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Achievability in information theory refers to demonstrating a coding strategy that accomplishes a prescribed performance benchmark for the underlying task. In quantum information theory, the crafted Hayashi-Nagaoka operator inequality is an essential technique in proving a wealth of one-shot achievability bounds since it effectively resembles a union bound in various problems. In this work, we show that the pretty-good measurement naturally plays a role as the union bound as well. A judicious application of it considerably simplifies the derivation of one-shot achievability for classical-quantum (c-q) channel coding via an elegant three-line proof. The proposed analysis enjoys the following favorable features. (i) The established one-shot bound admits a closed-form expression as in the celebrated Holevo-Helstrom Theorem. Namely, the error probability of sending $M$ messages through a c-q channel is upper bounded by the minimum error of distinguishing the joint channel input-output state against $(M-1)$ decoupled products states. (ii) Our bound directly yields asymptotic results in the large deviation, small deviation, and moderate deviation regimes in a unified manner. (iii) The coefficients incurred in applying the Hayashi-Nagaoka operator inequality are no longer needed. Hence, the derived one-shot bound sharpens existing results relying on the Hayashi-Nagaoka operator inequality. In particular, we obtain the tightest achievable $\epsilon$-one-shot capacity for c-q channel coding heretofore, improving the third-order coding rate in the asymptotic scenario. (iv) Our result holds for infinite-dimensional Hilbert space. (v) The proposed method applies to deriving one-shot achievability for classical data compression with quantum side information, entanglement-assisted classical communication over quantum channels, and various quantum network information-processing protocols.

Although robust statistical estimators are less affected by outlying observations, their computation is usually more challenging. This is particularly the case in high-dimensional sparse settings. The availability of new optimization procedures, mainly developed in the computer science domain, offers new possibilities for the field of robust statistics. This paper investigates how such procedures can be used for robust sparse association estimators. The problem can be split into a robust estimation step followed by an optimization for the remaining decoupled, (bi-)convex problem. A combination of the augmented Lagrangian algorithm and adaptive gradient descent is implemented to also include suitable constraints for inducing sparsity. We provide results concerning the precision of the algorithm and show the advantages over existing algorithms in this context. High-dimensional empirical examples underline the usefulness of this procedure. Extensions to other robust sparse estimators are possible.

In this paper, we study arbitrary infinite binary information systems each of which consists of an infinite set called universe and an infinite set of two-valued functions (attributes) defined on the universe. We consider the notion of a problem over information system, which is described by a finite number of attributes and a mapping associating a decision to each tuple of attribute values. As algorithms for problem solving, we investigate deterministic and nondeterministic decision trees that use only attributes from the problem description. Nondeterministic decision trees are representations of decision rule systems that sometimes have less space complexity than the original rule systems. As time and space complexity, we study the depth and the number of nodes in the decision trees. In the worst case, with the growth of the number of attributes in the problem description, (i) the minimum depth of deterministic decision trees grows either as a logarithm or linearly, (ii) the minimum depth of nondeterministic decision trees either is bounded from above by a constant or grows linearly, (iii) the minimum number of nodes in deterministic decision trees has either polynomial or exponential growth, and (iv) the minimum number of nodes in nondeterministic decision trees has either polynomial or exponential growth. Based on these results, we divide the set of all infinite binary information systems into three complexity classes. This allows us to identify nontrivial relationships between deterministic decision trees and decision rules systems represented by nondeterministic decision trees. For each class, we study issues related to time-space trade-off for deterministic and nondeterministic decision trees.

This paper aims to develop a new attribution method to explain the conflict between individual variables' attributions and their coalition's attribution from a fully new perspective. First, we find that the Shapley value can be reformulated as the allocation of Harsanyi interactions encoded by the AI model. Second, based the re-alloction of interactions, we extend the Shapley value to the attribution of coalitions. Third we ective. We derive the fundamental mechanism behind the conflict. This conflict come from the interaction containing partial variables in their coalition.

We propose a theory for matrix completion that goes beyond the low-rank structure commonly considered in the literature and applies to general matrices of low description complexity. Specifically, complexity of the sets of matrices encompassed by the theory is measured in terms of Hausdorff and upper Minkowski dimensions. Our goal is the characterization of the number of linear measurements, with an emphasis on rank-$1$ measurements, needed for the existence of an algorithm that yields reconstruction, either perfect, with probability 1, or with arbitrarily small probability of error, depending on the setup. Concretely, we show that matrices taken from a set $\mathcal{U}$ such that $\mathcal{U}-\mathcal{U}$ has Hausdorff dimension $s$ can be recovered from $k>s$ measurements, and random matrices supported on a set $\mathcal{U}$ of Hausdorff dimension $s$ can be recovered with probability 1 from $k>s$ measurements. What is more, we establish the existence of recovery mappings that are robust against additive perturbations or noise in the measurements. Concretely, we show that there are $\beta$-H\"older continuous mappings recovering matrices taken from a set of upper Minkowski dimension $s$ from $k>2s/(1-\beta)$ measurements and, with arbitrarily small probability of error, random matrices supported on a set of upper Minkowski dimension $s$ from $k>s/(1-\beta)$ measurements. The numerous concrete examples we consider include low-rank matrices, sparse matrices, QR decompositions with sparse R-components, and matrices of fractal nature.

The allure of aesthetic appeal in images captivates our senses, yet the underlying intricacies of aesthetic preferences remain elusive. In this study, we pioneer a novel perspective by utilizing machine learning models that focus on aesthetic attributes known to influence preferences. Through a data mining approach, our models process these attributes as inputs to predict the aesthetic scores of images. Moreover, to delve deeper and obtain interpretable explanations regarding the factors driving aesthetic preferences, we utilize the popular Explainable AI (XAI) technique known as SHapley Additive exPlanations (SHAP). Our methodology involves employing various machine learning models, including Random Forest, XGBoost, Support Vector Regression, and Multilayer Perceptron, to compare their performances in accurately predicting aesthetic scores, and consistently observing results in conjunction with SHAP. We conduct experiments on three image aesthetic benchmarks, providing insights into the roles of attributes and their interactions. Ultimately, our study aims to shed light on the complex nature of aesthetic preferences in images through machine learning and provides a deeper understanding of the attributes that influence aesthetic judgements.

Interactive segmentation is a crucial research area in medical image analysis aiming to boost the efficiency of costly annotations by incorporating human feedback. This feedback takes the form of clicks, scribbles, or masks and allows for iterative refinement of the model output so as to efficiently guide the system towards the desired behavior. In recent years, deep learning-based approaches have propelled results to a new level causing a rapid growth in the field with 121 methods proposed in the medical imaging domain alone. In this review, we provide a structured overview of this emerging field featuring a comprehensive taxonomy, a systematic review of existing methods, and an in-depth analysis of current practices. Based on these contributions, we discuss the challenges and opportunities in the field. For instance, we find that there is a severe lack of comparison across methods which needs to be tackled by standardized baselines and benchmarks.

We investigate how the potential use of algorithms and demonstrative evidence may affect potential jurors' feelings of reliability, credibility, and understanding of expert witnesses and presented evidence. The use of statistical methods in forensic science is motivated by a lack of scientific validity and error rate issues present in many forensic analysis methods. We explore how this new method may be perceived in the courtroom - where individuals unfamiliar with advanced statistical methods are asked to evaluate its use in order to assess guilt. In the course of our initial study, we discovered issues in scale compression of responses and survey format. We visually compare participants' notes to the provided transcript by highlighting phrase frequency based on collocations.

Due to their increasing spread, confidence in neural network predictions became more and more important. However, basic neural networks do not deliver certainty estimates or suffer from over or under confidence. Many researchers have been working on understanding and quantifying uncertainty in a neural network's prediction. As a result, different types and sources of uncertainty have been identified and a variety of approaches to measure and quantify uncertainty in neural networks have been proposed. This work gives a comprehensive overview of uncertainty estimation in neural networks, reviews recent advances in the field, highlights current challenges, and identifies potential research opportunities. It is intended to give anyone interested in uncertainty estimation in neural networks a broad overview and introduction, without presupposing prior knowledge in this field. A comprehensive introduction to the most crucial sources of uncertainty is given and their separation into reducible model uncertainty and not reducible data uncertainty is presented. The modeling of these uncertainties based on deterministic neural networks, Bayesian neural networks, ensemble of neural networks, and test-time data augmentation approaches is introduced and different branches of these fields as well as the latest developments are discussed. For a practical application, we discuss different measures of uncertainty, approaches for the calibration of neural networks and give an overview of existing baselines and implementations. Different examples from the wide spectrum of challenges in different fields give an idea of the needs and challenges regarding uncertainties in practical applications. Additionally, the practical limitations of current methods for mission- and safety-critical real world applications are discussed and an outlook on the next steps towards a broader usage of such methods is given.

This work considers the question of how convenient access to copious data impacts our ability to learn causal effects and relations. In what ways is learning causality in the era of big data different from -- or the same as -- the traditional one? To answer this question, this survey provides a comprehensive and structured review of both traditional and frontier methods in learning causality and relations along with the connections between causality and machine learning. This work points out on a case-by-case basis how big data facilitates, complicates, or motivates each approach.