由于迭代元素的结构诱导属性，尤其是在可行的集合上的线性最小化相比，弗兰克 - 沃尔夫方法在统计和机器学习应用中变得越来越有用，尤其是在线性最小化的设置上比投影更有效。在经验风险最小化的设置中，统计和机器学习中的基本优化问题之一 - 弗兰克 - 沃尔夫方法的计算有效性通常在数据观察数$ n $的数量中线性增长。这与典型随机投影方法的情况形成鲜明对比。为了减少对$ n $的依赖性，我们将寻求典型平滑损耗功能的二阶平滑度（例如，最小二乘损失和逻辑损失），我们建议使用泰勒串联序列的Frank-Wolfe方法修改Frank-Wolfe方法，包括确定性和随机设置的变体。与当前的最新方法相比，最佳公差$ \ varepsilon $足够小，我们的方法能够同时减少对大$ n $的依赖，同时获得Frank-Wolfe方法的最佳收敛速率，在凸和非凸设置中。我们还提出了一种新型的自适应阶梯尺寸方法，我们可以为其提供计算保证。最后，我们提出的计算实验表明，我们的方法对凸面和非convex二进制分类问题的现有数据集上的现有方法表现出非常明显的速度。

数据在于现代深度学习的核心。监督学习的令人印象深刻的表现建立在大量准确标记的数据基础上。但是，在某些现实世界中，准确的标签可能不可行。取而代之的是，为每个数据示例提供了多个注释者提供多个嘈杂标签（而不是一个精确的标签）。在这样的嘈杂培训数据集上学习分类器是一项具有挑战性的任务。以前的方法通常假设所有数据示例共享与注释误差相关的相同参数集，而我们证明标签错误学习应既是注释者，又是数据示例依赖性。在这一观察结果的激励下，我们提出了一种新颖的学习算法。与MNIST，CIFAR-100和Imagenet-100的几种最新基线方法相比，该方法显示出优势。我们的代码可在以下网址获得：https：//github.com/zhengqigao/learning-from-multiple-annotator-noisy-labels。

Given the increasingly intricate forms of partial differential equations (PDEs) in physics and related fields, computationally solving PDEs without analytic solutions inevitably suffers from the trade-off between accuracy and efficiency. Recent advances in neural operators, a kind of mesh-independent neural-network-based PDE solvers, have suggested the dawn of overcoming this challenge. In this emerging direction, Koopman neural operator (KNO) is a representative demonstration and outperforms other state-of-the-art alternatives in terms of accuracy and efficiency. Here we present KoopmanLab, a self-contained and user-friendly PyTorch module of the Koopman neural operator family for solving partial differential equations. Beyond the original version of KNO, we develop multiple new variants of KNO based on different neural network architectures to improve the general applicability of our module. These variants are validated by mesh-independent and long-term prediction experiments implemented on representative PDEs (e.g., the Navier-Stokes equation and the Bateman-Burgers equation) and ERA5 (i.e., one of the largest high-resolution data sets of global-scale climate fields). These demonstrations suggest the potential of KoopmanLab to be considered in diverse applications of partial differential equations.

Temporal sentence grounding (TSG) aims to identify the temporal boundary of a specific segment from an untrimmed video by a sentence query. All existing works first utilize a sparse sampling strategy to extract a fixed number of video frames and then conduct multi-modal interactions with query sentence for reasoning. However, we argue that these methods have overlooked two indispensable issues: 1) Boundary-bias: The annotated target segment generally refers to two specific frames as corresponding start and end timestamps. The video downsampling process may lose these two frames and take the adjacent irrelevant frames as new boundaries. 2) Reasoning-bias: Such incorrect new boundary frames also lead to the reasoning bias during frame-query interaction, reducing the generalization ability of model. To alleviate above limitations, in this paper, we propose a novel Siamese Sampling and Reasoning Network (SSRN) for TSG, which introduces a siamese sampling mechanism to generate additional contextual frames to enrich and refine the new boundaries. Specifically, a reasoning strategy is developed to learn the inter-relationship among these frames and generate soft labels on boundaries for more accurate frame-query reasoning. Such mechanism is also able to supplement the absent consecutive visual semantics to the sampled sparse frames for fine-grained activity understanding. Extensive experiments demonstrate the effectiveness of SSRN on three challenging datasets.

Time-series anomaly detection is an important task and has been widely applied in the industry. Since manual data annotation is expensive and inefficient, most applications adopt unsupervised anomaly detection methods, but the results are usually sub-optimal and unsatisfactory to end customers. Weak supervision is a promising paradigm for obtaining considerable labels in a low-cost way, which enables the customers to label data by writing heuristic rules rather than annotating each instance individually. However, in the time-series domain, it is hard for people to write reasonable labeling functions as the time-series data is numerically continuous and difficult to be understood. In this paper, we propose a Label-Efficient Interactive Time-Series Anomaly Detection (LEIAD) system, which enables a user to improve the results of unsupervised anomaly detection by performing only a small amount of interactions with the system. To achieve this goal, the system integrates weak supervision and active learning collaboratively while generating labeling functions automatically using only a few labeled data. All of these techniques are complementary and can promote each other in a reinforced manner. We conduct experiments on three time-series anomaly detection datasets, demonstrating that the proposed system is superior to existing solutions in both weak supervision and active learning areas. Also, the system has been tested in a real scenario in industry to show its practicality.

This paper investigates the use of artificial neural networks (ANNs) to solve differential equations (DEs) and the construction of the loss function which meets both differential equation and its initial/boundary condition of a certain DE. In section 2, the loss function is generalized to $n^\text{th}$ order ordinary differential equation(ODE). Other methods of construction are examined in Section 3 and applied to three different models to assess their effectiveness.

Kernels are efficient in representing nonlocal dependence and they are widely used to design operators between function spaces. Thus, learning kernels in operators from data is an inverse problem of general interest. Due to the nonlocal dependence, the inverse problem can be severely ill-posed with a data-dependent singular inversion operator. The Bayesian approach overcomes the ill-posedness through a non-degenerate prior. However, a fixed non-degenerate prior leads to a divergent posterior mean when the observation noise becomes small, if the data induces a perturbation in the eigenspace of zero eigenvalues of the inversion operator. We introduce a data-adaptive prior to achieve a stable posterior whose mean always has a small noise limit. The data-adaptive prior's covariance is the inversion operator with a hyper-parameter selected adaptive to data by the L-curve method. Furthermore, we provide a detailed analysis on the computational practice of the data-adaptive prior, and demonstrate it on Toeplitz matrices and integral operators. Numerical tests show that a fixed prior can lead to a divergent posterior mean in the presence of any of the four types of errors: discretization error, model error, partial observation and wrong noise assumption. In contrast, the data-adaptive prior always attains posterior means with small noise limits.

Deep learning has been widely used for protein engineering. However, it is limited by the lack of sufficient experimental data to train an accurate model for predicting the functional fitness of high-order mutants. Here, we develop SESNet, a supervised deep-learning model to predict the fitness for protein mutants by leveraging both sequence and structure information, and exploiting attention mechanism. Our model integrates local evolutionary context from homologous sequences, the global evolutionary context encoding rich semantic from the universal protein sequence space and the structure information accounting for the microenvironment around each residue in a protein. We show that SESNet outperforms state-of-the-art models for predicting the sequence-function relationship on 26 deep mutational scanning datasets. More importantly, we propose a data augmentation strategy by leveraging the data from unsupervised models to pre-train our model. After that, our model can achieve strikingly high accuracy in prediction of the fitness of protein mutants, especially for the higher order variants (> 4 mutation sites), when finetuned by using only a small number of experimental mutation data (<50). The strategy proposed is of great practical value as the required experimental effort, i.e., producing a few tens of experimental mutation data on a given protein, is generally affordable by an ordinary biochemical group and can be applied on almost any protein.

Inferring knowledge from clinical trials using knowledge graph embedding is an emerging area. However, customizing graph embeddings for different use cases remains a significant challenge. We propose custom2vec, an algorithmic framework to customize graph embeddings by incorporating user preferences in training the embeddings. It captures user preferences by adding custom nodes and links derived from manually vetted results of a separate information retrieval method. We propose a joint learning objective to preserve the original network structure while incorporating the user's custom annotations. We hypothesize that the custom training improves user-expected predictions, for example, in link prediction tasks. We demonstrate the effectiveness of custom2vec for clinical trials related to non-small cell lung cancer (NSCLC) with two customization scenarios: recommending immuno-oncology trials evaluating PD-1 inhibitors and exploring similar trials that compare new therapies with a standard of care. The results show that custom2vec training achieves better performance than the conventional training methods. Our approach is a novel way to customize knowledge graph embeddings and enable more accurate recommendations and predictions.

Because of the widespread existence of noise and data corruption, recovering the true regression parameters with a certain proportion of corrupted response variables is an essential task. Methods to overcome this problem often involve robust least-squares regression, but few methods perform well when confronted with severe adaptive adversarial attacks. In many applications, prior knowledge is often available from historical data or engineering experience, and by incorporating prior information into a robust regression method, we develop an effective robust regression method that can resist adaptive adversarial attacks. First, we propose the novel TRIP (hard Thresholding approach to Robust regression with sImple Prior) algorithm, which improves the breakdown point when facing adaptive adversarial attacks. Then, to improve the robustness and reduce the estimation error caused by the inclusion of priors, we use the idea of Bayesian reweighting to construct the more robust BRHT (robust Bayesian Reweighting regression via Hard Thresholding) algorithm. We prove the theoretical convergence of the proposed algorithms under mild conditions, and extensive experiments show that under different types of dataset attacks, our algorithms outperform other benchmark ones. Finally, we apply our methods to a data-recovery problem in a real-world application involving a space solar array, demonstrating their good applicability.