The quintessential learning algorithm of empirical risk minimization (ERM) is known to fail in various settings for which uniform convergence does not characterize learning. It is therefore unsurprising that the practice of machine learning is rife with considerably richer algorithmic techniques for successfully controlling model capacity. Nevertheless, no such technique or principle has broken away from the pack to characterize optimal learning in these more general settings. The purpose of this work is to characterize the role of regularization in perhaps the simplest setting for which ERM fails: multiclass learning with arbitrary label sets. Using one-inclusion graphs (OIGs), we exhibit optimal learning algorithms that dovetail with tried-and-true algorithmic principles: Occam's Razor as embodied by structural risk minimization (SRM), the principle of maximum entropy, and Bayesian reasoning. Most notably, we introduce an optimal learner which relaxes structural risk minimization on two dimensions: it allows the regularization function to be "local" to datapoints, and uses an unsupervised learning stage to learn this regularizer at the outset. We justify these relaxations by showing that they are necessary: removing either dimension fails to yield a near-optimal learner. We also extract from OIGs a combinatorial sequence we term the Hall complexity, which is the first to characterize a problem's transductive error rate exactly. Lastly, we introduce a generalization of OIGs and the transductive learning setting to the agnostic case, where we show that optimal orientations of Hamming graphs -- judged using nodes' outdegrees minus a system of node-dependent credits -- characterize optimal learners exactly. We demonstrate that an agnostic version of the Hall complexity again characterizes error rates exactly, and exhibit an optimal learner using maximum entropy programs.

Most of today's wearable technology provides seamless cardiac activity monitoring. Specifically, the vast majority employ Photoplethysmography (PPG) sensors to acquire blood volume pulse information, which is further analysed to extract useful and physiologically related features. Nevertheless, PPG-based signal reliability presents different challenges that strongly affect such data processing. This is mainly related to the fact of PPG morphological wave distortion due to motion artefacts, which can lead to erroneous interpretation of the extracted cardiac-related features. On this basis, in this paper, we propose a novel personalised and adjustable Interval Type-2 Fuzzy Logic System (IT2FLS) for assessing the quality of PPG signals. The proposed system employs a personalised approach to adapt the IT2FLS parameters to the unique characteristics of each individual's PPG signals.Additionally, the system provides adjustable levels of personalisation, allowing healthcare providers to adjust the system to meet specific requirements for different applications. The proposed system obtained up to 93.72\% for average accuracy during validation. The presented system has the potential to enable ultra-low complexity and real-time PPG quality assessment, improving the accuracy and reliability of PPG-based health monitoring systems at the edge.

Financial performance management is at the core of business management and has historically relied on financial ratio analysis using Balance Sheet and Income Statement data to assess company performance as compared with competitors. Little progress has been made in predicting how a company will perform or in assessing the risks (probabilities) of financial underperformance. In this study I introduce a new set of financial and macroeconomic ratios that supplement standard ratios of Balance Sheet and Income Statement. I also provide a set of supervised learning models (ML Regressors and Neural Networks) and Bayesian models to predict company performance. I conclude that the new proposed variables improve model accuracy when used in tandem with standard industry ratios. I also conclude that Feedforward Neural Networks (FNN) are simpler to implement and perform best across 6 predictive tasks (ROA, ROE, Net Margin, Op Margin, Cash Ratio and Op Cash Generation); although Bayesian Networks (BN) can outperform FNN under very specific conditions. BNs have the additional benefit of providing a probability density function in addition to the predicted (expected) value. The study findings have significant potential helping CFOs and CEOs assess risks of financial underperformance to steer companies in more profitable directions; supporting lenders in better assessing the condition of a company and providing investors with tools to dissect financial statements of public companies more accurately.

Human knowledge is subject to uncertainties, imprecision, incompleteness and inconsistencies. Moreover, the meaning of many everyday terms is dependent on the context. That poses a huge challenge for the Semantic Web. This paper introduces work on an intuitive notation and model for defeasible reasoning with imperfect knowledge, and relates it to previous work on argumentation theory. PKN is to N3 as defeasible reasoning is to deductive logic. Further work is needed on an intuitive syntax for describing reasoning strategies and tactics in declarative terms, drawing upon the AIF ontology for inspiration. The paper closes with observations on symbolic approaches in the era of large language models.

Choosing an appropriate representation of the environment for the underlying decision-making process of the RL agent is not always straightforward. The state representation should be inclusive enough to allow the agent to informatively decide on its actions and compact enough to increase sample efficiency for policy training. Given this outlook, this work examines the effect of various state representations in incentivizing the agent to solve a specific robotic task: antipodal and planar object grasping. A continuum of state representation abstractions is defined, starting from a model-based approach with complete system knowledge, through hand-crafted numerical, to image-based representations with decreasing level of induced task-specific knowledge. We examine the effects of each representation in the ability of the agent to solve the task in simulation and the transferability of the learned policy to the real robot. The results show that RL agents using numerical states can perform on par with non-learning baselines. Furthermore, we find that agents using image-based representations from pre-trained environment embedding vectors perform better than end-to-end trained agents, and hypothesize that task-specific knowledge is necessary for achieving convergence and high success rates in robot control.

In the context of general rough sets, the act of combining two things to form another is not straightforward. The situation is similar for other theories that concern uncertainty and vagueness. Such acts can be endowed with additional meaning that go beyond structural conjunction and disjunction as in the theory of $*$-norms and associated implications over $L$-fuzzy sets. In the present research, algebraic models of acts of combining things in generalized rough sets over lattices with approximation operators (called rough convenience lattices) is invented. The investigation is strongly motivated by the desire to model skeptical or pessimistic, and optimistic or possibilistic aggregation in human reasoning, and the choice of operations is constrained by the perspective. Fundamental results on the weak negations and implications afforded by the minimal models are proved. In addition, the model is suitable for the study of discriminatory/toxic behavior in human reasoning, and of ML algorithms learning such behavior.

In this research, new concepts of existential granules that determine themselves are invented, and are characterized from algebraic, topological, and mereological perspectives. Existential granules are those that determine themselves initially, and interact with their environment subsequently. Examples of the concept, such as those of granular balls, though inadequately defined, algorithmically established, and insufficiently theorized in earlier works by others, are already used in applications of rough sets and soft computing. It is shown that they fit into multiple theoretical frameworks (axiomatic, adaptive, and others) of granular computing. The characterization is intended for algorithm development, application to classification problems and possible mathematical foundations of generalizations of the approach. Additionally, many open problems are posed and directions provided.

A challenging category of robotics problems arises when sensing incurs substantial costs. This paper examines settings in which a robot wishes to limit its observations of state, for instance, motivated by specific considerations of energy management, stealth, or implicit coordination. We formulate the problem of planning under uncertainty when the robot's observations are intermittent but their timing is known via a pre-declared schedule. After having established the appropriate notion of an optimal policy for such settings, we tackle the problem of joint optimization of the cumulative execution cost and the number of state observations, both in expectation under discounts. To approach this multi-objective optimization problem, we introduce an algorithm that can identify the Pareto front for a class of schedules that are advantageous in the discounted setting. The algorithm proceeds in an accumulative fashion, prepending additions to a working set of schedules and then computing incremental changes to the value functions. Because full exhaustive construction becomes computationally prohibitive for moderate-sized problems, we propose a filtering approach to prune the working set. Empirical results demonstrate that this filtering is effective at reducing computation while incurring only negligible reduction in quality. In summarizing our findings, we provide a characterization of the run-time vs quality trade-off involved.

We release a new Bayesian neural network library for PyTorch for large-scale deep networks. Our library implements mainstream approximate Bayesian inference algorithms: variational inference, MC-dropout, stochastic-gradient MCMC, and Laplace approximation. The main differences from other existing Bayesian neural network libraries are as follows: 1) Our library can deal with very large-scale deep networks including Vision Transformers (ViTs).

Deep Gaussian Process (DGP) models offer a powerful nonparametric approach for Bayesian inference, but exact inference is typically intractable, motivating the use of various approximations. However, existing approaches, such as mean-field Gaussian assumptions, limit the expressiveness and efficacy of DGP models, while stochastic approximation can be computationally expensive. To tackle these challenges, we introduce Neural Operator Variational Inference (NOVI) for Deep Gaussian Processes. NOVI uses a neural generator to obtain a sampler and minimizes the Regularized Stein Discrepancy in L2 space between the generated distribution and true posterior. We solve the minimax problem using Monte Carlo estimation and subsampling stochastic optimization techniques. We demonstrate that the bias introduced by our method can be controlled by multiplying the Fisher divergence with a constant, which leads to robust error control and ensures the stability and precision of the algorithm. Our experiments on datasets ranging from hundreds to tens of thousands demonstrate the effectiveness and the faster convergence rate of the proposed method. We achieve a classification accuracy of 93.56 on the CIFAR10 dataset, outperforming SOTA Gaussian process methods. Furthermore, our method guarantees theoretically controlled prediction error for DGP models and demonstrates remarkable performance on various datasets. We are optimistic that NOVI has the potential to enhance the performance of deep Bayesian nonparametric models and could have significant implications for various practical applications