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Two existing approaches to functional principal components analysis (FPCA) are due to Rice and Silverman (1991) and Silverman (1996), both based on maximizing variance but introducing penalization in different ways. In this article we…

The growing need for uncertainty analysis of complex computational models has led to an expanding use of meta-models across engineering and sciences. The efficiency of meta-modeling techniques relies on their ability to provide…

Recent advances in large language models have demonstrated the effectiveness of length scaling during post-training, yet its potential in pre-training remains underexplored. We present the Parallel Hidden Decoding Transformer…

We present a simple dynamic batching approach applicable to a large class of dynamic architectures that consistently yields speedups of over 10x. We provide performance bounds when the architecture is not known a priori and a stronger bound…

Incremental versions of batch algorithms are often desired, for increased time efficiency in the streaming data setting, or increased memory efficiency in general. In this paper we present a novel algorithm for incremental kernel PCA, based…

As a typical model-based evolutionary algorithm (EA), estimation of distribution algorithm (EDA) possesses unique characteristics and has been widely applied to global optimization. However, the common-used Gaussian EDA (GEDA) usually…

This paper introduces a novel Bayesian approach for variable selection in high-dimensional and potentially sparse regression settings. Our method replaces the indicator variables in the traditional spike and slab prior with continuous,…

Classical Principal Component Analysis (PCA) approximates data in terms of projections on a small number of orthogonal vectors. There are simple procedures to efficiently compute various functions of the data from the PCA approximation. The…

Retrieval augmented language models have recently become the standard for knowledge intensive tasks. Rather than relying purely on latent semantics within the parameters of large neural models, these methods enlist a semi-parametric memory…

A popular robust alternative of the classic principal component analysis (PCA) is the $\ell_1$-norm PCA (L1-PCA), which aims to find a subspace that captures the most variation in a dataset as measured by the $\ell_1$-norm. L1-PCA has shown…

Variational quantum algorithms (VQAs) are leading strategies to reach practical utilities of near-term quantum devices. However, the no-cloning theorem in quantum mechanics precludes standard backpropagation, leading to prohibitive quantum…

This paper describes some applications of an incremental implementation of the principal component analysis (PCA). The algorithm updates the transformation coefficients matrix on-line for each new sample, without the need to keep all the…

In multivariate time series classification, although current sequence analysis models have excellent classification capabilities, they show significant shortcomings when dealing with long sequence multivariate data, such as prolonged…

Given a large graph, how can we determine similarity between nodes in a fast and accurate way? Random walk with restart (RWR) is a popular measure for this purpose and has been exploited in numerous data mining applications including…

We propose a single-loop variance-reduced acceleration framework, which relates checkpoint update probabilities to momentum parameters, for solving the composite general convex problem where the smooth part has the finite-sum structure.…

We introduce Predictive Batch Scheduling (PBS), a novel training optimization technique that accelerates language model convergence by dynamically prioritizing high-loss samples during batch construction. Unlike curriculum learning…

To analyze the worst-case running time of branching algorithms, the majority of work in exponential time algorithms focuses on designing complicated branching rules over developing better analysis methods for simple algorithms. In the…

Variant Stochastic cracking is a significantly more resilient approach to adaptive indexing. It showed [1]that Stochastic cracking uses each query as a hint on how to reorganize data, but not blindly so; it gains resilience and avoids…

Methods for supervised principal component analysis (SPCA) aim to incorporate label information into principal component analysis (PCA), so that the extracted features are more useful for a prediction task of interest. Prior work on SPCA…

Software engineers often have to estimate the performance of a software system before having full knowledge of the system parameters, such as workload and operational profile. These uncertain parameters inevitably affect the accuracy of…