Related papers: On the Automatic Parameter Selection for Permutati…

To quantify the complexity of a system, entropy-based methods have received considerable critical attentions in real-world data analysis. Among numerous entropy algorithms, amplitude-based formulas, represented by Sample Entropy, suffer…

Quantifying the complexity and irregularity of time series data is a primary pursuit across various data-scientific disciplines. Sample entropy (SampEn) is a widely adopted metric for this purpose, but its reliability is sensitive to the…

Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…

Weighted ensemble (WE) is an enhanced path-sampling method that is conceptually simple, widely applicable, and statistically exact. In a WE simulation, an ensemble of trajectories is periodically pruned or replicated to enhance sampling of…

Extracting relevant properties of empirical signals generated by nonlinear, stochastic, and high-dimensional systems is a challenge of complex systems research. Open questions are how to differentiate chaotic signals from stochastic ones,…

Recent scientific advances require complex experiment design, necessitating the meticulous tuning of many experiment parameters. Tree-structured Parzen estimator (TPE) is a widely used Bayesian optimization method in recent parameter tuning…

Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…

The minimum error entropy (MEE) criterion has been successfully used in fields such as parameter estimation, system identification and the supervised machine learning. There is in general no explicit expression for the optimal MEE estimate…

We consider a class of systems with time-varying parameters, which are written as linear regressions with bounded disturbances. The task is to estimate such parameters under the condition that the regressor is finitely exciting (FE).…

Parameter-efficient fine-tuning (PEFT) has become a popular way to adapt large pre-trained models to new tasks. Most PEFT methods update only a small subset of parameters while freezing the rest, avoiding redundant computation. As they…

Spectral methods employing non-standard polynomial bases, such as M\"untz polynomials, have proven effective for accurately solving problems with solutions exhibiting low regularity, notably including sub-diffusion equations. However, due…

Embedding techniques have become essential components of large databases in the deep learning era. By encoding discrete entities, such as words, items, or graph nodes, into continuous vector spaces, embeddings facilitate more efficient…

Byte-Pair Encoding (BPE) has become a widely adopted subword tokenization method in modern language models due to its simplicity and strong empirical performance across downstream tasks. However, applying BPE to unsegmented languages such…

We introduce Parameterized Exploration (PE), a simple family of methods for model-based tuning of the exploration schedule in sequential decision problems. Unlike common heuristics for exploration, our method accounts for the time horizon…

Fine-tuning all parameters of Large Language Models (LLMs) is computationally expensive. Parameter-Efficient Fine-Tuning (PEFT) methods address this by selectively fine-tuning specific parameters. Most of the parameter efficient fine-tuning…

Permutation entropy quantifies the diversity of possible orderings of the values a random or deterministic system can take, as Shannon entropy quantifies the diversity of values. We show that the metric and permutation entropy…

This work aims at making a comprehensive contribution in the general area of parametric inference for discretely observed diffusion processes. Established approaches for likelihood-based estimation invoke a time-discretisation scheme for…

Differential equations are pivotal in modeling and understanding the dynamics of various systems, offering insights into their future states through parameter estimation fitted to time series data. In fields such as economy, politics, and…

Fourier extensions have been shown to be an effective means for the approximation of smooth, nonperiodic functions on bounded intervals given their values on an equispaced, or in general, scattered grid. Related to this method are two…

Ensembling is now recognized as an effective approach for increasing the predictive performance and calibration of deep networks. We introduce a new approach, Parameter Ensembling by Perturbation (PEP), that constructs an ensemble of…