Comparative evaluation of forecasts of statistical functionals relies on comparing averaged losses of competing forecasts after the realization of the quantity $Y$, on which the functional is based, has been observed. Motivated by high-frequency finance, in this paper we investigate how proxies $\tilde Y$ for $Y$ - say volatility proxies - which are observed together with $Y$ can be utilized to improve forecast comparisons. We extend previous results on robustness of loss functions for the mean to general moments and ratios of moments, and show in terms of the variance of differences of losses that using proxies will increase the power in comparative forecast tests. These results apply both to testing conditional as well as unconditional dominance. Finally, we numerically illustrate the theoretical results, both for simulated high-frequency data as well as for high-frequency log returns of several cryptocurrencies.
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We consider the problem of estimating the optimal transport map between two probability distributions, $P$ and $Q$ in $\mathbb R^d$, on the basis of i.i.d. samples. All existing statistical analyses of this problem require the assumption that the transport map is Lipschitz, a strong requirement that, in particular, excludes any examples where the transport map is discontinuous. As a first step towards developing estimation procedures for discontinuous maps, we consider the important special case where the data distribution $Q$ is a discrete measure supported on a finite number of points in $\mathbb R^d$. We study a computationally efficient estimator initially proposed by Pooladian and Niles-Weed (2021), based on entropic optimal transport, and show in the semi-discrete setting that it converges at the minimax-optimal rate $n^{-1/2}$, independent of dimension. Other standard map estimation techniques both lack finite-sample guarantees in this setting and provably suffer from the curse of dimensionality. We confirm these results in numerical experiments, and provide experiments for other settings, not covered by our theory, which indicate that the entropic estimator is a promising methodology for other discontinuous transport map estimation problems.
Machine learning and deep learning play vital roles in predicting diseases in the medical field. Machine learning algorithms are widely classified as supervised, unsupervised, and reinforcement learning. This paper contains a detailed description of our experimental research work in that we used a supervised machine-learning algorithm to build our model for outbreaks of the novel Coronavirus that has spread over the whole world and caused many deaths, which is one of the most disastrous Pandemics in the history of the world. The people suffered physically and economically to survive in this lockdown. This work aims to understand better how machine learning, ensemble, and deep learning models work and are implemented in the real dataset. In our work, we are going to analyze the current trend or pattern of the coronavirus and then predict the further future of the covid-19 confirmed cases or new cases by training the past Covid-19 dataset by using the machine learning algorithm such as Linear Regression, Polynomial Regression, K-nearest neighbor, Decision Tree, Support Vector Machine and Random forest algorithm are used to train the model. The decision tree and the Random Forest algorithm perform better than SVR in this work. The performance of SVR and lasso regression are low in all prediction areas Because the SVR is challenging to separate the data using the hyperplane for this type of problem. So SVR mostly gives a lower performance in this problem. Ensemble (Voting, Bagging, and Stacking) and deep learning models(ANN) also predict well. After the prediction, we evaluated the model using MAE, MSE, RMSE, and MAPE. This work aims to find the trend/pattern of the covid-19.
Visualization plays a vital role in making sense of complex network data. Recent studies have shown the potential of using extended reality (XR) for the immersive exploration of networks. The additional depth cues offered by XR help users perform better in certain tasks when compared to using traditional desktop setups. However, prior works on immersive network visualization rely on mostly static graph layouts to present the data to the user. This poses a problem since there is no optimal layout for all possible tasks. The choice of layout heavily depends on the type of network and the task at hand. We introduce a multi-layout approach that allows users to effectively explore hierarchical network data in immersive space. The resulting system leverages different layout techniques and interactions to efficiently use the available space in VR and provide an optimal view of the data depending on the task and the level of detail required to solve it. To evaluate our approach, we have conducted a user study comparing it against the state of the art for immersive network visualization. Participants performed tasks at varying spatial scopes. The results show that our approach outperforms the baseline in spatially focused scenarios as well as when the whole network needs to be considered.
Probability forecasts for binary outcomes, often referred to as probabilistic classifiers or confidence scores, are ubiquitous in science and society, and methods for evaluating and comparing them are in great demand. We propose and study a triptych of diagnostic graphics that focus on distinct and complementary aspects of forecast performance: The reliability diagram addresses calibration, the receiver operating characteristic (ROC) curve diagnoses discrimination ability, and the Murphy diagram visualizes overall predictive performance and value. A Murphy curve shows a forecast's mean elementary scores, including the widely used misclassification rate, and the area under a Murphy curve equals the mean Brier score. For a calibrated forecast, the reliability curve lies on the diagonal, and for competing calibrated forecasts, the ROC and Murphy curves share the same number of crossing points. We invoke the recently developed CORP (Consistent, Optimally binned, Reproducible, and Pool-Adjacent-Violators (PAV) algorithm based) approach to craft reliability diagrams and decompose a mean score into miscalibration (MCB), discrimination (DSC), and uncertainty (UNC) components. Plots of the DSC measure of discrimination ability versus the calibration metric MCB visualize classifier performance across multiple competitors. The proposed tools are illustrated in empirical examples from astrophysics, economics, and social science.
The problem of speech separation, also known as the cocktail party problem, refers to the task of isolating a single speech signal from a mixture of speech signals. Previous work on source separation derived an upper bound for the source separation task in the domain of human speech. This bound is derived for deterministic models. Recent advancements in generative models challenge this bound. We show how the upper bound can be generalized to the case of random generative models. Applying a diffusion model Vocoder that was pretrained to model single-speaker voices on the output of a deterministic separation model leads to state-of-the-art separation results. It is shown that this requires one to combine the output of the separation model with that of the diffusion model. In our method, a linear combination is performed, in the frequency domain, using weights that are inferred by a learned model. We show state-of-the-art results on 2, 3, 5, 10, and 20 speakers on multiple benchmarks. In particular, for two speakers, our method is able to surpass what was previously considered the upper performance bound.
Current machine learning models achieve super-human performance in many real-world applications. Still, they are susceptible against imperceptible adversarial perturbations. The most effective solution for this problem is adversarial training that trains the model with adversarially perturbed samples instead of original ones. Various methods have been developed over recent years to improve adversarial training such as data augmentation or modifying training attacks. In this work, we examine the same problem from a new data-centric perspective. For this purpose, we first demonstrate that the existing model-based methods can be equivalent to applying smaller perturbation or optimization weights to the hard training examples. By using this finding, we propose detecting and removing these hard samples directly from the training procedure rather than applying complicated algorithms to mitigate their effects. For detection, we use maximum softmax probability as an effective method in out-of-distribution detection since we can consider the hard samples as the out-of-distribution samples for the whole data distribution. Our results on SVHN and CIFAR-10 datasets show the effectiveness of this method in improving the adversarial training without adding too much computational cost.
In the surface defect detection, there are some suspicious regions that cannot be uniquely classified as abnormal or normal. The annotating of suspicious regions is easily affected by factors such as workers' emotional fluctuations and judgment standard, resulting in noisy labels, which in turn leads to missing and false detections, and ultimately leads to inconsistent judgments of product quality. Unlike the usual noisy labels, the ones used for surface defect detection appear to be inconsistent rather than mislabeled. The noise occurs in almost every label and is difficult to correct or evaluate. In this paper, we proposed a framework that learns trustworthy models from noisy labels for surface defect defection. At first, to avoid the negative impact of noisy labels on the model, we represent the suspicious regions with consistent and precise elements at the pixel-level and redesign the loss function. Secondly, without changing network structure and adding any extra labels, pluggable spatially correlated Bayesian module is proposed. Finally, the defect discrimination confidence is proposed to measure the uncertainty, with which anomalies can be identified as defects. Our results indicate not only the effectiveness of the proposed method in learning from noisy labels, but also robustness and real-time performance.
Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases.
Deep convolutional neural networks (CNNs) have recently achieved great success in many visual recognition tasks. However, existing deep neural network models are computationally expensive and memory intensive, hindering their deployment in devices with low memory resources or in applications with strict latency requirements. Therefore, a natural thought is to perform model compression and acceleration in deep networks without significantly decreasing the model performance. During the past few years, tremendous progress has been made in this area. In this paper, we survey the recent advanced techniques for compacting and accelerating CNNs model developed. These techniques are roughly categorized into four schemes: parameter pruning and sharing, low-rank factorization, transferred/compact convolutional filters, and knowledge distillation. Methods of parameter pruning and sharing will be described at the beginning, after that the other techniques will be introduced. For each scheme, we provide insightful analysis regarding the performance, related applications, advantages, and drawbacks etc. Then we will go through a few very recent additional successful methods, for example, dynamic capacity networks and stochastic depths networks. After that, we survey the evaluation matrix, the main datasets used for evaluating the model performance and recent benchmarking efforts. Finally, we conclude this paper, discuss remaining challenges and possible directions on this topic.
With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.
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