In the paper, a problem of forecasting promotion efficiency is raised. The authors propose a new approach, using the gradient boosting method for this task. Six performance indicators are introduced to capture the promotion effect. For each of them, within predefined groups of products, a model was trained. A description of using these models for forecasting and optimising promotion efficiency is provided. Data preparation and hyperparameters tuning processes are also described. The experiments were performed for three groups of products from a large grocery company.

Tracking mouse cursor movements can be used to predict user attention on heterogeneous page layouts like SERPs. So far, previous work has relied heavily on handcrafted features, which is a time-consuming approach that often requires domain expertise. We investigate different representations of mouse cursor movements, including time series, heatmaps, and trajectory-based images, to build and contrast both recurrent and convolutional neural networks that can predict user attention to direct displays, such as SERP advertisements. Our models are trained over raw mouse cursor data and achieve competitive performance. We conclude that neural network models should be adopted for downstream tasks involving mouse cursor movements, since they can provide an invaluable implicit feedback signal for re-ranking and evaluation.

In recent years, semi-supervised learning (SSL) has shown tremendous success in leveraging unlabeled data to improve the performance of deep learning models, which significantly reduces the demand for large amounts of labeled data. Many SSL techniques have been proposed and have shown promising performance on famous datasets such as ImageNet and CIFAR-10. However, some exiting techniques (especially data augmentation based) are not suitable for industrial applications empirically. Therefore, this work proposes the pseudo-representation labeling, a simple and flexible framework that utilizes pseudo-labeling techniques to iteratively label a small amount of unlabeled data and use them as training data. In addition, our framework is integrated with self-supervised representation learning such that the classifier gains benefits from representation learning of both labeled and unlabeled data. This framework can be implemented without being limited at the specific model structure, but a general technique to improve the existing model. Compared with the existing approaches, the pseudo-representation labeling is more intuitive and can effectively solve practical problems in the real world. Empirically, it outperforms the current state-of-the-art semi-supervised learning methods in industrial types of classification problems such as the WM-811K wafer map and the MIT-BIH Arrhythmia dataset.

Testing large covariance matrices is of fundamental importance in statistical analysis with high-dimensional data. In the past decade, three types of test statistics have been studied in the literature: quadratic form statistics, maximum form statistics, and their weighted combination. It is known that quadratic form statistics would suffer from low power against sparse alternatives and maximum form statistics would suffer from low power against dense alternatives. The weighted combination methods were introduced to enhance the power of quadratic form statistics or maximum form statistics when the weights are appropriately chosen. In this paper, we provide a new perspective to exploit the full potential of quadratic form statistics and maximum form statistics for testing high-dimensional covariance matrices. We propose a scale-invariant power enhancement test based on Fisher's method to combine the p-values of quadratic form statistics and maximum form statistics. After carefully studying the asymptotic joint distribution of quadratic form statistics and maximum form statistics, we prove that the proposed combination method retains the correct asymptotic size and boosts the power against more general alternatives. Moreover, we demonstrate the finite-sample performance in simulation studies and a real application.

In this paper, we propose a novel accelerated stochastic gradient method with momentum, which momentum is the weighted average of previous gradients. The weights decays inverse proportionally with the iteration times. Stochastic gradient descent with momentum (Sgdm) use weights that decays exponentially with the iteration times to generate an momentum term. Using exponentially decaying weights, variants of Sgdm with well designed and complicated formats have been proposed to achieve better performance. The momentum update rules of our method is as simple as that of Sgdm. We provide theoretical convergence properties analyses for our method, which show both the exponentially decay weights and our inverse proportionally decay weights can limit the variance of the moving direction of parameters to be optimized to a region. Experimental results empirically show that our method works well with practical problems and outperforms Sgdm, and it outperforms Adam in convolutional neural networks.

Network regularization is an effective tool for incorporating structural prior knowledge to learn coherent models over networks, and has yielded provably accurate estimates in applications ranging from spatial economics to neuroimaging studies. Recently, there has been an increasing interest in extending network regularization to the spatio-temporal case to accommodate the evolution of networks. However, in both static and spatio-temporal cases, missing or corrupted edge weights can compromise the ability of network regularization to discover desired solutions. To address these gaps, we propose a novel approach---{\it discrepancy-aware network regularization} (DANR)---that is robust to inadequate regularizations and effectively captures model evolution and structural changes over spatio-temporal networks. We develop a distributed and scalable algorithm based on the alternating direction method of multipliers (ADMM) to solve the proposed problem with guaranteed convergence to global optimum solutions. Experimental results on both synthetic and real-world networks demonstrate that our approach achieves improved performance on various tasks, and enables interpretation of model changes in evolving networks.

A fundamental step in many data-analysis techniques is the construction of an affinity matrix describing similarities between data points. When the data points reside in Euclidean space, a widespread approach is to from an affinity matrix by the Gaussian kernel with pairwise distances, and to follow with a certain normalization (e.g. the row-stochastic normalization or its symmetric variant). We demonstrate that the doubly-stochastic normalization of the Gaussian kernel with zero main diagonal (i.e. no self loops) is robust to heteroskedastic noise. That is, the doubly-stochastic normalization is advantageous in that it automatically accounts for observations with different noise variances. Specifically, we prove that in a suitable high-dimensional setting where heteroskedastic noise does not concentrate too much in any particular direction in space, the resulting (doubly-stochastic) noisy affinity matrix converges to its clean counterpart with rate $m^{-1/2}$, where $m$ is the ambient dimension. We demonstrate this result numerically, and show that in contrast, the popular row-stochastic and symmetric normalizations behave unfavorably under heteroskedastic noise. Furthermore, we provide a prototypical example of simulated single-cell RNA sequence data with strong intrinsic heteroskedasticity, where the advantage of the doubly-stochastic normalization for exploratory analysis is evident.

Normalizing flows have received a great deal of recent attention as they allow flexible generative modeling as well as easy likelihood computation. While a wide variety of flow models have been proposed, there is little formal understanding of the representation power of these models. In this work, we study some basic normalizing flows and rigorously establish bounds on their expressive power. Our results indicate that while these flows are highly expressive in one dimension, in higher dimensions their representation power may be limited, especially when the flows have moderate depth.

Deep neural networks have achieved impressive performance on many machine learning tasks, which has led to growing interests in deploying these models in practical applications. However, recent studies have revealed that models trained on benign examples are susceptible to adversarial examples, examples crafted by an adversary to control model behavior at test time [4, 32, 12]. The adversarial perturbation overlaid on top of the benign examples is often small enough to be imperceptible to humans, yet can cause the model to misclassify the image. The existence of adversarial examples has raised security concerns for many high-stakes real-world applications such as street sign detection for autonomous vehicles. While initial works stated that digital adversarial examples built for sign-detection may not be a real threat since the camera can view the objects from different distances and angles [22], more recent attacks were proposed for making stronger adversarial examples that are invariant to various transformations by optimizing over the expected value of a set of predefined transformations [2]. In fact, this security concern has turned into an actual threat after a recent study showed that adversarial stickers are able to fool real-world self-driving cars [13].

Ridge or more formally $\ell_2$ regularization shows up in many areas of statistics and machine learning. It is one of those essential devices that any good data scientist needs to master for their craft. In this brief ridge fest I have collected together some of the magic and beauty of ridge that my colleagues and I have encountered over the past 40 years in applied statistics.