It is important to understand how dropout, a popular regularization method, aids in achieving a good generalization solution during neural network training. In this work, we present a theoretical derivation of an implicit regularization of dropout, which is validated by a series of experiments. Additionally, we numerically study two implications of the implicit regularization, which intuitively rationalizes why dropout helps generalization. Firstly, we find that input weights of hidden neurons tend to condense on isolated orientations trained with dropout. Condensation is a feature in the non-linear learning process, which makes the network less complex. Secondly, we experimentally find that the training with dropout leads to the neural network with a flatter minimum compared with standard gradient descent training, and the implicit regularization is the key to finding flat solutions. Although our theory mainly focuses on dropout used in the last hidden layer, our experiments apply to general dropout in training neural networks. This work points out a distinct characteristic of dropout compared with stochastic gradient descent and serves as an important basis for fully understanding dropout.

Traditional analyses of gradient descent show that when the largest eigenvalue of the Hessian, also known as the sharpness $S(\theta)$, is bounded by $2/\eta$, training is "stable" and the training loss decreases monotonically. Recent works, however, have observed that this assumption does not hold when training modern neural networks with full batch or large batch gradient descent. Most recently, Cohen et al. (2021) observed two important phenomena. The first, dubbed progressive sharpening, is that the sharpness steadily increases throughout training until it reaches the instability cutoff $2/\eta$. The second, dubbed edge of stability, is that the sharpness hovers at $2/\eta$ for the remainder of training while the loss continues decreasing, albeit non-monotonically. We demonstrate that, far from being chaotic, the dynamics of gradient descent at the edge of stability can be captured by a cubic Taylor expansion: as the iterates diverge in direction of the top eigenvector of the Hessian due to instability, the cubic term in the local Taylor expansion of the loss function causes the curvature to decrease until stability is restored. This property, which we call self-stabilization, is a general property of gradient descent and explains its behavior at the edge of stability. A key consequence of self-stabilization is that gradient descent at the edge of stability implicitly follows projected gradient descent (PGD) under the constraint $S(\theta) \le 2/\eta$. Our analysis provides precise predictions for the loss, sharpness, and deviation from the PGD trajectory throughout training, which we verify both empirically in a number of standard settings and theoretically under mild conditions. Our analysis uncovers the mechanism for gradient descent's implicit bias towards stability.

Human state recognition is a critical topic with pervasive and important applications in human-machine systems. Multi-modal fusion, the combination of metrics from multiple data sources, has been shown as a sound method for improving the recognition performance. However, while promising results have been reported by recent multi-modal-based models, they generally fail to leverage the sophisticated fusion strategies that would model sufficient cross-modal interactions when producing the fusion representation; instead, current methods rely on lengthy and inconsistent data preprocessing and feature crafting. To address this limitation, we propose an end-to-end multi-modal transformer framework for multi-modal human state recognition called Husformer. Specifically, we propose to use cross-modal transformers, which inspire one modality to reinforce itself through directly attending to latent relevance revealed in other modalities, to fuse different modalities while ensuring sufficient awareness of the cross-modal interactions introduced. Subsequently, we utilize a self-attention transformer to further prioritize contextual information in the fusion representation. Using two such attention mechanisms enables effective and adaptive adjustments to noise and interruptions in multi-modal signals during the fusion process and in relation to high-level features. Extensive experiments on two human emotion corpora (DEAP and WESAD) and two cognitive workload datasets (MOCAS and CogLoad) demonstrate that in the recognition of human state, our Husformer outperforms both state-of-the-art multi-modal baselines and the use of a single modality by a large margin, especially when dealing with raw multi-modal signals. We also conducted an ablation study to show the benefits of each component in Husformer.

Data imputation is a prevalent and important task due to the ubiquitousness of missing data. Many efforts try to first draft a completed data and second refine to derive the imputation results, or "draft-then-refine" for short. In this work, we analyze this widespread practice from the perspective of Dirichlet energy. We find that a rudimentary "draft" imputation will decrease the Dirichlet energy, thus an energy-maintenance "refine" step is in need to recover the overall energy. Since existing "refine" methods such as Graph Convolutional Network (GCN) tend to cause further energy decline, in this work, we propose a novel framework called Graph Laplacian Pyramid Network (GLPN) to preserve Dirichlet energy and improve imputation performance. GLPN consists of a U-shaped autoencoder and residual networks to capture global and local detailed information respectively. By extensive experiments on several real-world datasets, GLPN shows superior performance over state-of-the-art methods under three different missing mechanisms. Our source code is available at https://github.com/liguanlue/GLPN.

Preserving the individuals' privacy in sharing spatial-temporal datasets is critical to prevent re-identification attacks based on unique trajectories. Existing privacy techniques tend to propose ideal privacy-utility tradeoffs, however, largely ignore the fairness implications of mobility models and whether such techniques perform equally for different groups of users. The quantification between fairness and privacy-aware models is still unclear and there barely exists any defined sets of metrics for measuring fairness in the spatial-temporal context. In this work, we define a set of fairness metrics designed explicitly for human mobility, based on structural similarity and entropy of the trajectories. Under these definitions, we examine the fairness of two state-of-the-art privacy-preserving models that rely on GAN and representation learning to reduce the re-identification rate of users for data sharing. Our results show that while both models guarantee group fairness in terms of demographic parity, they violate individual fairness criteria, indicating that users with highly similar trajectories receive disparate privacy gain. We conclude that the tension between the re-identification task and individual fairness needs to be considered for future spatial-temporal data analysis and modelling to achieve a privacy-preserving fairness-aware setting.

We develop scalable randomized kernel methods for jointly associating data from multiple sources and simultaneously predicting an outcome or classifying a unit into one of two or more classes. The proposed methods model nonlinear relationships in multiview data together with predicting a clinical outcome and are capable of identifying variables or groups of variables that best contribute to the relationships among the views. We use the idea that random Fourier bases can approximate shift-invariant kernel functions to construct nonlinear mappings of each view and we use these mappings and the outcome variable to learn view-independent low-dimensional representations. Through simulation studies, we show that the proposed methods outperform several other linear and nonlinear methods for multiview data integration. When the proposed methods were applied to gene expression, metabolomics, proteomics, and lipidomics data pertaining to COVID-19, we identified several molecular signatures forCOVID-19 status and severity. Results from our real data application and simulations with small sample sizes suggest that the proposed methods may be useful for small sample size problems. Availability: Our algorithms are implemented in Pytorch and interfaced in R and would be made available at: https://github.com/lasandrall/RandMVLearn.

Developing applicable clinical machine learning models is a difficult task when the data includes spatial information, for example, radiation dose distributions across adjacent organs at risk. We describe the co-design of a modeling system, DASS, to support the hybrid human-machine development and validation of predictive models for estimating long-term toxicities related to radiotherapy doses in head and neck cancer patients. Developed in collaboration with domain experts in oncology and data mining, DASS incorporates human-in-the-loop visual steering, spatial data, and explainable AI to augment domain knowledge with automatic data mining. We demonstrate DASS with the development of two practical clinical stratification models and report feedback from domain experts. Finally, we describe the design lessons learned from this collaborative experience.

Artificial Intelligence for IT operations (AIOps) aims to combine the power of AI with the big data generated by IT Operations processes, particularly in cloud infrastructures, to provide actionable insights with the primary goal of maximizing availability. There are a wide variety of problems to address, and multiple use-cases, where AI capabilities can be leveraged to enhance operational efficiency. Here we provide a review of the AIOps vision, trends challenges and opportunities, specifically focusing on the underlying AI techniques. We discuss in depth the key types of data emitted by IT Operations activities, the scale and challenges in analyzing them, and where they can be helpful. We categorize the key AIOps tasks as - incident detection, failure prediction, root cause analysis and automated actions. We discuss the problem formulation for each task, and then present a taxonomy of techniques to solve these problems. We also identify relatively under explored topics, especially those that could significantly benefit from advances in AI literature. We also provide insights into the trends in this field, and what are the key investment opportunities.

I have observed two extreme approaches when it comes to aspiring data scientists attempting to learn machine learning algorithms. The first approach involves learning all the intricacies of the algorithms and implementing them from scratch to gain true mastery. The second approach, on the other hand, assumes that the computer will "learn" on its own, rendering the need for the individual to learn the algorithms unnecessary. This leads some to only rely on tools such as the package lazypredict. It is realistic to take an approach between the two extremes when learning machine learning algorithms. However, the question remains, where to start? In this article, I will categorize machine learning algorithms into three categories and provide my humble opinion on what to begin with and what can be skipped. Starting out in machine learning can be overwhelming due to the multitude of available algorithms. Linear regression, support vector machines (SVM), gradient descent, gradient boosting, decision trees, LASSO, ridge, grid search, and many more are some of the algorithms that come to mind when posed with the question.

A short guide on how to use image embeddings from OpenAI's CLIP and clustering techniques in order to group near-duplicate images together. CLIP is trained by trying to align image text embedding pairs, or "learning visual representations from natural language supervision". You can use it's text or image embeddings to accomplish a lot of different tasks, such as zero-shot image classification! It's embeddings are pretty powerful. For this task, we're going to use the AirBnB Duplicate Image Dataset, available on Kaggle.