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In a mixture experiment, we study the behavior and properties of $m$ mixture components, where the primary focus is on the proportions of the components that make up the mixture rather than the total amount. Mixture-amount experiments are specialized types of mixture experiments where both the proportions of the components in the mixture and the total amount of the mixture are of interest. Such experiments consider the total amount of the mixture as a variable. In this paper, we consider an Order-of-Addition (OofA) mixture-amount experiment in which the response depends on both the mixture amounts of components and their order of addition. Full Mixture OofA designs are constructed to maintain orthogonality between the mixture-amount model terms and the effects of the order of addition. These designs enable the estimation of mixture-component model parameters and the order-of-addition effects. The G-efficiency criterion assesses how well the design supports precise and unbiased estimation of the model parameters. The Fraction of Design Space (FDS) plot is used to provide a visual assessment of the prediction capabilities of a design across the entire design space., Comment: 12 pages figures 2 tables 5

Accurate modeling is essential in integer-valued real phenomena, including the distribution of entire data, zero-inflated (ZI) data, and discrete exceedances. The Poisson and Negative Binomial distributions, along with their ZI variants, are considered suitable for modeling the entire data distribution, but they fail to capture the heavy tail behavior effectively alongside the bulk of the distribution. In contrast, the discrete generalized Pareto distribution (DGPD) is preferred for high threshold exceedances, but it becomes less effective for low threshold exceedances. However, in some applications, the selection of a suitable high threshold is challenging, and the asymptotic conditions required for using DGPD are not always met. To address these limitations, extended versions of DGPD are proposed. These extensions are designed to model one of three scenarios: first, the entire distribution of the data, including both bulk and tail and bypassing the threshold selection step; second, the entire distribution along with ZI; and third, the tail of the distribution for low threshold exceedances. The proposed extensions offer improved estimates across all three scenarios compared to existing models, providing more accurate and reliable results in simulation studies and real data applications., Comment: 17 pages, Figures 8, tables 3

This study examines the interdependence between cryptocurrencies and international financial indices, such as MSCI World and MSCI Emerging Markets. We compute the value at risk, expected shortfall (ES), and range value at risk (RVaR) and investigate the dynamics of risk spillover. We employ a hybrid approach to derive these risk measures that integrate GARCH models, extreme value models, and copula functions. This framework uses a bivariate portfolio approach involving cryptocurrency data and traditional financial indices. To estimate the above risks of these portfolio structures, we employ symmetric and asymmetric GARCH and both tail flexible EVT models as marginal to model the marginal distribution of each return series and apply different copula functions to connect the pairs of marginal distributions into a multivariate distribution. The empirical findings indicate that the eGARCH EVT-based copula model adeptly captures intricate dependencies, surpassing conventional methodologies like Historical simulations and t-distributed parametric in VaR estimation. At the same time, the HS method proves superior for ES, and the t-distributed parametric method outperforms RVaR. Eventually, the Diebold-Yilmaz approach will be applied to compute risk spillovers between four sets of asset sequences. This phenomenon implies that cryptocurrencies reveal substantial spillover effects among themselves but minimal impact on other assets. From this, it can be concluded that cryptocurrencies propose diversification benefits and do not provide hedging advantages within an investor's portfolio. Our results underline RVaR superiority over ES regarding regulatory arbitrage and model misspecification. The conclusions of this study will benefit investors and financial market professionals who aspire to comprehend digital currencies as a novel asset class and attain perspicuity in regulatory arbitrage., Comment: 29 pages, 5 figures 13

Sufficient dimension reduction has received much interest over the past 30 years. Most existing approaches focus on statistical models linking the response to the covariate through a regression equation, and as such are not adapted to binary classification problems. We address the question of dimension reduction for binary classification by fitting a localized nearest-neighbor logistic model with $\ell_1$-penalty in order to estimate the gradient of the conditional probability of interest. Our theoretical analysis shows that the pointwise convergence rate of the gradient estimator is optimal under very mild conditions. The dimension reduction subspace is estimated using an outer product of such gradient estimates at several points in the covariate space. Our implementation uses cross-validation on the misclassification rate to estimate the dimension of this subspace. We find that the proposed approach outperforms existing competitors in synthetic and real data applications.

The statistical modeling of discrete extremes has received less attention than their continuous counterparts in the Extreme Value Theory (EVT) literature. One approach to the transition from continuous to discrete extremes is the modeling of threshold exceedances of integer random variables by the discrete version of the generalized Pareto distribution. However, the optimal choice of thresholds defining exceedances remains a problematic issue. Moreover, in a regression framework, the treatment of the majority of non-extreme data below the selected threshold is either ignored or separated from the extremes. To tackle these issues, we expand on the concept of employing a smooth transition between the bulk and the upper tail of the distribution. In the case of zero inflation, we also develop models with an additional parameter. To incorporate possible predictors, we relate the parameters to additive smoothed predictors via an appropriate link, as in the generalized additive model (GAM) framework. A penalized maximum likelihood estimation procedure is implemented. We illustrate our modeling proposal with a real dataset of avalanche activity in the French Alps. With the advantage of bypassing the threshold selection step, our results indicate that the proposed models are more flexible and robust than competing models, such as the negative binomial distribution, Comment: 19 pages, 6 figures including and 3 Tables

There exists a distribution discrepancy between training and testing, in the way images are fed to modern CNNs. Recent work tried to bridge this gap either by fine-tuning or re-training the network at different resolutions. However re-training a network is rarely cheap and not always viable. To this end, we propose a simple solution to address the train-test distributional shift and enhance the performance of pre-trained models -- which commonly ship as a package with deep learning platforms \eg, PyTorch. Specifically, we demonstrate that running inference on the center crop of an image is not always the best as important discriminatory information may be cropped-off. Instead we propose to combine results for multiple random crops for a test image. This not only matches the train time augmentation but also provides the full coverage of the input image. We explore combining representation of random crops through averaging at different levels \ie, deep feature level, logit level, and softmax level. We demonstrate that, for various families of modern deep networks, such averaging results in better validation accuracy compared to using a single central crop per image. The softmax averaging results in the best performance for various pre-trained networks without requiring any re-training or fine-tuning whatsoever. On modern GPUs with batch processing, the paper's approach to inference of pre-trained networks, is essentially free as all images in a batch can all be processed at once.

Skyline plays a pivotal role in mountainous visual geo-localization and localization/navigation of planetary rovers/UAVs and virtual/augmented reality applications. We present a novel mountainous skyline detection approach where we adapt a shallow learning approach to learn a set of filters to discriminate between edges belonging to sky-mountain boundary and others coming from different regions. Unlike earlier approaches, which either rely on extraction of explicit feature descriptors and their classification, or fine-tuning general scene parsing deep networks for sky segmentation, our approach learns linear filters based on local structure analysis. At test time, for every candidate edge pixel, a single filter is chosen from the set of learned filters based on pixel's structure tensor, and then applied to the patch around it. We then employ dynamic programming to solve the shortest path problem for the resultant multistage graph to get the sky-mountain boundary. The proposed approach is computationally faster than earlier methods while providing comparable performance and is more suitable for resource constrained platforms e.g., mobile devices, planetary rovers and UAVs. We compare our proposed approach against earlier skyline detection methods using four different data sets. Our code is available at \url{https://github.com/TouqeerAhmad/skyline_detection}., Comment: Accepted at International Joint Conference on Neural Networks, 2021

This paper identifies the flaws in existing open-world learning approaches and attempts to provide a complete picture in the form of \textbf{True Open-World Learning}. We accomplish this by proposing a comprehensive generalize-able open-world learning protocol capable of evaluating various components of open-world learning in an operational setting. We argue that in true open-world learning, the underlying feature representation should be learned in a self-supervised manner. Under this self-supervised feature representation, we introduce the problem of detecting unknowns as samples belonging to Out-of-Label space. We differentiate between Out-of-Label space detection and the conventional Out-of-Distribution detection depending upon whether the unknowns being detected belong to the native-world (same as feature representation) or a new-world, respectively. Our unifying open-world learning framework combines three individual research dimensions, which typically have been explored independently, i.e., Incremental Learning, Out-of-Distribution detection and Open-World Learning. Starting from a self-supervised feature space, an open-world learner has the ability to adapt and specialize its feature space to the classes in each incremental phase and hence perform better without incurring any significant overhead, as demonstrated by our experimental results. The incremental learning component of our pipeline provides the new state-of-the-art on established ImageNet-100 protocol. We also demonstrate the adaptability of our approach by showing how it can work as a plug-in with any of the self-supervised feature representation methods.

In open-world learning, an agent starts with a set of known classes, detects, and manages things that it does not know, and learns them over time from a non-stationary stream of data. Open-world learning is related to but also distinct from a multitude of other learning problems and this paper briefly analyzes the key differences between a wide range of problems including incremental learning, generalized novelty discovery, and generalized zero-shot learning. This paper formalizes various open-world learning problems including open-world learning without labels. These open-world problems can be addressed with modifications to known elements, we present a new framework that enables agents to combine various modules for novelty-detection, novelty-characterization, incremental learning, and instance management to learn new classes from a stream of unlabeled data in an unsupervised manner, survey how to adapt a few state-of-the-art techniques to fit the framework and use them to define seven baselines for performance on the open-world learning without labels problem. We then discuss open-world learning quality and analyze how that can improve instance management. We also discuss some of the general ambiguity issues that occur in open-world learning without labels.

Image classification in the open-world must handle out-of-distribution (OOD) images. Systems should ideally reject OOD images, or they will map atop of known classes and reduce reliability. Using open-set classifiers that can reject OOD inputs can help. However, optimal accuracy of open-set classifiers depend on the frequency of OOD data. Thus, for either standard or open-set classifiers, it is important to be able to determine when the world changes and increasing OOD inputs will result in reduced system reliability. However, during operations, we cannot directly assess accuracy as there are no labels. Thus, the reliability assessment of these classifiers must be done by human operators, made more complex because networks are not 100% accurate, so some failures are to be expected. To automate this process, herein, we formalize the open-world recognition reliability problem and propose multiple automatic reliability assessment policies to address this new problem using only the distribution of reported scores/probability data. The distributional algorithms can be applied to both classic classifiers with SoftMax as well as the open-world Extreme Value Machine (EVM) to provide automated reliability assessment. We show that all of the new algorithms significantly outperform detection using the mean of SoftMax., Comment: 2021 IEEE Winter Conference on Applications of Computer Vision (WACV)

Horizon or skyline detection plays a vital role towards mountainous visual geo-localization, however most of the recently proposed visual geo-localization approaches rely on \textbf{user-in-the-loop} skyline detection methods. Detecting such a segmenting boundary fully autonomously would definitely be a step forward for these localization approaches. This paper provides a quantitative comparison of four such methods for autonomous horizon/sky line detection on an extensive data set. Specifically, we provide the comparison between four recently proposed segmentation methods; one explicitly targeting the problem of horizon detection\cite{Ahmad15}, second focused on visual geo-localization but relying on accurate detection of skyline \cite{Saurer16} and other two proposed for general semantic segmentation -- Fully Convolutional Networks (FCN) \cite{Long15} and SegNet\cite{Badrinarayanan15}. Each of the first two methods is trained on a common training set \cite{Baatz12} comprised of about 200 images while models for the third and fourth method are fine tuned for sky segmentation problem through transfer learning using the same data set. Each of the method is tested on an extensive test set (about 3K images) covering various challenging geographical, weather, illumination and seasonal conditions. We report average accuracy and average absolute pixel error for each of the presented formulation., Comment: Proceedings of the International Joint Conference on Neural Networks (IJCNN) (oral presentation), IEEE Computational Intelligence Society, 2017