The problem of inhomogeneous cluster densities has been a long-standing issue for distance-based and density-based algorithms in clustering and anomaly detection. These algorithms implicitly assume that all clusters have approximately the same density. As a result, they often exhibit a bias towards dense clusters in the presence of sparse clusters. Many remedies have been suggested; yet, we show that they are partial solutions which do not address the issue satisfactorily. To match the implicit assumption, we propose to transform a given dataset such that the transformed clusters have approximately the same density while all regions of locally low density become globally low density -- homogenising cluster density while preserving the cluster structure of the dataset. We show that this can be achieved by using a new multi-dimensional Cumulative Distribution Function in a transform-and-shift method. The method can be applied to every dataset, before the dataset is used in many existing algorithms to match their implicit assumption without algorithmic modification. We show that the proposed method performs better than existing remedies.

Abstract: Intelligent information systems that contain emergent elements often encounter trust problems because results do not get sufficiently explained and the procedure itself can not be fully retraced. This is caused by a control flow depending either on stochastic elements or on the structure and relevance of the input data. Trust in such algorithms can be established by letting users interact with the system so that they can explore results and find patterns that can be compared with their expected solution. Reflecting features and patterns of human understanding of a domain against algorithmic results can create awareness of such patterns and may increase the trust that a user has in the solution. If expectations are not met, close inspection can be used to decide whether a solution conforms to the expectations or whether it goes beyond the expected. By either accepting or rejecting a solution, the user's set of expectations evolves and a learning process for the users is established. In this paper we present a conceptual framework that reflects and supports this process. The framework is the result of an analysis of two exemplary case studies from two different disciplines with information systems that assist experts in their complex tasks. Keywords: Intelligent Systems, AI, Trust, Explainable AI, Knowledge Management, Knowledge Patterns 1. INTRODUCTION uncommon and have been constructed in uncommon ways. Such techniques, a class to which systems that we now Human expertise in many aspects is largely based on call intelligent systems belong to, produce results of high prior knowledge and familiar patterns, which have either complexity (e.g.

Variational inference is a popular alternative to Markov chain Monte Carlo methods that constructs a Bayesian posterior approximation by minimizing a discrepancy to the true posterior within a pre-specified family. This converts Bayesian inference into an optimization problem, enabling the use of simple and scalable stochastic optimization algorithms. However, a key limitation of variational inference is that the optimal approximation is typically not tractable to compute; even in simple settings the problem is nonconvex. Thus, recently developed statistical guarantees -- which all involve the (data) asymptotic properties of the optimal variational distribution -- are not reliably obtained in practice. In this work, we provide two major contributions: a theoretical analysis of the asymptotic convexity properties of variational inference in the popular setting with a Gaussian family; and consistent stochastic variational inference (CSVI), an algorithm that exploits these properties to find the optimal approximation in the asymptotic regime. CSVI consists of a tractable initialization procedure that finds the local basin of the optimal solution, and a scaled gradient descent algorithm that stays locally confined to that basin. Experiments on nonconvex synthetic and real-data examples show that compared with standard stochastic gradient descent, CSVI improves the likelihood of obtaining the globally optimal posterior approximation.

A broad class of unsupervised deep learning methods such as Generative Adversarial Networks (GANs) involve training of overparameterized models where the number of parameters of the model exceeds a certain threshold. Indeed, most successful GANs used in practice are trained using overparameterized generator and discriminator networks, both in terms of depth and width. A large body of work in supervised learning have shown the importance of model overparameterization in the convergence of the gradient descent (GD) to globally optimal solutions. In contrast, the unsupervised setting and GANs in particular involve non-convex concave mini-max optimization problems that are often trained using Gradient Descent/Ascent (GDA). The role and benefits of model overparameterization in the convergence of GDA to a global saddle point in non-convex concave problems is far less understood. In this work, we present a comprehensive analysis of the importance of model overparameterization in GANs both theoretically and empirically. We theoretically show that in an overparameterized GAN model with a 1-layer neural network generator and a linear discriminator, GDA converges to a global saddle point of the underlying non-convex concave min-max problem. To the best of our knowledge, this is the first result for global convergence of GDA in such settings. Our theory is based on a more general result that holds for a broader class of nonlinear generators and discriminators that obey certain assumptions (including deeper generators and random feature discriminators). Our theory utilizes and builds upon a novel connection with the convergence analysis of linear timevarying dynamical systems which may have broader implications for understanding the convergence behavior of GDA for non-convex concave problems involving overparameterized models. We also empirically study the role of model overparameterization in GANs using several large-scale experiments on CIFAR-10 and Celeb-A datasets.

State-of-the-art deep neural networks require large-scale labeled training data that is often expensive to obtain or not available for many tasks. Weak supervision in the form of domain-specific rules has been shown to be useful in such settings to automatically generate weakly labeled training data. However, learning with weak rules is challenging due to their inherent heuristic and noisy nature. An additional challenge is rule coverage and overlap, where prior work on weak supervision only considers instances that are covered by weak rules, thus leaving valuable unlabeled data behind. In this work, we develop a weak supervision framework (ASTRA) that leverages all the available data for a given task. To this end, we leverage task-specific unlabeled data through self-training with a model (student) that considers contextualized representations and predicts pseudo-labels for instances that may not be covered by weak rules. We further develop a rule attention network (teacher) that learns how to aggregate student pseudo-labels with weak rule labels, conditioned on their fidelity and the underlying context of an instance. Finally, we construct a semi-supervised learning objective for end-to-end training with unlabeled data, domain-specific rules, and a small amount of labeled data. Extensive experiments on six benchmark datasets for text classification demonstrate the effectiveness of our approach with significant improvements over state-of-the-art baselines.

Due to the scarcity and often high acquisition cost of labelled data, machine learning methods that make effective use of large quantities of unlabelled data are being increasingly used. One such method is semi-supervised learning (SSL) where, in addition to labelled data, possibly large numbers of unlabelled observations are available at the time of the construction of the classification rule (classifier) to be used. Not surprisingly, semisupervised learning approaches have been gaining much attention in both the application oriented and the theoretical machine learning communities. However, theoretical analysis of SSL has so far been scarce. But last year, Ahfock and McLachlan (2020) provided an asymptotic basis on how to increase in certain situations the accuracy of the commonly used linear discriminant function formed from a partially classified sample as in SSL (Ahfock and McLachlan, 2020). The increase in accuracy can be of sufficient magnitude for this SSL-based classifier to have smaller error rate than that if it were formed from a completely classified sample.

Bayes' theorem is used as foundation Autoencoders are a family of unsupervised learning methods for inference in Bayesian neural networks, and Markov that use neural network architectures and learning algorithms chain Monte Carlo (MCMC) sampling methods [25] are used to learn a lower-dimensional representation (encoding) for constructing the posterior distribution. Variational inference of the data, which can then be used to reconstruct a representation [26] is another way to approximate the posterior distribution, close to the original input. They thus facilitate dimensionality which approximates an intractable posterior distribution by a reduction for prediction and classification [1, 2], and have tractable one. This makes it particularly suited to large data been successfully applied to image classification [3, 4], face sets and models, and so it has been popular for autoencoders recognition [5, 6], geoscience and remote sensing [7], speechbased and neural networks [13, 27].

Relational knowledge bases (KBs) are established tools for world knowledge representation in machines. While they are advantageous for their precision and interpretability, they usually sacrifice some data modeling flexibility for these advantages because they adhere to a manually engineered schema. In this review, we take a natural language processing perspective to the limitations of KBs, examining how they may be addressed in part by training neural contextual language models (LMs) to internalize and express relational knowledge in free-text form. We propose a novel taxonomy for relational knowledge representation in contextual LMs based on the level of KB supervision provided, considering both works that probe LMs for implicit relational knowledge acquired during self-supervised pretraining on unstructured text alone, and works that explicitly supervise LMs at the level of KB entities and/or relations. We conclude that LMs and KBs are complementary representation tools, as KBs provide a high standard of factual precision which can in turn be flexibly and expressively modeled by LMs, and provide suggestions for future research in this direction.

While traditional corpus-level evaluation metrics for machine translation (MT) correlate well with fluency, they struggle to reflect adequacy. Model-based MT metrics trained on segment-level human judgments have emerged as an attractive replacement due to strong correlation results. These models, however, require potentially expensive re-training for new domains and languages. Furthermore, their decisions are inherently non-transparent and appear to reflect unwelcome biases. We explore the simple type-based classifier metric, MacroF1, and study its applicability to MT evaluation. We find that MacroF1 is competitive on direct assessment, and outperforms others in indicating downstream cross-lingual information retrieval task performance. Further, we show that MacroF1 can be used to effectively compare supervised and unsupervised neural machine translation, and reveal significant qualitative differences in the methods' outputs.

Machine learning algorithms have been very successful to solve problems in the natural language processing (NLP) domain for many years, especially supervised and unsupervised methods. However, this is not the case with reinforcement learning (RL), which is somewhat surprising since in other domains, reinforcement learning methods have experienced an increased level of success with some impressive results, for instance in board games such as AlphaGo Zero [106]. Yet, deep reinforcement learning for natural language processing is still in its infancy when compared to supervised learning [65]. Thus, the goal of this article is to provide a review of applications of reinforcement learning to NLP and we present an analysis of the underlying structure of the problems that make them viable to be treated entirely or partially as RL problems intended as an aid to newcomers to the field. We also analyze some existing research gaps and provide a list of promising research directions in which natural language systems might benefit from reinforcement learning algorithms.