The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are rarely used and considered in numerical analysis due to their lack of strict positive definiteness. In particular they do not enjoy the usual property of unisolvency for arbitrary point sets, which is one of the key properties used to build kernel-based interpolation methods. This paper is devoted to establish some initial results for the study of these kernels, and their related interpolation algorithms, in the context of approximation theory. We will first prove necessary and sufficient conditions on point sets which guarantee the existence and uniqueness of an interpolant. We will then study the Reproducing Kernel Hilbert Spaces (or native spaces) of these kernels and their norms, and provide inclusion relations between spaces corresponding to different kernel parameters. With these spaces at hand, it will be further possible to derive generic error estimates which apply to sufficiently smooth functions, thus escaping the native space. Finally, we will show how to employ an efficient stable algorithm to these kernels to obtain accurate interpolants, and we will test them in some numerical experiment. After this analysis several computational and theoretical aspects remain open, and we will outline possible further research directions in a concluding section. This work builds some bridges between kernel and polynomial interpolation, two topics to which the authors, to different extents, have been introduced under the supervision or through the work of Stefano De Marchi. For this reason, they wish to dedicate this work to him in the occasion of his 60th birthday.

Metric learning aims to learn distances from the data, which enhances the performance of similarity-based algorithms. An author style detection task is a metric learning problem, where learning style features with small intra-class variations and larger inter-class differences is of great importance to achieve better performance. Recently, metric learning based on softmax loss has been used successfully for style detection. While softmax loss can produce separable representations, its discriminative power is relatively poor. In this work, we propose NBC-Softmax, a contrastive loss based clustering technique for softmax loss, which is more intuitive and able to achieve superior performance. Our technique meets the criterion for larger number of samples, thus achieving block contrastiveness, which is proven to outperform pair-wise losses. It uses mini-batch sampling effectively and is scalable. Experiments on 4 darkweb social forums, with NBCSAuthor that uses the proposed NBC-Softmax for author and sybil detection, shows that our negative block contrastive approach constantly outperforms state-of-the-art methods using the same network architecture. Our code is publicly available at : https://github.com/gayanku/NBC-Softmax

The correct functioning of photovoltaic (PV) cells is critical to ensuring the optimal performance of a solar plant. Anomaly detection techniques for PV cells can result in significant cost savings in operation and maintenance (O&M). Recent research has focused on deep learning techniques for automatically detecting anomalies in Electroluminescence (EL) images. Automated anomaly annotations can improve current O&M methodologies and help develop decision-making systems to extend the life-cycle of the PV cells and predict failures. This paper addresses the lack of anomaly segmentation annotations in the literature by proposing a combination of state-of-the-art data-driven techniques to create a Golden Standard benchmark. The proposed method stands out for (1) its adaptability to new PV cell types, (2) cost-efficient fine-tuning, and (3) leverage public datasets to generate advanced annotations. The methodology has been validated in the annotation of a widely used dataset, obtaining a reduction of the annotation cost by 60%.

Recent developments of advanced driver-assistance systems necessitate an increasing number of tests to validate new technologies. These tests cannot be carried out on track in a reasonable amount of time and automotive groups rely on simulators to perform most tests. The reliability of these simulators for constantly refined tasks is becoming an issue and, to increase the number of tests, the industry is now developing surrogate models, that should mimic the behavior of the simulator while being much faster to run on specific tasks. In this paper we aim to construct a surrogate model to mimic and replace the simulator. We first test several classical methods such as random forests, ridge regression or convolutional neural networks. Then we build three hybrid models that use all these methods and combine them to obtain an efficient hybrid surrogate model.

Designing powerful adversarial attacks is of paramount importance for the evaluation of $\ell_p$-bounded adversarial defenses. Projected Gradient Descent (PGD) is one of the most effective and conceptually simple algorithms to generate such adversaries. The search space of PGD is dictated by the steepest ascent directions of an objective. Despite the plethora of objective function choices, there is no universally superior option and robustness overestimation may arise from ill-suited objective selection. Driven by this observation, we postulate that the combination of different objectives through a simple loss alternating scheme renders PGD more robust towards design choices. We experimentally verify this assertion on a synthetic-data example and by evaluating our proposed method across 25 different $\ell_{\infty}$-robust models and 3 datasets. The performance improvement is consistent, when compared to the single loss counterparts. In the CIFAR-10 dataset, our strongest adversarial attack outperforms all of the white-box components of AutoAttack (AA) ensemble, as well as the most powerful attacks existing on the literature, achieving state-of-the-art results in the computational budget of our study ($T=100$, no restarts).

As organizations increasingly use machine learning in real world systems to provide insights on the data generated by real users (Team, 2017), issues of user data privacy have risen to the forefront of existing problems in machine learning. Differential privacy (DP) (Dwork et al., 2006) is the de facto standard for privacy preserving statistics. Common algorithms for privately training machine learning models are differentially private stochastic gradient descent (DP-SGD) (Song et al., 2013; Abadi et al., 2016) and differentially private empirical risk minimization (DP-ERM) (Chaudhuri et al., 2011). While advancements in deep learning can be partially attributed to scaling up the number of model parameters (Kaplan et al., 2020; Brown et al., 2020), as shown by (Kurakin et al., 2022; Tramèr and Boneh, 2020; Yu et al., 2021b; Shen et al., 2021) increasing the number of model parameters in DP-SGD often has an adverse impact on the privacy-utility tradeoff due to the curse of dimensionality present in DP-SGD. Briefly, the "curse" is that the magnitude of the noise added scales with d the square root of the number of parameters, and because the signal does not scale with the number of parameters, the signal to noise ratio (SNR) suffers at scale.

We present a novel corpus for French dialect identification comprising 413,522 French text samples collected from public news websites in Belgium, Canada, France and Switzerland. To ensure an accurate estimation of the dialect identification performance of models, we designed the corpus to eliminate potential biases related to topic, writing style, and publication source. More precisely, the training, validation and test splits are collected from different news websites, while searching for different keywords (topics). This leads to a French cross-domain (FreCDo) dialect identification task. We conduct experiments with four competitive baselines, a fine-tuned CamemBERT model, an XGBoost based on fine-tuned CamemBERT features, a Support Vector Machines (SVM) classifier based on fine-tuned CamemBERT features, and an SVM based on word n-grams. Aside from presenting quantitative results, we also make an analysis of the most discriminative features learned by CamemBERT. Our corpus is available at https://github.com/MihaelaGaman/FreCDo.

The sensitivity of many physics analyses can be enhanced by constructing discriminants that preferentially select signal events. Such discriminants become much more useful if they are uncorrelated with a set of protected attributes. In this paper we show that a normalizing flow conditioned on the protected attributes can be used to find a decorrelated representation for any discriminant. As a normalizing flow is invertible the separation power of the resulting discriminant will be unchanged at any fixed value of the protected attributes. We demonstrate the efficacy of our approach by building supervised jet taggers that produce almost no sculpting in the mass distribution of the background.

Learning-based low rank approximation algorithms can significantly improve the performance of randomized low rank approximation with sketch matrix. With the learned value and fixed non-zero positions for sketch matrices from learning-based algorithms, these matrices can reduce the test error of low rank approximation significantly. However, there is still no good method to learn non-zero positions as well as overcome the out-of-distribution performance loss. In this work, we introduce two new methods Learning Sparsity and Learning Randomness which try to learn a better sparsity patterns and add randomness to the value of sketch matrix. These two methods can be applied with any learning-based algorithms which use sketch matrix directly. Our experiments show that these two methods can improve the performance of previous learning-based algorithm for both test error and out-of-distribution test error without adding too much complexity.

A methodology is proposed, which addresses the caveat that line-of-sight emission spectroscopy presents in that it cannot provide spatially resolved temperature measurements in nonhomogeneous temperature fields. The aim of this research is to explore the use of data-driven models in measuring temperature distributions in a spatially resolved manner using emission spectroscopy data. Two categories of data-driven methods are analyzed: (i) Feature engineering and classical machine learning algorithms, and (ii) end-to-end convolutional neural networks (CNN). In total, combinations of fifteen feature groups and fifteen classical machine learning models, and eleven CNN models are considered and their performances explored. The results indicate that the combination of feature engineering and machine learning provides better performance than the direct use of CNN. Notably, feature engineering which is comprised of physics-guided transformation, signal representation-based feature extraction and Principal Component Analysis is found to be the most effective. Moreover, it is shown that when using the extracted features, the ensemble-based, light blender learning model offers the best performance with RMSE, RE, RRMSE and R values of 64.3, 0.017, 0.025 and 0.994, respectively. The proposed method, based on feature engineering and the light blender model, is capable of measuring nonuniform temperature distributions from low-resolution spectra, even when the species concentration distribution in the gas mixtures is unknown.