Practical results have shown that deep learning optimizers using small constant learning rates, hyperparameters close to one, and large batch sizes can find the model parameters of deep neural networks that minimize the loss functions. We first show theoretical evidence that the momentum method (Momentum) and adaptive moment estimation (Adam) perform well in the sense that the upper bound of the theoretical performance measure is small with a small constant learning rate, hyperparameters close to one, and a large batch size. Next, we show that there exists a batch size called the critical batch size minimizing the stochastic first-order oracle (SFO) complexity, which is the stochastic gradient computation cost, and that SFO complexity increases once the batch size exceeds the critical batch size. Finally, we provide numerical results that support our theoretical results. That is, the numerical results indicate that Adam using a small constant learning rate, hyperparameters close to one, and the critical batch size minimizing SFO complexity has faster convergence than Momentum and stochastic gradient descent (SGD).

We propose and analyze several stochastic gradient algorithms for finding stationary points or local minimum in nonconvex, possibly with nonsmooth regularizer, finite-sum and online optimization problems. First, we propose a simple proximal stochastic gradient algorithm based on variance reduction called ProxSVRG+. We provide a clean and tight analysis of ProxSVRG+, which shows that it outperforms the deterministic proximal gradient descent (ProxGD) for a wide range of minibatch sizes, hence solves an open problem proposed in Reddi et al. (2016b). Also, ProxSVRG+ uses much less proximal oracle calls than ProxSVRG (Reddi et al., 2016b) and extends to the online setting by avoiding full gradient computations. Then, we further propose an optimal algorithm, called SSRGD, based on SARAH (Nguyen et al., 2017) and show that SSRGD further improves the gradient complexity of ProxSVRG+ and achieves the optimal upper bound, matching the known lower bound of (Fang et al., 2018; Li et al., 2021). Moreover, we show that both ProxSVRG+ and SSRGD enjoy automatic adaptation with local structure of the objective function such as the Polyak-\L{}ojasiewicz (PL) condition for nonconvex functions in the finite-sum case, i.e., we prove that both of them can automatically switch to faster global linear convergence without any restart performed in prior work ProxSVRG (Reddi et al., 2016b). Finally, we focus on the more challenging problem of finding an $(\epsilon, \delta)$-local minimum instead of just finding an $\epsilon$-approximate (first-order) stationary point (which may be some bad unstable saddle points). We show that SSRGD can find an $(\epsilon, \delta)$-local minimum by simply adding some random perturbations. Our algorithm is almost as simple as its counterpart for finding stationary points, and achieves similar optimal rates.

Generative Adversarial Networks (GANs) are a widely-used tool for generative modeling of complex data. Despite their empirical success, the training of GANs is not fully understood due to the min-max optimization of the generator and discriminator. This paper analyzes these joint dynamics when the true samples, as well as the generated samples, are discrete, finite sets, and the discriminator is kernel-based. A simple yet expressive framework for analyzing training called the $\textit{Isolated Points Model}$ is introduced. In the proposed model, the distance between true samples greatly exceeds the kernel width, so each generated point is influenced by at most one true point. Our model enables precise characterization of the conditions for convergence, both to good and bad minima. In particular, the analysis explains two common failure modes: (i) an approximate mode collapse and (ii) divergence. Numerical simulations are provided that predictably replicate these behaviors.

Deep neural networks achieve excellent performance in many real applications. However, they require a large-scale (CLL) (Ishida et al., 2017), the number of candidate labels training set with correctly labeled samples. Obtaining such a is only one less than the number of classes, making this task set is time-consuming, expensive, and, in some domains, impossible even more challenging.. due to discrepancies between labeling experts (Armato III et al., 2011). In consequence, many contemporary The standard approaches to partial and complementary label datasets are weakly labeled, forcing researchers to propose learning are incompatible with high-efficient stochastic optimization adequate learning strategies within the Weakly Supervised and cannot handle large-scale datasets (Liu & Dietterich, Learning paradigm (Zhou, 2018).

The quality of Artificial Intelligence (AI) algorithms is of significant importance for confidently adopting algorithms in various applications such as cybersecurity, healthcare, and autonomous driving. This work presents a principled framework of using a design-of-experimental approach to systematically evaluate the quality of AI algorithms, named as Do-AIQ. Specifically, we focus on investigating the quality of the AI mislabel data algorithm against data poisoning. The performance of AI algorithms is affected by hyperparameters in the algorithm and data quality, particularly, data mislabeling, class imbalance, and data types. To evaluate the quality of the AI algorithms and obtain a trustworthy assessment on the quality of the algorithms, we establish a design-of-experiment framework to construct an efficient space-filling design in a high-dimensional constraint space and develop an effective surrogate model using additive Gaussian process to enable the emulation of the quality of AI algorithms. Both theoretical and numerical studies are conducted to justify the merits of the proposed framework. The proposed framework can set an exemplar for AI algorithm to enhance the AI assurance of robustness, reproducibility, and transparency.

Airlines are critical today for carrying people and commodities on time. Any delay in the schedule of these planes can potentially disrupt the business and trade of thousands of employees at any given time. Therefore, precise flight delay prediction is beneficial for the aviation industry and passenger travel. Recent research has focused on using artificial intelligence algorithms to predict the possibility of flight delays. Earlier prediction algorithms were designed for a specific air route or airfield. Many present flight delay prediction algorithms rely on tiny samples and are challenging to understand, allowing almost no room for machine learning implementation. This research study develops a flight delay prediction system by analyzing data from domestic flights inside the United States of America. The proposed models learn about the factors that cause flight delays and cancellations and the link between departure and arrival delays.

The primary assumption of conventional supervised learning or classification is that the test samples are drawn from the same distribution as the training samples, which is called closed set learning or classification. In many practical scenarios, this is not the case because there are unknowns or unseen class samples in the test data, which is called the open set scenario, and the unknowns need to be detected. This problem is referred to as the open set recognition problem and is important in safetycritical applications. We propose to detect unknowns (or unseen class samples) through learning pairwise similarities. The proposed method works in two steps. It first learns a closed set classifier using the seen classes that have appeared in training, and then learns how to compare seen classes with pseudo-unseen (automatically generated unseen class samples). The pseudo-unseen generation is carried out by performing distribution shifting augmentations on the seen or training samples. We call our method OPG (Open set recognition based on Pseudo unseen data Generation). The experimental evaluation shows that the learned similarity-based features can successfully distinguish seen from unseen in benchmark datasets for open set recognition. Deep classification models trained with cross-entropy loss are expected to produce a high probability score for the ground-truth class.

With rising powerful, low-cost embedded devices, the edge computing has become an increasingly popular choice. In this paper, we propose a new incremental local stochastic gradient descent (SGD) tailored on the Raspberry Pi to deal with large ImageNet ILSVRC 2010 dataset having 1,261,405 images with 1,000 classes. The local SGD splits the data block into $k$ partitions using $k$means algorithm and then it learns in the parallel way SGD models in each data partition to classify the data locally. The incremental local SGD sequentially loads small data blocks of the training dataset to learn local SGD models. The numerical test results on Imagenet dataset show that our incremental local SGD algorithm with the Raspberry Pi 4 is faster and more accurate than the state-of-the-art linear SVM run on a PC Intel(R) Core i7-4790 CPU, 3.6 GHz, 4 cores.

Atmospheric pollution remains one of the major public health threat worldwide with an estimated 7 millions deaths annually. In Africa, rapid urbanization and poor transport infrastructure are worsening the problem. In this paper, we have analysed spatio-temporal variations of PM2.5 across different geographical regions in Africa. The West African region remains the most affected by the high levels of pollution with a daily average of 40.856 $\mu g/m^3$ in some cities like Lagos, Abuja and Bamako. In East Africa, Uganda is reporting the highest pollution level with a daily average concentration of 56.14 $\mu g/m^3$ and 38.65 $\mu g/m^3$ for Kigali. In countries located in the central region of Africa, the highest daily average concentration of PM2.5 of 90.075 $\mu g/m^3$ was recorded in N'Djamena. We compare three data driven models in predicting future trends of pollution levels. Neural network is outperforming Gaussian processes and ARIMA models.

Graphs are widely used to model the relational structure of data, and the research of graph machine learning (ML) has a wide spectrum of applications ranging from drug design in molecular graphs to friendship recommendation in social networks. Prevailing approaches for graph ML typically require abundant labeled instances in achieving satisfactory results, which is commonly infeasible in real-world scenarios since labeled data for newly emerged concepts (e.g., new categorizations of nodes) on graphs is limited. Though meta-learning has been applied to different few-shot graph learning problems, most existing efforts predominately assume that all the data from those seen classes is gold-labeled, while those methods may lose their efficacy when the seen data is weakly-labeled with severe label noise. As such, we aim to investigate a novel problem of weakly-supervised graph meta-learning for improving the model robustness in terms of knowledge transfer. To achieve this goal, we propose a new graph meta-learning framework -- Graph Hallucination Networks (Meta-GHN) in this paper. Based on a new robustness-enhanced episodic training, Meta-GHN is meta-learned to hallucinate clean node representations from weakly-labeled data and extracts highly transferable meta-knowledge, which enables the model to quickly adapt to unseen tasks with few labeled instances. Extensive experiments demonstrate the superiority of Meta-GHN over existing graph meta-learning studies on the task of weakly-supervised few-shot node classification.