We develop fast and scalable algorithms based on block-coordinate descent to solve the group lasso and the group elastic net for generalized linear models along a regularization path. Special attention is given when the loss is the usual least squares loss (Gaussian loss). We show that each block-coordinate update can be solved efficiently using Newton's method and further improved using an adaptive bisection method, solving these updates with a quadratic convergence rate. Our benchmarks show that our package adelie performs 3 to 10 times faster than the next fastest package on a wide array of both simulated and real datasets. Moreover, we demonstrate that our package is a competitive lasso solver as well, matching the performance of the popular lasso package glmnet.

The authors in [1] detailed this approach, providing a their adaptive activation functions for enhanced predictive comprehensive methodology foundational for subsequent statistical modeling. Inspired by the Kolmogorov-Arnold representation forecasting methods. Extensions of ARIMA, like Seasonal theorem, KANs replace traditional linear weights with ARIMA (SARIMA), adapt the model to handle seasonality spline-parametrized univariate functions, allowing them to in data series, particularly useful in fields like retail and learn activation patterns dynamically. We demonstrate that climatology [2]. Exponential Smoothing techniques constitute KANs outperforms conventional Multi-Layer Perceptrons another popular set of traditional (non-ML-based) forecasting (MLPs) in a real-world satellite traffic forecasting task, providing methods. They are characterized by their simplicity more accurate results with considerably fewer number and effectiveness in handling data with trends and seasonality. of learnable parameters. We also provide an ablation study of An exponent of this family of techniques is the so-called Holt-KAN-specific parameters impact on performance. The proposed Winters seasonal technique, which adjusts the model parameters approach opens new avenues for adaptive forecasting in response to changes in trend and seasonality within the models, emphasizing the potential of KANs as a powerful time series data [3, 4]. These models have been widely used tool in predictive analytics.

This is a lecture note produced for DS-GA 3001.003 "Special Topics in DS - Causal Inference in Machine Learning" at the Center for Data Science, New York University in Spring, 2024. This course was created to target master's and PhD level students with basic background in machine learning but who were not exposed to causal inference or causal reasoning in general previously. In particular, this course focuses on introducing such students to expand their view and knowledge of machine learning to incorporate causal reasoning, as this aspect is at the core of so-called out-of-distribution generalization (or lack thereof.)

Randomized smoothing has shown promising certified robustness against adversaries in classification tasks. Despite such success with only zeroth-order access to base models, randomized smoothing has not been extended to a general form of regression. By defining robustness in regression tasks flexibly through probabilities, we demonstrate how to establish upper bounds on input data point perturbation (using the $\ell_2$ norm) for a user-specified probability of observing valid outputs. Furthermore, we showcase the asymptotic property of a basic averaging function in scenarios where the regression model operates without any constraint. We then derive a certified upper bound of the input perturbations when dealing with a family of regression models where the outputs are bounded. Our simulations verify the validity of the theoretical results and reveal the advantages and limitations of simple smoothing functions, i.e., averaging, in regression tasks. The code is publicly available at \url{https://github.com/arekavandi/Certified_Robust_Regression}.

Multivariate time series forecasting tasks are usually conducted in a channel-dependent (CD) way since it can incorporate more variable-relevant information. However, it may also involve a lot of irrelevant variables, and this even leads to worse performance than the channel-independent (CI) strategy. This paper combines the strengths of both strategies and proposes the Deep Graph Clustering Transformer (DGCformer) for multivariate time series forecasting. Specifically, it first groups these relevant variables by a graph convolutional network integrated with an autoencoder, and a former-latter masked self-attention mechanism is then considered with the CD strategy being applied to each group of variables while the CI one for different groups. Extensive experimental results on eight datasets demonstrate the superiority of our method against state-of-the-art models, and our code will be publicly available upon acceptance.

Many Machine Learning (ML) models are referred to as black box models, providing no real insights into why a prediction is made. Feature importance and explainability are important for increasing transparency and trust in ML models, particularly in settings such as healthcare and finance. With quantum computing's unique capabilities, such as leveraging quantum mechanical phenomena like superposition, which can be combined with ML techniques to create the field of Quantum Machine Learning (QML), and such techniques may be applied to QML models. This article explores feature importance and explainability insights in QML compared to Classical ML models. Utilizing the widely recognized Iris dataset, classical ML algorithms such as SVM and Random Forests, are compared against hybrid quantum counterparts, implemented via IBM's Qiskit platform: the Variational Quantum Classifier (VQC) and Quantum Support Vector Classifier (QSVC). This article aims to provide a comparison of the insights generated in ML by employing permutation and leave one out feature importance methods, alongside ALE (Accumulated Local Effects) and SHAP (SHapley Additive exPlanations) explainers.

Stochastic Gradient (SG) Markov Chain Monte Carlo algorithms (MCMC) are popular algorithms for Bayesian sampling in the presence of large datasets. However, they come with little theoretical guarantees and assessing their empirical performances is non-trivial. In such context, it is crucial to develop algorithms that are robust to the choice of hyperparameters and to gradients heterogeneity since, in practice, both the choice of step-size and behaviour of target gradients induce hard-to-control biases in the invariant distribution. In this work we introduce the stochastic gradient Barker dynamics (SGBD) algorithm, extending the recently developed Barker MCMC scheme, a robust alternative to Langevin-based sampling algorithms, to the stochastic gradient framework. We characterize the impact of stochastic gradients on the Barker transition mechanism and develop a bias-corrected version that, under suitable assumptions, eliminates the error due to the gradient noise in the proposal. We illustrate the performance on a number of high-dimensional examples, showing that SGBD is more robust to hyperparameter tuning and to irregular behavior of the target gradients compared to the popular stochastic gradient Langevin dynamics algorithm.

There exist endless examples of dynamical systems with vast available data and unsatisfying mathematical descriptions. Sparse regression applied to symbolic libraries has quickly emerged as a powerful tool for learning governing equations directly from data; these learned equations balance quantitative accuracy with qualitative simplicity and human interpretability. Here, I present a general purpose, model agnostic sparse regression algorithm that extends a recently proposed exhaustive search leveraging iterative Singular Value Decompositions (SVD). This accelerated scheme, Scalable Pruning for Rapid Identification of Null vecTors (SPRINT), uses bisection with analytic bounds to quickly identify optimal rank-1 modifications to null vectors. It is intended to maintain sensitivity to small coefficients and be of reasonable computational cost for large symbolic libraries. A calculation that would take the age of the universe with an exhaustive search but can be achieved in a day with SPRINT.

Kalman filtering and smoothing are the foundational mechanisms for efficient inference in Gauss-Markov models. However, their time and memory complexities scale prohibitively with the size of the state space. This is particularly problematic in spatiotemporal regression problems, where the state dimension scales with the number of spatial observations. Existing approximate frameworks leverage low-rank approximations of the covariance matrix. Since they do not model the error introduced by the computational approximation, their predictive uncertainty estimates can be overly optimistic. In this work, we propose a probabilistic numerical method for inference in high-dimensional Gauss-Markov models which mitigates these scaling issues. Our matrix-free iterative algorithm leverages GPU acceleration and crucially enables a tunable trade-off between computational cost and predictive uncertainty. Finally, we demonstrate the scalability of our method on a large-scale climate dataset.

Laser powder bed fusion (LPBF) has shown promise for wide range of applications due to its ability to fabricate freeform geometries and generate a controlled microstructure. However, components generated by LPBF still possess sub-optimal mechanical properties due to the defects that are created during laser-material interactions. In this work, we investigate mechanism of spatter formation, using a high-fidelity modelling tool that was built to simulate the multi-physics phenomena in LPBF. The modelling tool have the capability to capture the 3D resolution of the meltpool and the spatter behavior. To understand spatter behavior and formation, we reveal its properties at ejection and evaluate its variation from the meltpool, the source where it is formed. The dataset of the spatter and the meltpool collected consist of 50 % spatter and 50 % melt pool samples, with features that include position components, velocity components, velocity magnitude, temperature, density and pressure. The relationship between the spatter and the meltpool were evaluated via correlation analysis and machine learning (ML) algorithms for classification tasks. Upon screening different ML algorithms on the dataset, a high accuracy was observed for all the ML models, with ExtraTrees having the highest at 96 % and KNN having the lowest at 94 %.