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We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…
TimeCluster is a visual analytics technique for discovering structure in long multivariate time series by projecting overlapping windows of data into a low-dimensional space. We show that, when Principal Component Analysis (PCA) is chosen…
Models with latent factors recently attract a lot of attention. However, most investigations focus on linear regression models and thus cannot capture nonlinearity. To address this issue, we propose a novel Factor Augmented Single-Index…
We introduce a novel deep learning approach that harnesses the power of generative artificial intelligence to enhance the accuracy of contextual forecasting in sewerage systems. By developing a diffusion-based model that processes…
Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…
Dynamic statistical process monitoring methods have been widely studied and applied in modern industrial processes. These methods aim to extract the most predictable temporal information and develop the corresponding dynamic monitoring…
We present a novel class of projected methods, to perform statistical analysis on a data set of probability distributions on the real line, with the 2-Wasserstein metric. We focus in particular on Principal Component Analysis (PCA) and…
Financial scenario simulation is essential for risk management and portfolio optimization, yet it remains challenging especially in high-dimensional and small data settings common in finance. We propose a diffusion factor model that…
Deep learning has been actively applied to time series forecasting, leading to a deluge of new methods, belonging to the class of historical-value models. Yet, despite the attractive properties of time-index models, such as being able to…
We consider multi-class classification problems for high dimensional data. Following the idea of reduced-rank linear discriminant analysis (LDA), we introduce a new dimension reduction tool with a flavor of supervised principal component…
Diffusion models have been shown to be capable of generating high-quality images, suggesting that they could contain meaningful internal representations. Unfortunately, the feature maps that encode a diffusion model's internal information…
This paper proposes a variational Bayes algorithm for computationally efficient posterior and predictive inference in time-varying parameter (TVP) models. Within this context we specify a new dynamic variable/model selection strategy for…
Predicting the dependencies between observations from multiple time series is critical for applications such as anomaly detection, financial risk management, causal analysis, or demand forecasting. However, the computational and numerical…
Time series forecasting is a critical task in various domains, where accurate predictions can drive informed decision-making. Traditional forecasting methods often rely on current observations of variables to predict future outcomes,…
Diffusion models have shown promise in forecasting future data from multivariate time series. However, few existing methods account for recurring structures, or patterns, that appear within the data. We present Pattern-Guided Diffusion…
Score-based methods have recently seen increasing popularity in modeling and generation. Methods have been constructed to perform hypothesis testing and change-point detection with score functions, but these methods are in general not as…
An important task for any large-scale organization is to prepare forecasts of key performance metrics. Often these organizations are structured in a hierarchical manner and for operational reasons, projections of these metrics may have been…
The computational complexity of simultaneous inference methods in high-dimensional linear regression models quickly increases with the number variables. This paper proposes a computationally efficient method based on the Moore-Penrose…
In this article, we study large-dimensional matrix factor models and estimate the factor loading matrices and factor score matrix by minimizing square loss function. Interestingly, the resultant estimators coincide with the Projected…
We introduce a novel diffusion-based spectral algorithm to tackle regression analysis on high-dimensional data, particularly data embedded within lower-dimensional manifolds. Traditional spectral algorithms often fall short in such…