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Principal component analysis (PCA) is a popular dimension reduction technique for vector data. Factored PCA (FPCA) is a probabilistic extension of PCA for matrix data, which can substantially reduce the number of parameters in PCA while…

We introduce Adaptive Functional Principal Component Analysis, a novel method to capture directions of variation in functional data that exhibit sharp changes in smoothness. We first propose a new adaptive scatterplot smoothing technique…

Conformal prediction is widely adopted in uncertainty quantification, due to its post-hoc, distribution-free, and model-agnostic properties. In the realm of modern deep learning, researchers have proposed Feature Conformal Prediction (FCP),…

We propose a clustered local projection (clustered LP) method to estimate impulse response functions in a class of time-varying models where parameter variation is linked to a low-dimensional matrix of observables. We show that the…

We propose a novel algorithm - Multifractal Cross-Correlation Analysis (MFCCA) - that constitutes a consistent extension of the Detrended Cross-Correlation Analysis (DCCA) and is able to properly identify and quantify subtle characteristics…

Sparse Principal Component Analysis (PCA) is a prevalent tool across a plethora of subfields of applied statistics. While several results have characterized the recovery error of the principal eigenvectors, these are typically in spectral…

This paper presents static and dynamic versions of univariate, multivariate, and multilevel functional time-series methods to forecast implied volatility surfaces in foreign exchange markets. We find that dynamic functional principal…

In this paper, we address the dichotomy between heterogeneous models and simultaneous training in Federated Learning (FL) via a clustering framework. We define a new clustering model for FL based on the (optimal) local models of the users:…

An improved mixture of probabilistic principal component analysis (PPCA) has been introduced for nonlinear data-driven process monitoring in this paper. To realize this purpose, the technique of a mixture of probabilistic principal…

The rapid growth of AI applications is dramatically increasing data center energy demand, exacerbating carbon emissions, and necessitating a shift towards 24/7 carbon-free energy (CFE). Unlike traditional annual energy matching, 24/7 CFE…

This paper introduces the Fractal-Chaotic Oscillation Co-driven (FCOC) framework, a novel paradigm for financial volatility forecasting that systematically resolves the dual challenges of feature fidelity and model responsiveness. FCOC…

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…

Functional principal component analysis (FPCA) could become invalid when data involve non-Gaussian features. Therefore, we aim to develop a general FPCA method to adapt to such non-Gaussian cases. A Kenall's $\tau$ function, which possesses…

Quantile regression is useful for characterizing the conditional distribution of a response variable and understanding heterogeneity in the covariate effects at different quantiles. The rise of high-dimensional physiological data in…

This paper studies the numerical computation of integrals, representing estimates or predictions, over the output $f(x)$ of a computational model with respect to a distribution $p(\mathrm{d}x)$ over uncertain inputs $x$ to the model. For…

LoRA has emerged as one of the most promising fine-tuning techniques, especially for federated learning (FL), since it significantly reduces communication and computation costs at resource-constrained clients. However, data heterogeneity…

This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of…

In this paper we extend the known methodology for fitting stable distributions to the multivariate case and apply the suggested method to the modelling of daily cryptocurrency-return data. The investigated time period is cut into 10…

Advances in neural computation have predominantly relied on the gradient backpropagation algorithm (BP). However, the recent shift towards non-stationary data modeling has highlighted the limitations of this heuristic, exposing that its…

The emerging cryptocurrency market has lately received great attention for asset allocation due to its decentralization uniqueness. However, its volatility and brand new trading mode have made it challenging to devising an acceptable…