The dependency of the generalization error of neural networks on model and dataset size is of critical importance both in practice and for understanding the theory of neural networks. Nevertheless, the functional form of this dependency remains elusive. In this work, we present a functional form which approximates well the generalization error in practice. Capitalizing on the successful concept of model scaling (e.g., width, depth), we are able to simultaneously construct such a form and specify the exact models which can attain it across model/data scales. Our construction follows insights obtained from observations conducted over a range of model/data scales, in various model types and datasets, in vision and language tasks. We show that the form both fits the observations well across scales, and provides accurate predictions from small- to large-scale models and data.

The application of standard sufficient dimension reduction methods for reducing the dimension space of predictors without losing regression information requires inverting the covariance matrix of the predictors. This has posed a number of challenges especially when analyzing high-dimensional data sets in which the number of predictors $\mathit{p}$ is much larger than number of samples $n,~(n\ll p)$. A new covariance estimator, called the \textit{Maximum Entropy Covariance} (MEC) that addresses loss of covariance information when similar covariance matrices are linearly combined using \textit{Maximum Entropy} (ME) principle is proposed in this work. By benefitting naturally from slicing or discretizing range of the response variable, y into \textit{H} non-overlapping categories, $\mathit{h_{1},\ldots ,h_{H}}$, MEC first combines covariance matrices arising from samples in each y slice $\mathit{h\in H}$ and then select the one that maximizes entropy under the principle of maximum uncertainty. The MEC estimator is then formed from convex mixture of such entropy-maximizing sample covariance $S_{\mbox{mec}}$ estimate and pooled sample covariance $\mathbf{S}_{\mathit{p}}$ estimate across the $\mathit{H}$ slices without requiring time-consuming covariance optimization procedures. MEC deals directly with singularity and instability of sample group covariance estimate in both regression and classification problems. The efficiency of the MEC estimator is studied with the existing sufficient dimension reduction methods such as \textit{Sliced Inverse Regression} (SIR) and \textit{Sliced Average Variance Estimator} (SAVE) as demonstrated on both classification and regression problems using real life Leukemia cancer data and customers' electricity load profiles from smart meter data sets respectively.

News items have a significant impact on stock markets but the ways are obscure. Many previous works have aimed at finding accurate stock market forecasting models. In this paper, we use text mining and sentiment analysis on Chinese online financial news, to predict Chinese stock tendency and stock prices based on support vector machine (SVM). Firstly, we collect 2,302,692 news items, which date from 1/1/2008 to 1/1/2015. Secondly, based on this dataset, a specific domain stop-word dictionary and a precise sentiment dictionary are formed. Thirdly, we propose a forecasting model using SVM. On the algorithm of SVM implementation, we also propose two-parameter optimization algorithms to search for the best initial parameter setting. The result shows that parameter G has the main effect, while parameter C's effect is not obvious. Furthermore, support vector regression (SVR) models for different Chinese stocks are similar whereas in support vector classification (SVC) models best parameters are quite differential. Series of contrast experiments show that: a) News has significant influence on stock market; b) Expansion input vector for additional situations when that day has no news data is better than normal input in SVR, yet is worse in SVC; c) SVR shows a fantastic degree of fitting in predicting stock fluctuation while such result has some time lag; d) News effect time lag for stock market is less than two days; e) In SVC, historic stock data has a most efficient time lag which is about 10 days, whereas in SVR this effect is not obvious. Besides, based on the special structure of the input vector, we also design a method to calculate the financial source impact factor. Result suggests that the news quality and audience number both have a significant effect on the source impact factor. Besides, for Chinese investors, traditional media has more influence than digital media.

In this era of big data, databases are growing rapidly in terms of the number of records. Fast automatic detection of anomalous records in these massive databases is a challenging task. Traditional distance based anomaly detectors are not applicable in these massive datasets. Recently, a simple but extremely fast anomaly detector using one-dimensional histograms has been introduced. The anomaly score of a data instance is computed as the product of the probability mass of histograms in each dimensions where it falls into. It is shown to produce competitive results compared to many state-of-the-art methods in many datasets. Because it assumes data features are independent of each other, it results in poor detection accuracy when there is correlation between features. To address this issue, we propose to increase the feature size by adding more features based on principal components. Our results show that using the original input features together with principal components improves the detection accuracy of histogram-based anomaly detector significantly without compromising much in terms of run-time.

Collaborative personalization, such as through learned user representations (em-beddings), can improve the prediction accuracy of neural-network-based models significantly. We propose Federated User Representation Learning (FURL), a simple, scalable, privacy-preserving and resource-efficient way to utilize existing neural personalization techniques in the Federated Learning (FL) setting. FURL divides model parameters into federated and private parameters. Private parameters, such as private user embeddings, are trained locally, but unlike federated parameters, they are not transferred to or averaged on the server. We show theoretically that this parameter split does not affect training for most model per-sonalization approaches. Storing user embeddings locally not only preserves user privacy, but also improves memory locality of personalization compared to on-server training. We evaluate FURL on two datasets, demonstrating a significant improvement in model quality with 8% and 51% performance increases, and approximately the same level of performance as centralized training with only 0% and 4% reductions. Furthermore, we show that user embeddings learned in FL and the centralized setting have a very similar structure, indicating that FURL can learn collaboratively through the shared parameters while preserving user privacy.

In 2000, I published a relatively comprehensive study of mappings between propositional satisfiability (SAT) and constraint satisfaction problems (CSPs) [Wal00]. I analysed four different mappings of SAT problems into CSPs, and two of CSPs into SAT problems. For each mapping, I compared the impact of achieving arc-consistency on the CSP with unit propagation on the corresponding SAT problems, and lifted these results to CSP algorithms that maintain (some level of ) arc-consistency during search like FC and MAC, and to the Davis- Putnam procedure (which performs unit propagation at each search node). These results helped provide some insight into the relationship between propositional satisfiability and constraint satisfaction that set the scene for an important and valuable body of work that followed. I discuss here what prompted the paper, and what followed.

In this paper, we propose a Dual Focal Loss (DFL) function, as a replacement for the standard cross entropy (CE) function to achieve a better treatment of the unbalanced classes in a dataset. Our DFL method is an improvement on the recently reported Focal Loss (FL) cross-entropy function, which proposes a scaling method that puts more weight on the examples that are difficult to classify over those that are easy. However, the scaling parameter of FL is empirically set, which is problem-dependent. In addition, like other CE variants, FL only focuses on the loss of true classes. Therefore, no loss feedback is gained from the false classes. Although focusing only on true examples increases probability on true classes and correspondingly reduces probability on false classes due to the nature of the softmax function, it does not achieve the best convergence due to avoidance of the loss on false classes. Our DFL method improves on the simple FL in two ways. Firstly, it takes the idea of FL to focus more on difficult examples than the easy ones, but evaluates loss on both true and negative classes with equal importance. Secondly, the scaling parameter of DFL has been made learnable so that it can tune itself by backpropagation rather than being dependent on manual tuning. In this way, our proposed DFL method offers an auto-tunable loss function that can reduce the class imbalance effect as well as put more focus on both true difficult examples and negative easy examples. Experimental results show that our proposed method provides better accuracy in every test run conducted over a variety of different network models and datasets.

Deep neural networks trained on a wide range of datasets demonstrate impressive transferability. Deep features appear general in that they are applicable to many datasets and tasks. Such property is in prevalent use in real-world applications. A neural network pretrained on large datasets, such as ImageNet, can significantly boost generalization and accelerate training if fine-tuned to a smaller target dataset. Despite its pervasiveness, few effort has been devoted to uncovering the reason of transferability in deep feature representations. This paper tries to understand transferability from the perspectives of improved generalization, optimization and the feasibility of transferability. We demonstrate that 1) Transferred models tend to find flatter minima, since their weight matrices stay close to the original flat region of pretrained parameters when transferred to a similar target dataset; 2) Transferred representations make the loss landscape more favorable with improved Lipschitzness, which accelerates and stabilizes training substantially. The improvement largely attributes to the fact that the principal component of gradient is suppressed in the pretrained parameters, thus stabilizing the magnitude of gradient in back-propagation. 3) The feasibility of transferability is related to the similarity of both input and label. And a surprising discovery is that the feasibility is also impacted by the training stages in that the transferability first increases during training, and then declines. We further provide a theoretical analysis to verify our observations.

Arbitrary style transfer is an important problem in computer vision that aims to transfer style patterns from an arbitrary style image to a given content image. However, current methods either rely on slow iterative optimization or fast pre-determined feature transformation, but at the cost of compromised visual quality of the styled image; especially, distorted content structure. In this work, we present an effective and efficient approach for arbitrary style transfer that seamlessly transfers style patterns as well as keep content structure intact in the styled image. We achieve this by aligning style features to content features using rigid alignment; thus modifying style features, unlike the existing methods that do the opposite. We demonstrate the effectiveness of the proposed approach by generating high-quality stylized images and compare the results with the current state-of-the-art techniques for arbitrary style transfer.

Machine learning models for medical image analysis often suffer from poor performance on important subsets of a population that are not identified during training or testing. For example, overall performance of a cancer detection model may be high, but the model still consistently misses a rare but aggressive cancer subtype. We refer to this problem as hidden stratification, and observe that it results from incompletely describing the meaningful variation in a dataset. While hidden stratification can substantially reduce the clinical efficacy of machine learning models, its effects remain difficult to measure. In this work, we assess the utility of several possible techniques for measuring and describing hidden stratification effects, and characterize these effects both on multiple medical imaging datasets and via synthetic experiments on the well-characterised CIFAR-100 benchmark dataset. We find evidence that hidden stratification can occur in unidentified imaging subsets with low prevalence, low label quality, subtle distinguishing features, or spurious correlates, and that it can result in relative performance differences of over 20% on clinically important subsets. Finally, we explore the clinical implications of our findings, and suggest that evaluation of hidden stratification should be a critical component of any machine learning deployment in medical imaging.