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We revisit the classical, full-fledged Bayesian model averaging (BMA) paradigm to ensemble pre-trained and/or lightly-finetuned foundation models to enhance the classification performance on image and text data. To make BMA tractable under…

The problem of aggregation is considerable importance in many disciplines. In this paper, a new type of operator called visibility graph averaging (VGA) aggregation operator is proposed. This proposed operator is based on the visibility…

The recently-introduced class of ordinary differential equation networks (ODE-Nets) establishes a fruitful connection between deep learning and dynamical systems. In this work, we reconsider formulations of the weights as…

We study the convergence of these operators in a weighted space of functions on a positive semi-axis and estimate the approximation by using a new type of weighted modulus of continuity and error estimation.

We present the new Orthogonal Polynomials Approximation Algorithm (OPAA), a parallelizable algorithm that estimates probability distributions using functional analytic approach: first, it finds a smooth functional estimate of the…

Supervised operator learning is an emerging machine learning paradigm with applications to modeling the evolution of spatio-temporal dynamical systems and approximating general black-box relationships between functional data. We propose a…

Model Weight Averaging (MWA) is a technique that seeks to enhance model's performance by averaging the weights of multiple trained models. This paper first empirically finds that 1) the vanilla MWA can benefit the class-imbalanced learning,…

Many real-world applications require aligning two temporal sequences, including bioinformatics, handwriting recognition, activity recognition, and human-robot coordination. Dynamic Time Warping (DTW) is a popular alignment method, but can…

In linear models it is common to have situations where several regression coefficients are zero. In these situations a common tool to perform regression is a variable selection operator. One of the most common such operators is the LASSO…

Weighted average derivative effects (WADEs) are nonparametric estimands with uses in economics and causal inference. Debiased WADE estimators typically require learning the conditional mean outcome as well as a Riesz representer (RR) that…

Weight-ensembles are formed when the parameters of multiple neural networks are directly averaged into a single model. They have demonstrated generalization capability in-distribution (ID) and out-of-distribution (OOD) which is not…

Averaging neural network weights sampled by a backbone stochastic gradient descent (SGD) is a simple yet effective approach to assist the backbone SGD in finding better optima, in terms of generalization. From a statistical perspective,…

We give the cumulative distribution functions, the expected values, and the moments of weighted lattice polynomials when regarded as real functions of independent random variables. Since weighted lattice polynomial functions include…

Whale Optimization Algorithm (WOA) is a nature-inspired meta-heuristic optimization algorithm, which was proposed by Mirjalili and Lewis in 2016. This algorithm has shown its ability to solve many problems. Comprehensive surveys have been…

We investigate the continuity of the \omega-functions and real functions defined by weighted finite automata (WFA). We concentrate on the case of average preserving WFA. We show that every continuous \omega-function definable by some WFA…

The ordered weighted $\ell_1$ norm (OWL) was recently proposed, with two different motivations: its good statistical properties as a sparsity promoting regularizer; the fact that it generalizes the so-called {\it octagonal shrinkage and…

The performance of deep neural networks is enhanced by ensemble methods, which average the output of several models. However, this comes at an increased cost at inference. Weight averaging methods aim at balancing the generalization of…

These are the lecture notes for a course taught at Tsinghua University in the spring of 2022. In these notes, we develop the basic theory of vertex operator algebras (VOAs) and their conformal blocks using complex-analytic methods. In…

Many data-driven algorithms in dynamical systems rely on ergodic averages that converge painfully slowly. One simple idea changes this: taper the ends. Weighted Birkhoff averages can converge much faster (sometimes superpolynomially, even…

Robot manipulation learning from human demonstrations offers a rapid means to acquire skills but often lacks generalization across diverse scenes and object placements. This limitation hinders real-world applications, particularly in…