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Quantification represents the problem of predicting class distributions in a dataset. It also represents a growing research field in supervised machine learning, for which a large variety of different algorithms has been proposed in recent years. However, a comprehensive empirical comparison of quantification methods that supports algorithm selection is not available yet. In this work, we close this research gap by conducting a thorough empirical performance comparison of 24 different quantification methods on overall more than 40 data sets, considering binary as well as multiclass quantification settings. We observe that no single algorithm generally outperforms all competitors, but identify a group of methods including the threshold selection-based Median Sweep and TSMax methods, the DyS framework, and Friedman's method that performs best in the binary setting. For the multiclass setting, we observe that a different group of algorithms yields good performance, including the Generalized Probabilistic Adjusted Count, the readme method, the energy distance minimization method, the EM algorithm for quantification, and Friedman's method. We also find that tuning the underlying classifiers has in most cases only a limited impact on the quantification performance. More generally, we find that the performance on multiclass quantification is inferior to the results obtained in the binary setting. Our results can guide practitioners who intend to apply quantification algorithms and help researchers to identify opportunities for future research.

Automated text simplification aims to produce simple versions of complex texts. This task is especially useful in the medical domain, where the latest medical findings are typically communicated via complex and technical articles. This creates barriers for laypeople seeking access to up-to-date medical findings, consequently impeding progress on health literacy. Most existing work on medical text simplification has focused on monolingual settings, with the result that such evidence would be available only in just one language (most often, English). This work addresses this limitation via multilingual simplification, i.e., directly simplifying complex texts into simplified texts in multiple languages. We introduce MultiCochrane, the first sentence-aligned multilingual text simplification dataset for the medical domain in four languages: English, Spanish, French, and Farsi. We evaluate fine-tuned and zero-shot models across these languages, with extensive human assessments and analyses. Although models can now generate viable simplified texts, we identify outstanding challenges that this dataset might be used to address.

Many modern datasets, such as those in ecology and geology, are composed of samples with spatial structure and dependence. With such data violating the usual independent and identically distributed (IID) assumption in machine learning and classical statistics, it is unclear a priori how one should measure the performance and generalization of models. Several authors have empirically investigated cross-validation (CV) methods in this setting, reaching mixed conclusions. We provide a class of unbiased estimation methods for general quadratic errors, correlated Gaussian response, and arbitrary prediction function $g$, for a noise-elevated version of the error. Our approach generalizes the coupled bootstrap (CB) from the normal means problem to general normal data, allowing correlation both within and between the training and test sets. CB relies on creating bootstrap samples that are intelligently decoupled, in the sense of being statistically independent. Specifically, the key to CB lies in generating two independent "views" of our data and using them as stand-ins for the usual independent training and test samples. Beginning with Mallows' $C_p$, we generalize the estimator to develop our generalized $C_p$ estimators (GC). We show at under only a moment condition on $g$, this noise-elevated error estimate converges smoothly to the noiseless error estimate. We show that when Stein's unbiased risk estimator (SURE) applies, GC converges to SURE as in the normal means problem. Further, we use these same tools to analyze CV and provide some theoretical analysis to help understand when CV will provide good estimates of error. Simulations align with our theoretical results, demonstrating the effectiveness of GC and illustrating the behavior of CV methods. Lastly, we apply our estimator to a model selection task on geothermal data in Nevada.

Inverse problems are characterized by their inherent non-uniqueness and sensitivity with respect to data perturbations. Their stable solution requires the application of regularization methods including variational and iterative regularization methods. Superiorization is a heuristic approach that can steer basic iterative algorithms to have small value of certain regularization functional while keeping the algorithms simplicity and computational efforts, but is able to account for additional prior information. In this note, we combine the superiorization methodology with iterative regularization methods and show that the superiorized version of the scheme yields again a regularization method, however accounting for different prior information.

Representing graphs by their homomorphism counts has led to the beautiful theory of homomorphism indistinguishability in recent years. Moreover, homomorphism counts have promising applications in database theory and machine learning, where one would like to answer queries or classify graphs solely based on the representation of a graph $G$ as a finite vector of homomorphism counts from some fixed finite set of graphs to $G$. We study the computational complexity of the arguably most fundamental computational problem associated to these representations, the homomorphism reconstructability problem: given a finite sequence of graphs and a corresponding vector of natural numbers, decide whether there exists a graph $G$ that realises the given vector as the homomorphism counts from the given graphs. We show that this problem yields a natural example of an $\mathsf{NP}^{#\mathsf{P}}$-hard problem, which still can be $\mathsf{NP}$-hard when restricted to a fixed number of input graphs of bounded treewidth and a fixed input vector of natural numbers, or alternatively, when restricted to a finite input set of graphs. We further show that, when restricted to a finite input set of graphs and given an upper bound on the order of the graph $G$ as additional input, the problem cannot be $\mathsf{NP}$-hard unless $\mathsf{P} = \mathsf{NP}$. For this regime, we obtain partial positive results. We also investigate the problem's parameterised complexity and provide fpt-algorithms for the case that a single graph is given and that multiple graphs of the same order with subgraph instead of homomorphism counts are given.

Class imbalance exists in many classification problems, and since the data is designed for accuracy, imbalance in data classes can lead to classification challenges with a few classes having higher misclassification costs. The Backblaze dataset, a widely used dataset related to hard discs, has a small amount of failure data and a large amount of health data, which exhibits a serious class imbalance. This paper provides a comprehensive overview of research in the field of imbalanced data classification. The discussion is organized into three main aspects: data-level methods, algorithmic-level methods, and hybrid methods. For each type of method, we summarize and analyze the existing problems, algorithmic ideas, strengths, and weaknesses. Additionally, the challenges of unbalanced data classification are discussed, along with strategies to address them. It is convenient for researchers to choose the appropriate method according to their needs.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.

We describe the new field of mathematical analysis of deep learning. This field emerged around a list of research questions that were not answered within the classical framework of learning theory. These questions concern: the outstanding generalization power of overparametrized neural networks, the role of depth in deep architectures, the apparent absence of the curse of dimensionality, the surprisingly successful optimization performance despite the non-convexity of the problem, understanding what features are learned, why deep architectures perform exceptionally well in physical problems, and which fine aspects of an architecture affect the behavior of a learning task in which way. We present an overview of modern approaches that yield partial answers to these questions. For selected approaches, we describe the main ideas in more detail.

Co-evolving time series appears in a multitude of applications such as environmental monitoring, financial analysis, and smart transportation. This paper aims to address the following challenges, including (C1) how to incorporate explicit relationship networks of the time series; (C2) how to model the implicit relationship of the temporal dynamics. We propose a novel model called Network of Tensor Time Series, which is comprised of two modules, including Tensor Graph Convolutional Network (TGCN) and Tensor Recurrent Neural Network (TRNN). TGCN tackles the first challenge by generalizing Graph Convolutional Network (GCN) for flat graphs to tensor graphs, which captures the synergy between multiple graphs associated with the tensors. TRNN leverages tensor decomposition to model the implicit relationships among co-evolving time series. The experimental results on five real-world datasets demonstrate the efficacy of the proposed method.