and engineering disciplines. Distilling analytical expressions that govern nonlinear dynamics from limited data remains vital but challenging. To tackle this fundamental issue, we propose a novel Symbolic Physics Learner (SPL) machine to discover the mathematical structure of nonlinear dynamics. The key concept is to interpret mathematical operations and system state variables by computational rules and symbols, establish symbolic reasoning of mathematical formulas via expression trees, and employ a Monte Carlo tree search (MCTS) agent to explore optimal expression trees based on measurement data. The MCTS agent obtains an optimistic selection policy through the traversal of expression trees, featuring the one that maps to the arithmetic expression of underlying physics. Salient features of the proposed framework include search flexibility and enforcement of parsimony for discovered equations. The efficacy and superiority of the SPL machine are demonstrated by numerical examples, compared with state-of-the-art baselines.

Several recent works on self-supervised learning are trained by mapping different augmentations of the same image to the same feature representation. The data augmentations used are of crucial importance to the quality of learned feature representations. In this paper, we analyze how the color jitter traditionally used in data augmentation negatively impacts the quality of the color features in learned feature representations. To address this problem, we propose a more realistic, physics-based color data augmentation - which we call Planckian Jitter - that creates realistic variations in chromaticity and produces a model robust to illumination changes that can be commonly observed in real life, while maintaining the ability to discriminate image content based on color information. Experiments confirm that such a representation is complementary to the representations learned with the currently-used color jitter augmentation and that a simple concatenation leads to significant performance gains on a wide range of downstream datasets. In addition, we present a color sensitivity analysis that documents the impact of different training methods on model neurons and shows that the performance of the learned features is robust with respect to illuminant variations.

The unsupervised nature of the models makes them suitable for exploring topics in a corpus without prior knowledge. However, researchers find that these models often fail to measure specific concepts of substantive interest by inadvertently creating multiple topics with similar content and combining distinct themes into a single topic. In this paper, we empirically demonstrate that providing a small number of keywords can substantially enhance the measurement performance of topic models. An important advantage of the proposed keyword assisted topic model (keyATM) is that the specification of keywords requires researchers to label topics prior to fitting a model to the data. This contrasts with a widespread practice of post-hoc topic interpretation and adjustments that compromises the objectivity of empirical findings. In our application, we find that keyATM provides more interpretable results, has better document classification performance, and is less sensitive to the number of topics than the standard topic models. Finally, we show that keyATM can also incorporate covariates and model time trends. An open-source software package is available for implementing the proposed methodology. Verification Materials: The data and materials required to verify the computational reproducibility of the results, procedures and analyses in this article are available on the American Journal of Political Science Dataverse within the Harvard Dataverse Network, at: https://doi.org/10.7910/DVN/RKNNVL

By understanding the hidden locational clues in images, entirely new approaches of analyzing the natural and built environment are being opened up with profound implications for a number of fields, ranging from the recognition of weather, season, and climate patterns to rural and urban scene understanding, and improvements in navigation and self-driving car technology. Since the beginning of 2022, image geolocalization has additionally garnered extensive media coverage for becoming an immediate priority of investigative journalists and open source intelligence (OSINT) researchers in their attempt to verify information and to document war atrocities in Ukraine, extracting geolocational information from social media content. Despite high academic and public interest, image geolocalization remains an extremely challenging problem. This is because training datasets are geographically sparse, often limited to specific countries, and biased towards urban or rural scenes. The task is further complicated by the fact that geolocalization requires reasoning on multiple levels of geographic granularity (e.g.