In high-dimensional data analysis, such as financial index tracking or biomedical applications, it is crucial to select the few relevant variables while maintaining control over the false discovery rate (FDR). In these applications, strong dependencies often exist among the variables (e.g., stock returns), which can undermine the FDR control property of existing methods like the model-X knockoff method or the T-Rex selector. To address this issue, we have expanded the T-Rex framework to accommodate overlapping groups of highly correlated variables. This is achieved by integrating a nearest neighbors penalization mechanism into the framework, which provably controls the FDR at the user-defined target level. A real-world example of sparse index tracking demonstrates the proposed method's ability to accurately track the S&P 500 index over the past 20 years based on a small number of stocks. An open-source implementation is provided within the R package TRexSelector on CRAN.

Support vector regression (SVR) has garnered significant popularity over the past two decades owing to its wide range of applications across various fields. Despite its versatility, SVR encounters challenges when confronted with outliers and noise, primarily due to the use of the $\varepsilon$-insensitive loss function. To address this limitation, SVR with bounded loss functions has emerged as an appealing alternative, offering enhanced generalization performance and robustness. Notably, recent developments focus on designing bounded loss functions with smooth characteristics, facilitating the adoption of gradient-based optimization algorithms. However, it's crucial to highlight that these bounded and smooth loss functions do not possess an insensitive zone. In this paper, we address the aforementioned constraints by introducing a novel symmetric loss function named the HawkEye loss function. It is worth noting that the HawkEye loss function stands out as the first loss function in SVR literature to be bounded, smooth, and simultaneously possess an insensitive zone. Leveraging this breakthrough, we integrate the HawkEye loss function into the least squares framework of SVR and yield a new fast and robust model termed HE-LSSVR. The optimization problem inherent to HE-LSSVR is addressed by harnessing the adaptive moment estimation (Adam) algorithm, known for its adaptive learning rate and efficacy in handling large-scale problems. To our knowledge, this is the first time Adam has been employed to solve an SVR problem. To empirically validate the proposed HE-LSSVR model, we evaluate it on UCI, synthetic, and time series datasets. The experimental outcomes unequivocally reveal the superiority of the HE-LSSVR model both in terms of its remarkable generalization performance and its efficiency in training time.

We We introduce ensembles within score-based sampling build on these ideas and introduce ensemble strategies that methods to develop gradient-free approximate leverage the collective dynamics of a particle ensemble to sampling techniques that leverage the collective approximately compute the score function within a reverse dynamics of particle ensembles to compute diffusion process. Compared to the aforementioned Föllmer approximate reverse diffusion drifts. We sampler, a goal is to reduce evaluations of the probability introduce the underlying methodology, emphasizing distribution that one wants to sample from. In the setting its relationship with generative diffusion of Bayesian inverse problems, this helps to reduce forward models and the previously introduced Föllmer model evaluations, thereby offering an efficient sampling sampler. We demonstrate the efficacy of ensemble technique. More concretely, we introduce an importance strategies through various examples, ranging sampling Monte Carlo estimator for the score function of a from low-to medium-dimensionality sampling forward diffusion process in order to sample from a probability problems, including multi-modal and highly non-distribution using the associated reverse diffusion Gaussian probability distributions, and provide process. Because there is some flexibility in the choice of comparisons to traditional methods like NUTS.

This study presents a Bayesian maximum \textit{a~posteriori} (MAP) framework for dynamical system identification from time-series data. This is shown to be equivalent to a generalized zeroth-order Tikhonov regularization, providing a rational justification for the choice of the residual and regularization terms, respectively, from the negative logarithms of the likelihood and prior distributions. In addition to the estimation of model coefficients, the Bayesian interpretation gives access to the full apparatus for Bayesian inference, including the ranking of models, the quantification of model uncertainties and the estimation of unknown (nuisance) hyperparameters. Two Bayesian algorithms, joint maximum \textit{a~posteriori} (JMAP) and variational Bayesian approximation (VBA), are compared to the popular SINDy algorithm for thresholded least-squares regression, by application to several dynamical systems with added noise. For multivariate Gaussian likelihood and prior distributions, the Bayesian formulation gives Gaussian posterior and evidence distributions, in which the numerator terms can be expressed in terms of the Mahalanobis distance or ``Gaussian norm'' $||\vy-\hat{\vy}||^2_{M^{-1}} = (\vy-\hat{\vy})^\top {M^{-1}} (\vy-\hat{\vy})$, where $\vy$ is a vector variable, $\hat{\vy}$ is its estimator and $M$ is the covariance matrix. The posterior Gaussian norm is shown to provide a robust metric for quantitative model selection.

Nonnegative Matrix Factorization (NMF) is an important unsupervised learning method to extract meaningful features from data. To address the NMF problem within a polynomial time framework, researchers have introduced a separability assumption, which has recently evolved into the concept of coseparability. This advancement offers a more efficient core representation for the original data. However, in the real world, the data is more natural to be represented as a multi-dimensional array, such as images or videos. The NMF's application to high-dimensional data involves vectorization, which risks losing essential multi-dimensional correlations. To retain these inherent correlations in the data, we turn to tensors (multidimensional arrays) and leverage the tensor t-product. This approach extends the coseparable NMF to the tensor setting, creating what we term coseparable Nonnegative Tensor Factorization (NTF). In this work, we provide an alternating index selection method to select the coseparable core. Furthermore, we validate the t-CUR sampling theory and integrate it with the tensor Discrete Empirical Interpolation Method (t-DEIM) to introduce an alternative, randomized index selection process. These methods have been tested on both synthetic and facial analysis datasets. The results demonstrate the efficiency of coseparable NTF when compared to coseparable NMF.

In the dynamic landscape of machine learning, where datasets vary widely in size and complexity, selecting the most effective model poses a significant challenge. Rather than fixating on a single model, our research propels the field forward with a novel emphasis on dynamic model switching. This paradigm shift allows us to harness the inherent strengths of different models based on the evolving size of the dataset. Consider the scenario where CatBoost demonstrates exceptional efficacy in handling smaller datasets, providing nuanced insights and accurate predictions. However, as datasets grow in size and intricacy, XGBoost, with its scalability and robustness, becomes the preferred choice. Our approach introduces an adaptive ensemble that intuitively transitions between CatBoost and XGBoost. This seamless switching is not arbitrary; instead, it's guided by a user-defined accuracy threshold, ensuring a meticulous balance between model sophistication and data requirements. The user sets a benchmark, say 80% accuracy, prompting the system to dynamically shift to the new model only if it guarantees improved performance. This dynamic model-switching mechanism aligns with the evolving nature of data in real-world scenarios. It offers practitioners a flexible and efficient solution, catering to diverse dataset sizes and optimising predictive accuracy at every juncture. Our research, therefore, stands at the forefront of innovation, redefining how machine learning models adapt and excel in the face of varying dataset dynamics.

We consider the task of learning individual-specific intensities of counting processes from a set of static variables and irregularly sampled time series. We introduce a novel modelization approach in which the intensity is the solution to a controlled differential equation. We first design a neural estimator by building on neural controlled differential equations. In a second time, we show that our model can be linearized in the signature space under sufficient regularity conditions, yielding a signature-based estimator which we call CoxSig. We provide theoretical learning guarantees for both estimators, before showcasing the performance of our models on a vast array of simulated and real-world datasets from finance, predictive maintenance and food supply chain management.

Nearest-neighbor methods have become popular in statistics and play a key role in statistical learning. Important decisions in nearest-neighbor methods concern the variables to use (when many potential candidates exist) and how to measure the dissimilarity between units. The first decision depends on the scope of the application while second depends mainly on the type of variables. Unfortunately, relatively few options permit to handle mixed-type variables, a situation frequently encountered in practical applications. The most popular dissimilarity for mixed-type variables is derived as the complement to one of the Gower's similarity coefficient. It is appealing because ranges between 0 and 1, being an average of the scaled dissimilarities calculated variable by variable, handles missing values and allows for a user-defined weighting scheme when averaging dissimilarities. The discussion on the weighting schemes is sometimes misleading since it often ignores that the unweighted "standard" setting hides an unbalanced contribution of the single variables to the overall dissimilarity. We address this drawback following the recent idea of introducing a weighting scheme that minimizes the differences in the correlation between each contributing dissimilarity and the resulting weighted Gower's dissimilarity. In particular, this note proposes different approaches for measuring the correlation depending on the type of variables. The performances of the proposed approaches are evaluated in simulation studies related to classification and imputation of missing values.

Algorithms that ensure reproducible findings from large-scale, high-dimensional data are pivotal in numerous signal processing applications. In recent years, multivariate false discovery rate (FDR) controlling methods have emerged, providing guarantees even in high-dimensional settings where the number of variables surpasses the number of samples. However, these methods often fail to reliably control the FDR in the presence of highly dependent variable groups, a common characteristic in fields such as genomics and finance. To tackle this critical issue, we introduce a novel framework that accounts for general dependency structures. Our proposed dependency-aware T-Rex selector integrates hierarchical graphical models within the T-Rex framework to effectively harness the dependency structure among variables. Leveraging martingale theory, we prove that our variable penalization mechanism ensures FDR control. We further generalize the FDR-controlling framework by stating and proving a clear condition necessary for designing both graphical and non-graphical models that capture dependencies. Additionally, we formulate a fully integrated optimal calibration algorithm that concurrently determines the parameters of the graphical model and the T-Rex framework, such that the FDR is controlled while maximizing the number of selected variables. Numerical experiments and a breast cancer survival analysis use-case demonstrate that the proposed method is the only one among the state-of-the-art benchmark methods that controls the FDR and reliably detects genes that have been previously identified to be related to breast cancer. An open-source implementation is available within the R package TRexSelector on CRAN.

Understanding various humour styles is essential for comprehending the multifaceted nature of humour and its impact on fields such as psychology and artificial intelligence. This understanding has revealed that humour, depending on the style employed, can either have therapeutic or detrimental effects on an individual's health and relationships. Although studies dedicated exclusively to computational-based humour style analysis remain somewhat rare, an expansive body of research thrives within related task, particularly binary humour and sarcasm recognition. In this systematic literature review (SLR), we survey the landscape of computational techniques applied to these related tasks and also uncover their fundamental relevance to humour style analysis. Through this study, we unveil common approaches, illuminate various datasets and evaluation metrics, and effectively navigate the complex terrain of humour research. Our efforts determine potential research gaps and outlined promising directions. Furthermore, the SLR identifies a range of features and computational models that can seamlessly transition from related tasks like binary humour and sarcasm detection to invigorate humour style classification. These features encompass incongruity, sentiment and polarity analysis, ambiguity detection, acoustic nuances, visual cues, contextual insights, and more. The computational models that emerge contain traditional machine learning paradigms, neural network architectures, transformer-based models, and specialised models attuned to the nuances of humour. Finally, the SLR provides access to existing datasets related to humour and sarcasm, facilitating the work of future researchers.