In this sense, the operating principle for adaptive sampling is simple and involves beginning with an initial number of examples and then iteratively learning the model, evaluating it and acquiring additional observations if necessary. Accordingly, there are two questions to be considered: it is necessary to determine the training data to be acquired at each cycle, and also to define a halting condition to terminate the loop once a certain degree of performance has been achieved by the learner. Both tasks confer the character of research issues to the formalization of scheduling and stopping criteria (John and Langley, 1996), respectively. The former has been researched for decades in terms of fixed (John and Langley, 1996; Provost et al., 1999) or adaptive (Provost et al., 1999) sequencing, and it is not our objective. As regards the halting criteria, they are independent of the scheduling and mostly start from the hypothesis that learning curves are wellbehaved, including an initial steeply sloping portion, a more gently sloping middle one and a final balanced zone (Meek et al., 2002). Accordingly, the purpose is to identify the moment in which such a curve reaches a plateau, namely when adding more data instances does not improve the accuracy, although this often does not strictly verify. Instead, extra learning efforts almost always result in modest increases. This justifies the interest in having a proximity condition, understood as a measure of the degree of convergence attained from a given iteration, rather than a stopping one. In short, this will make it possible to select the level of reliability in predicting a learner's performance, both in terms of accuracy and computational costs.

However, managing large amounts of information is an expensive, time-consuming and non-trivial activity, especially when expert knowledge is needed. Furthermore, having access to vast data bases does not imply that ml algorithms must use them all and a subset is therefore preferred, provided it does not reduce the quality of the mined knowledge. Such observations then supply the same learning power with far less computational cost and allow the training process to be speeded up, whilst their nature and optimal size are rarely obvious. This justifies the interest of developing efficient sampling techniques, which involves anticipating the link between performance and experience regarding the accuracy of the system we are generating. At this point, correctness with respect to the working hypotheses and robustness against changes to them should be guaranteed in order to supply a practical solution. The former ensures the effectiveness of the proposed strategy in the framework considered, while the latter enables fluctuations in the learning conditions to be assimilated without compromising correctness, thus providing reliability to our calculations. An area of work that is particularly sensitive to these inconveniences is natural language processing (nlp), the components of which are increasingly based on ml [3, 50].

An algorithm to estimate the evolution of learning curves on the whole of a training data base, based on the results obtained from a portion and using a functional strategy, is introduced. We approximate iteratively the sought value at the desired time, independently of the learning technique used and once a point in the process, called prediction level, has been passed. The proposal proves to be formally correct with respect to our working hypotheses and includes a reliable proximity condition. This allows the user to fix a convergence threshold with respect to the accuracy finally achievable, which extends the concept of stopping criterion and seems to be effective even in the presence of distorting observations. Our aim is to evaluate the training effort, supporting decision making in order to reduce the need for both human and computational resources during the learning process. The proposal is of interest in at least three operational procedures. The first is the anticipation of accuracy gain, with the purpose of measuring how much work is needed to achieve a certain degree of performance. The second relates the comparison of efficiency between systems at training time, with the objective of completing this task only for the one that best suits our requirements. The prediction of accuracy is also a valuable item of information for customizing systems, since we can estimate in advance the impact of settings on both the performance and the development costs. Using the generation of part-of-speech taggers as an example application, the experimental results are consistent with our expectations.

Federated Learning (FL) is a promising machine learning approach for Internet of Things (IoT), but it has to address network congestion problems when the population of IoT devices grows. Hierarchical FL (HFL) alleviates this issue by distributing model aggregation to multiple edge servers. Nevertheless, the challenge of communication overhead remains, especially in scenarios where all IoT devices simultaneously join the training process. For scalability, practical HFL schemes select a subset of IoT devices to participate in the training, hence the notion of device scheduling. In this setting, only selected IoT devices are scheduled to participate in the global training, with each of them being assigned to one edge server. Existing HFL assignment methods are primarily based on search mechanisms, which suffer from high latency in finding the optimal assignment. This paper proposes an improved K-Center algorithm for device scheduling and introduces a deep reinforcement learning-based approach for assigning IoT devices to edge servers. Experiments show that scheduling 50% of IoT devices is generally adequate for achieving convergence in HFL with much lower time delay and energy consumption. In cases where reduction in energy consumption (such as in Green AI) and reduction of messages (to avoid burst traffic) are key objectives, scheduling 30% IoT devices allows a substantial reduction in energy and messages with similar model accuracy.

We propose a fast method for solving compressed sensing, Lasso regression, and Logistic Lasso regression problems that iteratively runs an appropriate solver using an active set approach. We design a strategy to update the active set that achieves a large speedup over a single call of several solvers, including gradient projection for sparse reconstruction (GPSR), lassoglm of Matlab, and glmnet. For compressed sensing, the hybrid of our method and GPSR is 31.41 times faster than GPSR on average for Gaussian ensembles and 25.64 faster on average for binary ensembles. For Lasso regression, the hybrid of our method and GPSR achieves a 30.67-fold average speedup in our experiments. In our experiments on Logistic Lasso regression, the hybrid of our method and lassoglm gives an 11.95-fold average speedup, and the hybrid of our method and glmnet gives a 1.40-fold average speedup.

Dimensionality reduction methods, such as principal component analysis (PCA) and factor analysis, are central to many problems in data science. There are, however, serious and well-understood challenges to finding robust low dimensional approximations for data with significant heteroskedastic noise. This paper introduces a relaxed version of Minimum Trace Factor Analysis (MTFA), a convex optimization method with roots dating back to the work of Ledermann in 1940. This relaxation is particularly effective at not overfitting to heteroskedastic perturbations and addresses the commonly cited Heywood cases in factor analysis and the recently identified "curse of ill-conditioning" for existing spectral methods. We provide theoretical guarantees on the accuracy of the resulting low rank subspace and the convergence rate of the proposed algorithm to compute that matrix. We develop a number of interesting connections to existing methods, including HeteroPCA, Lasso, and Soft-Impute, to fill an important gap in the already large literature on low rank matrix estimation. Numerical experiments benchmark our results against several recent proposals for dealing with heteroskedastic noise.

Despite Deep Learning's (DL) empirical success, our theoretical understanding of its efficacy remains limited. One notable paradox is that while conventional wisdom discourages perfect data fitting, deep neural networks are designed to do just that, yet they generalize effectively. This study focuses on exploring this phenomenon attributed to the implicit bias at play. Various sources of implicit bias have been identified, such as step size, weight initialization, optimization algorithm, and number of parameters. In this work, we focus on investigating the implicit bias originating from weight initialization. To this end, we examine the problem of solving underdetermined linear systems in various contexts, scrutinizing the impact of initialization on the implicit regularization when using deep networks to solve such systems. Our findings elucidate the role of initialization in the optimization and generalization paradoxes, contributing to a more comprehensive understanding of DL's performance characteristics.

The recent trend towards the application of deep structured techniques has revealed the limits of huge models in natural language processing. This has reawakened the interest in traditional machine learning algorithms, which have proved still to be competitive in certain contexts, in particular low-resource settings. In parallel, model selection has become an essential task to boost performance at reasonable cost, even more so when we talk about processes involving domains where the training and/or computational resources are scarce. Against this backdrop, we evaluate the early estimation of learning curves as a practical mechanism for selecting the most appropriate model in scenarios characterized by the use of non-deep learners in resource-lean settings. On the basis of a formal approximation model previously evaluated under conditions of wide availability of training and validation resources, we study the reliability of such an approach in a different and much more demanding operationalenvironment. Using as case study the generation of PoS taggers for Galician, a language belonging to the Western Ibero-Romance group, the experimental results are consistent with our expectations.

Learning quickly from very few labeled samples is a fundamental attribute that separates machines and humans in the era of deep representation learning. Unsupervised few-shot learning (U-FSL) aspires to bridge this gap by discarding the reliance on annotations at training time. Intrigued by the success of contrastive learning approaches in the realm of U-FSL, we structurally approach their shortcomings in both pretraining and downstream inference stages. We propose a novel Dynamic Clustered mEmory (DyCE) module to promote a highly separable latent representation space for enhancing positive sampling at the pretraining phase and infusing implicit class-level insights into unsupervised contrastive learning. We then tackle the, somehow overlooked yet critical, issue of sample bias at the fewshot inference stage. We propose an iterative Optimal Transport-based distribution Alignment (OpTA) strategy and demonstrate that it efficiently addresses the problem, especially in low-shot scenarios where FSL approaches suffer the most from sample bias. We later on discuss that DyCE and OpTA are two intertwined pieces of a novel end-to-end approach (we coin as BECLR), constructively magnifying each other's impact. We then present a suite of extensive quantitative and qualitative experimentation to corroborate that BECLR sets a new state-of-the-art across ALL existing U-FSL benchmarks (to the best of our knowledge), and significantly outperforms the best of the current baselines (codebase available at GitHub). Achieving acceptable performance in deep representation learning comes at the cost of humongous data collection, laborious annotation, and excessive supervision. As we move towards more complex downstream tasks, this becomes increasingly prohibitive; in other words, supervised representation learning simply does not scale. In stark contrast, humans can quickly learn new tasks from a handful of samples, without extensive supervision. Few-shot learning (FSL) aspires to bridge this fundamental gap between humans and machines, using a suite of approaches such as metric learning (Wang et al., 2019; Bateni et al., 2020; Yang Figure 1: FSL has shown promising results in a supervised setting so far on a number of benchmarks (Hu et al., 2022; Singh & Jamali-Rad, 2022; Hu et al., 2023b); however, the need for supervision still lingers on.

Support Vector Machines (SVMs) are an important tool for performing classification on scattered data, where one usually has to deal with many data points in high-dimensional spaces. We propose solving SVMs in primal form using feature maps based on trigonometric functions or wavelets. In small dimensional settings the Fast Fourier Transform (FFT) and related methods are a powerful tool in order to deal with the considered basis functions. For growing dimensions the classical FFT-based methods become inefficient due to the curse of dimensionality. Therefore, we restrict ourselves to multivariate basis functions, each one of them depends only on a small number of dimensions. This is motivated by the well-known sparsity of effects and recent results regarding the reconstruction of functions from scattered data in terms of truncated analysis of variance (ANOVA) decomposition, which makes the resulting model even interpretable in terms of importance of the features as well as their couplings. The usage of small superposition dimensions has the consequence that the computational effort no longer grows exponentially but only polynomially with respect to the dimension. In order to enforce sparsity regarding the basis coefficients, we use the frequently applied $\ell_2$-norm and, in addition, $\ell_1$-norm regularization. The found classifying function, which is the linear combination of basis functions, and its variance can then be analyzed in terms of the classical ANOVA decomposition of functions. Based on numerical examples we show that we are able to recover the signum of a function that perfectly fits our model assumptions. We obtain better results with $\ell_1$-norm regularization, both in terms of accuracy and clarity of interpretability.