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Nonlinear regression analysis is a popular and important tool for scientists and engineers. In this article, we introduce theories and methods of nonlinear regression and its statistical inferences using the frequentist and Bayesian statistical modeling and computation. Least squares with the Gauss-Newton method is the most widely used approach to parameters estimation. Under the assumption of normally distributed errors, maximum likelihood estimation is equivalent to least squares estimation. The Wald confidence regions for parameters in a nonlinear regression model are affected by the curvatures in the mean function. Furthermore, we introduce the Newton-Raphson method and the generalized least squares method to deal with variance heterogeneity. Examples of simulation data analysis are provided to illustrate important properties of confidence regions and the statistical inferences using the nonlinear least squares estimation and Bayesian inference.

In this work, we introduce a novel paradigm called Simulated Overparametrization (SOP). SOP merges the computational efficiency of compact models with the advanced learning proficiencies of overparameterized models. SOP proposes a unique approach to model training and inference, where a model with a significantly larger number of parameters is trained in such a way that a smaller, efficient subset of these parameters is used for the actual computation during inference. Building upon this framework, we present a novel, architecture agnostic algorithm called "majority kernels", which seamlessly integrates with predominant architectures, including Transformer models. Majority kernels enables the simulated training of overparameterized models, resulting in performance gains across architectures and tasks. Furthermore, our approach adds minimal overhead to the cost incurred (wall clock time) at training time. The proposed approach shows strong performance on a wide variety of datasets and models, even outperforming strong baselines such as combinatorial optimization methods based on submodular optimization.

In the past several decades, various techniques have been developed and used for multiple-access (MA) communications. With the new applications for 6G, it is desirable to find new resources, physical or virtual, to confront the fast development of MA communication systems. For binary source transmission, this paper proposes an element-pair (EP) coding scheme for supporting massive users with short packet traffic, which solves the finite block length of multiuser reliability transmission problem. Each user is assigned to a unique EP and the collection of EPs assigned to the users has the unique sum-pattern mapping (USPM) structural property. In this paper, we first present methods for constructing two specific types of EP codes with USPM structural property based on finite fields, and their encoding. Based on the EP-coding, we propose finite-field MA (FFMA) systems, in which an EP is viewed as a virtual resource for MA communications. The proposed FFMA is then applied to network layer and forms network FFMA systems for pure digital networks. Simulation results show that the error performance of the proposed FFMA over a Gaussian multiple-access channel can approach the error performance as that of the single-user transmission.

This book is the result of a seminar in which we reviewed multimodal approaches and attempted to create a solid overview of the field, starting with the current state-of-the-art approaches in the two subfields of Deep Learning individually. Further, modeling frameworks are discussed where one modality is transformed into the other, as well as models in which one modality is utilized to enhance representation learning for the other. To conclude the second part, architectures with a focus on handling both modalities simultaneously are introduced. Finally, we also cover other modalities as well as general-purpose multi-modal models, which are able to handle different tasks on different modalities within one unified architecture. One interesting application (Generative Art) eventually caps off this booklet.

In order to overcome the expressive limitations of graph neural networks (GNNs), we propose the first method that exploits vector flows over graphs to develop globally consistent directional and asymmetric aggregation functions. We show that our directional graph networks (DGNs) generalize convolutional neural networks (CNNs) when applied on a grid. Whereas recent theoretical works focus on understanding local neighbourhoods, local structures and local isomorphism with no global information flow, our novel theoretical framework allows directional convolutional kernels in any graph. First, by defining a vector field in the graph, we develop a method of applying directional derivatives and smoothing by projecting node-specific messages into the field. Then we propose the use of the Laplacian eigenvectors as such vector field, and we show that the method generalizes CNNs on an n-dimensional grid, and is provably more discriminative than standard GNNs regarding the Weisfeiler-Lehman 1-WL test. Finally, we bring the power of CNN data augmentation to graphs by providing a means of doing reflection, rotation and distortion on the underlying directional field. We evaluate our method on different standard benchmarks and see a relative error reduction of 8\% on the CIFAR10 graph dataset and 11% to 32% on the molecular ZINC dataset. An important outcome of this work is that it enables to translate any physical or biological problems with intrinsic directional axes into a graph network formalism with an embedded directional field.

In this paper, we propose a one-stage online clustering method called Contrastive Clustering (CC) which explicitly performs the instance- and cluster-level contrastive learning. To be specific, for a given dataset, the positive and negative instance pairs are constructed through data augmentations and then projected into a feature space. Therein, the instance- and cluster-level contrastive learning are respectively conducted in the row and column space by maximizing the similarities of positive pairs while minimizing those of negative ones. Our key observation is that the rows of the feature matrix could be regarded as soft labels of instances, and accordingly the columns could be further regarded as cluster representations. By simultaneously optimizing the instance- and cluster-level contrastive loss, the model jointly learns representations and cluster assignments in an end-to-end manner. Extensive experimental results show that CC remarkably outperforms 17 competitive clustering methods on six challenging image benchmarks. In particular, CC achieves an NMI of 0.705 (0.431) on the CIFAR-10 (CIFAR-100) dataset, which is an up to 19\% (39\%) performance improvement compared with the best baseline.

In this paper we provide a comprehensive introduction to knowledge graphs, which have recently garnered significant attention from both industry and academia in scenarios that require exploiting diverse, dynamic, large-scale collections of data. After a general introduction, we motivate and contrast various graph-based data models and query languages that are used for knowledge graphs. We discuss the roles of schema, identity, and context in knowledge graphs. We explain how knowledge can be represented and extracted using a combination of deductive and inductive techniques. We summarise methods for the creation, enrichment, quality assessment, refinement, and publication of knowledge graphs. We provide an overview of prominent open knowledge graphs and enterprise knowledge graphs, their applications, and how they use the aforementioned techniques. We conclude with high-level future research directions for knowledge graphs.

In this paper, we propose Latent Relation Language Models (LRLMs), a class of language models that parameterizes the joint distribution over the words in a document and the entities that occur therein via knowledge graph relations. This model has a number of attractive properties: it not only improves language modeling performance, but is also able to annotate the posterior probability of entity spans for a given text through relations. Experiments demonstrate empirical improvements over both a word-based baseline language model and a previous approach that incorporates knowledge graph information. Qualitative analysis further demonstrates the proposed model's ability to learn to predict appropriate relations in context.

This paper discusses and demonstrates the outcomes from our experimentation on Image Captioning. Image captioning is a much more involved task than image recognition or classification, because of the additional challenge of recognizing the interdependence between the objects/concepts in the image and the creation of a succinct sentential narration. Experiments on several labeled datasets show the accuracy of the model and the fluency of the language it learns solely from image descriptions. As a toy application, we apply image captioning to create video captions, and we advance a few hypotheses on the challenges we encountered.

Inferring missing links in knowledge graphs (KG) has attracted a lot of attention from the research community. In this paper, we tackle a practical query answering task involving predicting the relation of a given entity pair. We frame this prediction problem as an inference problem in a probabilistic graphical model and aim at resolving it from a variational inference perspective. In order to model the relation between the query entity pair, we assume that there exists an underlying latent variable (paths connecting two nodes) in the KG, which carries the equivalent semantics of their relations. However, due to the intractability of connections in large KGs, we propose to use variation inference to maximize the evidence lower bound. More specifically, our framework (\textsc{Diva}) is composed of three modules, i.e. a posterior approximator, a prior (path finder), and a likelihood (path reasoner). By using variational inference, we are able to incorporate them closely into a unified architecture and jointly optimize them to perform KG reasoning. With active interactions among these sub-modules, \textsc{Diva} is better at handling noise and coping with more complex reasoning scenarios. In order to evaluate our method, we conduct the experiment of the link prediction task on multiple datasets and achieve state-of-the-art performances on both datasets.