Kernel-based methods are heavily used in machine learning. However, they suffer from $O(N^2)$ complexity in the number $N$ of considered data points. In this paper, we propose an approximation procedure, which reduces this complexity to $O(N)$. Our approach is based on two ideas. First, we prove that any radial kernel with analytic basis function can be represented as sliced version of some one-dimensional kernel and derive an analytic formula for the one-dimensional counterpart. It turns out that the relation between one- and $d$-dimensional kernels is given by a generalized Riemann-Liouville fractional integral. Hence, we can reduce the $d$-dimensional kernel summation to a one-dimensional setting. Second, for solving these one-dimensional problems efficiently, we apply fast Fourier summations on non-equispaced data, a sorting algorithm or a combination of both. Due to its practical importance we pay special attention to the Gaussian kernel, where we show a dimension-independent error bound and represent its one-dimensional counterpart via a closed-form Fourier transform. We provide a run time comparison and error estimate of our fast kernel summations.

Privacy preservation has become a critical concern in high-dimensional data analysis due to the growing prevalence of data-driven applications. Proposed by Li (1991), sliced inverse regression has emerged as a widely utilized statistical technique for reducing covariate dimensionality while maintaining sufficient statistical information. In this paper, we propose optimally differentially private algorithms specifically designed to address privacy concerns in the context of sufficient dimension reduction. We proceed to establish lower bounds for differentially private sliced inverse regression in both the low and high-dimensional settings. Moreover, we develop differentially private algorithms that achieve the minimax lower bounds up to logarithmic factors. Through a combination of simulations and real data analysis, we illustrate the efficacy of these differentially private algorithms in safeguarding privacy while preserving vital information within the reduced dimension space. As a natural extension, we can readily offer analogous lower and upper bounds for differentially private sparse principal component analysis, a topic that may also be of potential interest to the statistical and machine learning community.

Dynamic graph learning has gained significant attention as it offers a powerful means to model intricate interactions among entities across various real-world and scientific domains. Notably, graphs serve as effective representations for diverse networks such as transportation, brain, social, and internet networks. Furthermore, the rapid advancements in machine learning have expanded the scope of dynamic graph applications beyond the aforementioned domains. In this paper, we present a review of lesser-explored applications of dynamic graph learning. This study revealed the potential of machine learning on dynamic graphs in addressing challenges across diverse domains, including those with limited levels of association with the field.

With the rapid growth of Vehicle Ad-hoc Network (VANET) as a promising technology for efficient and reliable communication among vehicles and infrastructure, the security and integrity of VANET communications has become a critical concern. One of the significant threats to VANET is the presence of blackhole attacks, where malicious nodes disrupt the network's functionality and compromise data confidentiality, integrity, and availability. In this paper, we propose a machine learning-based approach for blackhole detection in VANET. To achieve this task, we first create a comprehensive dataset comprising normal and malicious traffic flows. Afterward, we study and define a promising set of features to discriminate the blackhole attacks. Finally, we evaluate various machine learning algorithms, including Gradient Boosting, Random Forest, Support Vector Machines, k-Nearest Neighbors, Gaussian Naive Bayes, and Logistic Regression. Experimental results demonstrate the effectiveness of these algorithms in distinguishing between normal and malicious nodes. Our findings also highlight the potential of machine learning based approach in enhancing the security of VANET by detecting and mitigating blackhole attacks.

Federated learning (FL) is a collaborative learning paradigm allowing multiple clients to jointly train a model without sharing their training data. However, FL is susceptible to poisoning attacks, in which the adversary injects manipulated model updates into the federated model aggregation process to corrupt or destroy predictions (untargeted poisoning) or implant hidden functionalities (targeted poisoning or backdoors). Existing defenses against poisoning attacks in FL have several limitations, such as relying on specific assumptions about attack types and strategies or data distributions or not sufficiently robust against advanced injection techniques and strategies and simultaneously maintaining the utility of the aggregated model. To address the deficiencies of existing defenses, we take a generic and completely different approach to detect poisoning (targeted and untargeted) attacks. We present FreqFed, a novel aggregation mechanism that transforms the model updates (i.e., weights) into the frequency domain, where we can identify the core frequency components that inherit sufficient information about weights. This allows us to effectively filter out malicious updates during local training on the clients, regardless of attack types, strategies, and clients' data distributions. We extensively evaluate the efficiency and effectiveness of FreqFed in different application domains, including image classification, word prediction, IoT intrusion detection, and speech recognition. We demonstrate that FreqFed can mitigate poisoning attacks effectively with a negligible impact on the utility of the aggregated model.

Data-driven unit discovery in self-supervised learning (SSL) of speech has embarked on a new era of spoken language processing. Yet, the discovered units often remain in phonetic space and the units beyond phonemes are largely underexplored. Here, we demonstrate that a syllabic organization emerges in learning sentence-level representation of speech. In particular, we adopt "self-distillation" objective to fine-tune the pretrained HuBERT with an aggregator token that summarizes the entire sentence. Without any supervision, the resulting model draws definite boundaries in speech, and the representations across frames exhibit salient syllabic structures. We demonstrate that this emergent structure largely corresponds to the ground truth syllables. Furthermore, we propose a new benchmark task, Spoken Speech ABX, for evaluating sentence-level representation of speech. When compared to previous models, our model outperforms in both unsupervised syllable discovery and learning sentence-level representation. Together, we demonstrate that the self-distillation of HuBERT gives rise to syllabic organization without relying on external labels or modalities, and potentially provides novel data-driven units for spoken language modeling.

Some of the most successful knowledge graph embedding (KGE) models for link prediction -- CP, RESCAL, TuckER, ComplEx -- can be interpreted as energy-based models. Under this perspective they are not amenable for exact maximum-likelihood estimation (MLE), sampling and struggle to integrate logical constraints. This work re-interprets the score functions of these KGEs as circuits -- constrained computational graphs allowing efficient marginalisation. Then, we design two recipes to obtain efficient generative circuit models by either restricting their activations to be non-negative or squaring their outputs. Our interpretation comes with little or no loss of performance for link prediction, while the circuits framework unlocks exact learning by MLE, efficient sampling of new triples, and guarantee that logical constraints are satisfied by design. Furthermore, our models scale more gracefully than the original KGEs on graphs with millions of entities.

Characters do not convey meaning, but sequences of characters do. We propose an unsupervised distributional method to learn the abstract meaningful units in a sequence of characters. Rather than segmenting the sequence, our Dynamic Capacity Slot Attention model discovers continuous representations of the objects in the sequence, extending an architecture for object discovery in images. We train our model on different languages and evaluate the quality of the obtained representations with forward and reverse probing classifiers. These experiments show that our model succeeds in discovering units which are similar to those proposed previously in form, content and level of abstraction, and which show promise for capturing meaningful information at a higher level of abstraction.

Sparse regression and feature extraction are the cornerstones of knowledge discovery from massive data. Their goal is to discover interpretable and predictive models that provide simple relationships among scientific variables. While the statistical tools for model discovery are well established in the context of linear regression, their generalization to nonlinear regression in material modeling is highly problem-specific and insufficiently understood. Here we explore the potential of neural networks for automatic model discovery and induce sparsity by a hybrid approach that combines two strategies: regularization and physical constraints. We integrate the concept of Lp regularization for subset selection with constitutive neural networks that leverage our domain knowledge in kinematics and thermodynamics. We train our networks with both, synthetic and real data, and perform several thousand discovery runs to infer common guidelines and trends: L2 regularization or ridge regression is unsuitable for model discovery; L1 regularization or lasso promotes sparsity, but induces strong bias that may aggressively change the results; only L0 regularization allows us to transparently fine-tune the trade-off between interpretability and predictability, simplicity and accuracy, and bias and variance. With these insights, we demonstrate that Lp regularized constitutive neural networks can simultaneously discover both, interpretable models and physically meaningful parameters. We anticipate that our findings will generalize to alternative discovery techniques such as sparse and symbolic regression, and to other domains such as biology, chemistry, or medicine. Our ability to automatically discover material models from data could have tremendous applications in generative material design and open new opportunities to manipulate matter, alter properties of existing materials, and discover new materials with user-defined properties.

Predictive maintenance is a well studied collection of techniques that aims to prolong the life of a mechanical system by using artificial intelligence and machine learning to predict the optimal time to perform maintenance. The methods allow maintainers of systems and hardware to reduce financial and time costs of upkeep. As these methods are adopted for more serious and potentially life-threatening applications, the human operators need trust the predictive system. This attracts the field of Explainable AI (XAI) to introduce explainability and interpretability into the predictive system. XAI brings methods to the field of predictive maintenance that can amplify trust in the users while maintaining well-performing systems. This survey on explainable predictive maintenance (XPM) discusses and presents the current methods of XAI as applied to predictive maintenance while following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) 2020 guidelines. We categorize the different XPM methods into groups that follow the XAI literature. Additionally, we include current challenges and a discussion on future research directions in XPM.