The generalized equation (also called the [non]linear inclusion) provides a unified template to model various problems in computational mathematics and related fields su ch as the optimality condition of optimization problems (in both unconstrained and constrained settings), minimax optimization, variational inequality, complementarity, two-person game, and fixed-point problem s, see, e.g., [11, 24, 50, 112, 116, 118, 120]. Theory and numerical methods for this equation and its special case s have been extensively studied for many decades, see, e.g., the following monographs and the references quot ed therein [11, 50, 94, 119]. At the same time, several applications of this mathematical tool in operatio ns research, economics, uncertainty quantification, and transportations have been investigated [14, 52, 61, 50, 72]. In the last few years, there has been a surge of research in minimax problems due to new applications in mach ine learning and robust optimization, especially in generative adversarial networks (GANs), adversarial tr aining, and distributionally robust optimization, see, e.g., [4, 14, 55, 76, 84, 114] as a few examples. Minimax probl ems have also found new applications in online learning and reinforcement learning, among many others, se e, e.g., [4, 9, 15, 55, 67, 76, 78, 84, 114, 139]. Such prominent applications have motivated the research in minimax optimization and variational inequality problems (VIPs). On the one hand, classical algorithms such as gradient descent-ascent, extragradient, and primal-dual methods have been revisited, improved, and ext ended. On the other hand, new variants such as accelerated extragradient and accelerated operator split ting schemes have also been developed and equipped with rigorous convergence guarantees and practical perfor mance evaluation. This new development motivates us to write this survey paper, with the focus on sublinear con vergence rate analysis.

For large-scale IT corpora with hundreds of classes organized in a hierarchy, the task of accurate classification of classes at the higher level in the hierarchies is crucial to avoid errors propagating to the lower levels. In the business world, an efficient and explainable ML model is preferred over an expensive black-box model, especially if the performance increase is marginal. A current trend in the Natural Language Processing (NLP) community is towards employing huge pre-trained language models (PLMs) or what is known as self-attention models (e.g., BERT) for almost any kind of NLP task (e.g., question-answering, sentiment analysis, text classification). Despite the widespread use of PLMs and the impressive performance in a broad range of NLP tasks, there is a lack of a clear and well-justified need to as why these models are being employed for domain-specific text classification (TC) tasks, given the monosemic nature of specialized words (i.e., jargon) found in domain-specific text which renders the purpose of contextualized embeddings (e.g., PLMs) futile. In this paper, we compare the accuracies of some state-of-the-art (SOTA) models reported in the literature against a Linear SVM classifier and TFIDF vectorization model on three TC datasets. Results show a comparable performance for the LinearSVM. The findings of this study show that for domain-specific TC tasks, a linear model can provide a comparable, cheap, reproducible, and interpretable alternative to attention-based models.

Evaluating machine learning algorithms is a common task performed by data scientists. While a data scientist needs to know the different types of machine learning algorithms to use for different types of problems, it is nevertheless paramount that he puts the different algorithms to work on his/her specific dataset. Only by doing that would he/she have a better sense of which algorithm to use to train the model and how to perform hyper-parameter tuning after that. However, choosing the right algorithms is a time-consuming and exhausting process. Ideally, there should be an automated process where you just need to supply your data and the ideal machine learning algorithm to use would be chosen for you. The answer to this is LazyPredict.

With all this, let's end this blog as this is of ArgMax and SoftMax. If you will find any issue regarding the concept or code, you can message me on my Twitter or LinkedIn. The next blog will be published on 02 April 2023. You can also call me Chessman. Most of my time is spent staring at a computer screen.

Partial differential equations (PDEs) have been a cornerstone of mathematical physics and engineering design for over 250 years, since the introduction of the one-dimensional wave equation by d'Alembert in 1752 [20]. PDEs provide a formal mathematical infrastructure for relating how quantities of interest change in several variables, typically space and time. As such, PDEs provide a foundational description of the governing equations of many canonical spatio-temporal physical systems, including electrodynamics, quantum mechanics, fluid mechanics, heat transfer, etc. Today, nearly every aspect of our engineered world is based in some way on the predictive capability of PDEs, from structural modeling of buildings and bridges, to the design of aircraft and other vehicles, to the thermal and electromagnetic management systems in modern portable electronics.

We are currently in a great era for researchers and scientists studying and developing in the field of complex systems. Half of the physics Nobel prize of 2021 was awarded to the physicist Giorgio Parisi for his contributions to the theory of complex systems [9] and the other half to two meteorologists Syukuro Manabe and Klaus Hasselmann to the modeling of the Earth's climate [10]. Parisi has made significant contributions to the literature on complex systems, including areas such as spin glass [11, 12, 13], stochastic resonance [14], surface growth [15], multifractality [16], and bird flocking [17].

Federated Learning (FL) has emerged as a promising approach for privacy preservation, allowing sharing of the model parameters between users and the cloud server rather than the raw local data. FL approaches have been adopted as a cornerstone of distributed machine learning (ML) to solve several complex use cases. FL presents an interesting interplay between communication and ML performance when implemented over distributed wireless nodes. Both the dynamics of networking and learning play an important role. In this article, we investigate the performance of FL on an application that might be used to improve a remote healthcare system over ad hoc networks which employ CSMA/CA to schedule its transmissions. Our FL over CSMA/CA (FLCC) model is designed to eliminate untrusted devices and harness frequency reuse and spatial clustering techniques to improve the throughput required for coordinating a distributed implementation of FL in the wireless network. In our proposed model, frequency allocation is performed on the basis of spatial clustering performed using virtual cells. Each cell assigns a FL server and dedicated carrier frequencies to exchange the updated model's parameters within the cell. We present two metrics to evaluate the network performance: 1) probability of successful transmission while minimizing the interference, and 2) performance of distributed FL model in terms of accuracy and loss while considering the networking dynamics. We benchmark the proposed approach using a well-known MNIST dataset for performance evaluation. We demonstrate that the proposed approach outperforms the baseline FL algorithms in terms of explicitly defining the chosen users' criteria and achieving high accuracy in a robust network.

Federated learning is a popular collaborative learning approach that enables clients to train a global model without sharing their local data. Vertical federated learning (VFL) deals with scenarios in which the data on clients have different feature spaces but share some overlapping samples. Existing VFL approaches suffer from high communication costs and cannot deal efficiently with limited overlapping samples commonly seen in the real world. We propose a practical vertical federated learning (VFL) framework called \textbf{one-shot VFL} that can solve the communication bottleneck and the problem of limited overlapping samples simultaneously based on semi-supervised learning. We also propose \textbf{few-shot VFL} to improve the accuracy further with just one more communication round between the server and the clients. In our proposed framework, the clients only need to communicate with the server once or only a few times. We evaluate the proposed VFL framework on both image and tabular datasets. Our methods can improve the accuracy by more than 46.5\% and reduce the communication cost by more than 330$\times$ compared with state-of-the-art VFL methods when evaluated on CIFAR-10. Our code will be made publicly available at \url{https://nvidia.github.io/NVFlare/research/one-shot-vfl}.

Deep recommender systems (DRS) are intensively applied in modern web services. To deal with the massive web contents, DRS employs a two-stage workflow: retrieval and ranking, to generate its recommendation results. The retriever aims to select a small set of relevant candidates from the entire items with high efficiency; while the ranker, usually more precise but time-consuming, is supposed to further refine the best items from the retrieved candidates. Traditionally, the two components are trained either independently or within a simple cascading pipeline, which is prone to poor collaboration effect. Though some latest works suggested to train retriever and ranker jointly, there still exist many severe limitations: item distribution shift between training and inference, false negative, and misalignment of ranking order. As such, it remains to explore effective collaborations between retriever and ranker.

Relational events are a type of social interactions, that sometimes are referred to as dynamic networks. Its dynamics typically depends on emerging patterns, so-called endogenous variables, or external forces, referred to as exogenous variables. Comprehensive information on the actors in the network, especially for huge networks, is rare, however. A latent space approach in network analysis has been a popular way to account for unmeasured covariates that are driving network configurations. Bayesian and EM-type algorithms have been proposed for inferring the latent space, but both the sheer size many social network applications as well as the dynamic nature of the process, and therefore the latent space, make computations prohibitively expensive. In this work we propose a likelihood-based algorithm that can deal with huge relational event networks. We propose a hierarchical strategy for inferring network community dynamics embedded into an interpretable latent space. Node dynamics are described by smooth spline processes. To make the framework feasible for large networks we borrow from machine learning optimization methodology. Model-based clustering is carried out via a convex clustering penalization, encouraging shared trajectories for ease of interpretation. We propose a model-based approach for separating macro-microstructures and perform a hierarchical analysis within successive hierarchies. The method can fit millions of nodes on a public Colab GPU in a few minutes. The code and a tutorial are available in a Github repository.