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Nonlinear dynamical systems can be handily described by the associated Koopman operator, whose action evolves every observable of the system forward in time. Learning the Koopman operator and its spectral decomposition from data is enabled by a number of algorithms. In this work we present for the first time non-asymptotic learning bounds for the Koopman eigenvalues and eigenfunctions. We focus on time-reversal-invariant stochastic dynamical systems, including the important example of Langevin dynamics. We analyze two popular estimators: Extended Dynamic Mode Decomposition (EDMD) and Reduced Rank Regression (RRR). Our results critically hinge on novel {minimax} estimation bounds for the operator norm error, that may be of independent interest. Our spectral learning bounds are driven by the simultaneous control of the operator norm error and a novel metric distortion functional of the estimated eigenfunctions. The bounds indicates that both EDMD and RRR have similar variance, but EDMD suffers from a larger bias which might be detrimental to its learning rate. Our results shed new light on the emergence of spurious eigenvalues, an issue which is well known empirically. Numerical experiments illustrate the implications of the bounds in practice.

Crowd counting models in highly congested areas confront two main challenges: weak localization ability and difficulty in differentiating between foreground and background, leading to inaccurate estimations. The reason is that objects in highly congested areas are normally small and high-level features extracted by convolutional neural networks are less discriminative to represent small objects. To address these problems, we propose a learning discriminative features framework for crowd counting, which is composed of a masked feature prediction module (MPM) and a supervised pixel-level contrastive learning module (CLM). The MPM randomly masks feature vectors in the feature map and then reconstructs them, allowing the model to learn about what is present in the masked regions and improving the model's ability to localize objects in high-density regions. The CLM pulls targets close to each other and pushes them far away from background in the feature space, enabling the model to discriminate foreground objects from background. Additionally, the proposed modules can be beneficial in various computer vision tasks, such as crowd counting and object detection, where dense scenes or cluttered environments pose challenges to accurate localization. The proposed two modules are plug-and-play, incorporating the proposed modules into existing models can potentially boost their performance in these scenarios.

Novels are often adapted into feature films, but the differences between the two media usually require dropping sections of the source text from the movie script. Here we study this screen adaptation process by constructing narrative alignments using the Smith-Waterman local alignment algorithm coupled with SBERT embedding distance to quantify text similarity between scenes and book units. We use these alignments to perform an automated analysis of 40 adaptations, revealing insights into the screenwriting process concerning (i) faithfulness of adaptation, (ii) importance of dialog, (iii) preservation of narrative order, and (iv) gender representation issues reflective of the Bechdel test.

Negative sampling methods are vital in implicit recommendation models as they allow us to obtain negative instances from massive unlabeled data. Most existing approaches focus on sampling hard negative samples in various ways. These studies are orthogonal to the recommendation model and implicit datasets. However, such an idea contradicts the common belief in AutoML that the model and dataset should be matched. Empirical experiments suggest that the best-performing negative sampler depends on the implicit dataset and the specific recommendation model. Hence, we propose a hypothesis that the negative sampler should align with the capacity of the recommendation models as well as the statistics of the datasets to achieve optimal performance. A mismatch between these three would result in sub-optimal outcomes. An intuitive idea to address the mismatch problem is to exhaustively select the best-performing negative sampler given the model and dataset. However, such an approach is computationally expensive and time-consuming, leaving the problem unsolved. In this work, we propose the AutoSample framework that adaptively selects the best-performing negative sampler among candidates. Specifically, we propose a loss-to-instance approximation to transform the negative sampler search task into the learning task over a weighted sum, enabling end-to-end training of the model. We also designed an adaptive search algorithm to extensively and efficiently explore the search space. A specific initialization approach is also obtained to better utilize the obtained model parameters during the search stage, which is similar to curriculum learning and leads to better performance and less computation resource consumption. We evaluate the proposed framework on four benchmarks over three models. Extensive experiments demonstrate the effectiveness and efficiency of our proposed framework.

Recommendation systems are designed to provide personalized predictions for items that are most appealing to individual customers. Among various types of recommendation algorithms, k-nearest neighbor based collaborative filtering algorithm attracts tremendous attention and are widely used in practice. However, the k-nearest neighbor scheme can only capture the local relationship among users and the uniform neighborhood size is also not suitable to represent the underlying data structure. In this paper, we leverage emerging graph signal processing (GSP) theory to construct sparse yet high quality graph to enhance the solution quality and efficiency of collaborative filtering algorithm. Experimental results show that our method outperforms k-NN based collaborative filtering algorithm by a large margin on the benchmark data set.

Time series discords are a useful primitive for time series anomaly detection, and the matrix profile is capable of capturing discord effectively. There exist many research efforts to improve the scalability of discord discovery with respect to the length of time series. However, there is surprisingly little work focused on reducing the time complexity of matrix profile computation associated with dimensionality of a multidimensional time series. In this work, we propose a sketch for discord mining among multi-dimensional time series. After an initial pre-processing of the sketch as fast as reading the data, the discord mining has runtime independent of the dimensionality of the original data. On several real world examples from water treatment and transportation, the proposed algorithm improves the throughput by at least an order of magnitude (50X) and only has minimal impact on the quality of the approximated solution. Additionally, the proposed method can handle the dynamic addition or deletion of dimensions inconsequential overhead. This allows a data analyst to consider "what-if" scenarios in real time while exploring the data.

Creating accurate and geologically realistic reservoir facies based on limited measurements is crucial for field development and reservoir management, especially in the oil and gas sector. Traditional two-point geostatistics, while foundational, often struggle to capture complex geological patterns. Multi-point statistics offers more flexibility, but comes with its own challenges. With the rise of Generative Adversarial Networks (GANs) and their success in various fields, there has been a shift towards using them for facies generation. However, recent advances in the computer vision domain have shown the superiority of diffusion models over GANs. Motivated by this, a novel Latent Diffusion Model is proposed, which is specifically designed for conditional generation of reservoir facies. The proposed model produces high-fidelity facies realizations that rigorously preserve conditioning data. It significantly outperforms a GAN-based alternative.

Video anomaly detection deals with the recognition of abnormal events in videos. Apart from the visual signal, video anomaly detection has also been addressed with the use of skeleton sequences. We propose a holistic representation of skeleton trajectories to learn expected motions across segments at different times. Our approach uses multitask learning to reconstruct any continuous unobserved temporal segment of the trajectory allowing the extrapolation of past or future segments and the interpolation of in-between segments. We use an end-to-end attention-based encoder-decoder. We encode temporally occluded trajectories, jointly learn latent representations of the occluded segments, and reconstruct trajectories based on expected motions across different temporal segments. Extensive experiments on three trajectory-based video anomaly detection datasets show the advantages and effectiveness of our approach with state-of-the-art results on anomaly detection in skeleton trajectories.

Recent advances in maximizing mutual information (MI) between the source and target have demonstrated its effectiveness in text generation. However, previous works paid little attention to modeling the backward network of MI (i.e., dependency from the target to the source), which is crucial to the tightness of the variational information maximization lower bound. In this paper, we propose Adversarial Mutual Information (AMI): a text generation framework which is formed as a novel saddle point (min-max) optimization aiming to identify joint interactions between the source and target. Within this framework, the forward and backward networks are able to iteratively promote or demote each other's generated instances by comparing the real and synthetic data distributions. We also develop a latent noise sampling strategy that leverages random variations at the high-level semantic space to enhance the long term dependency in the generation process. Extensive experiments based on different text generation tasks demonstrate that the proposed AMI framework can significantly outperform several strong baselines, and we also show that AMI has potential to lead to a tighter lower bound of maximum mutual information for the variational information maximization problem.

Deep learning has revolutionized many machine learning tasks in recent years, ranging from image classification and video processing to speech recognition and natural language understanding. The data in these tasks are typically represented in the Euclidean space. However, there is an increasing number of applications where data are generated from non-Euclidean domains and are represented as graphs with complex relationships and interdependency between objects. The complexity of graph data has imposed significant challenges on existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph data have emerged. In this survey, we provide a comprehensive overview of graph neural networks (GNNs) in data mining and machine learning fields. We propose a new taxonomy to divide the state-of-the-art graph neural networks into different categories. With a focus on graph convolutional networks, we review alternative architectures that have recently been developed; these learning paradigms include graph attention networks, graph autoencoders, graph generative networks, and graph spatial-temporal networks. We further discuss the applications of graph neural networks across various domains and summarize the open source codes and benchmarks of the existing algorithms on different learning tasks. Finally, we propose potential research directions in this fast-growing field.