Related papers: Nonlinear Granger Causality using Kernel Ridge Reg…
This paper introduces a kernel discrepancy-based framework for rerandomization to enhance the precision of causal inference in controlled experiments. We demonstrate that the kernel discrepancy is the key part of the variance upper bound…
Identifying directed interactions between species from time series of their population densities has many uses in ecology. This key statistical task is equivalent to causal time series inference, which connects to the Granger causality (GC)…
This study presents an efficient incremental/decremental approach for big streams based on Kernel Ridge Regression (KRR), a frequently used data analysis in cloud centers. To avoid reanalyzing the whole dataset whenever sensors receive new…
Distributional robustness is a central goal of prediction algorithms due to the prevalent distribution shifts in real-world data. The prediction model aims to minimize the worst-case risk among a class of distributions, a.k.a., an…
Exploratory analysis of time series data can yield a better understanding of complex dynamical systems. Granger causality is a practical framework for analysing interactions in sequential data, applied in a wide range of domains. In this…
Understanding causal relationships in time series is fundamental to many domains, including neuroscience, economics, and behavioral science. Granger causality is one of the well-known techniques for inferring causality in time series.…
Multivariate time series anomaly detection has numerous real-world applications and is being extensively studied. Modeling pairwise correlations between variables is crucial. Existing methods employ learnable graph structures and graph…
This paper carries out a large dimensional analysis of a variation of kernel ridge regression that we call \emph{centered kernel ridge regression} (CKRR), also known in the literature as kernel ridge regression with offset. This modified…
A fundamental goal in network neuroscience is to understand how activity in one region drives activity elsewhere, a process referred to as effective connectivity. Here we propose to model this causal interaction using integro-differential…
The cellwise robust M regression estimator is introduced as the first estimator of its kind that intrinsically yields both a map of cellwise outliers consistent with the linear model, and a vector of regression coefficients that is robust…
We here focus on the task of learning Granger causality matrices for multivariate point processes. In order to accomplish this task, our work is the first to explore the use of Wold processes. By doing so, we are able to develop…
This paper addresses the issues of insufficient coverage, unstable results, and limited reliability in retrieval-augmented generation under complex knowledge environments, and proposes a confidence control method that integrates…
We propose a specialized string kernel for small bio-molecules, peptides and pseudo-sequences of binding interfaces. The kernel incorporates physico-chemical properties of amino acids and elegantly generalize eight kernels, such as the…
Multi-electrode neurophysiological recordings produce massive quantities of data. Multivariate time series analysis provides the basic framework for analyzing the patterns of neural interactions in these data. It has long been recognized…
As a novel similarity measure that is defined as the expectation of a kernel function between two random variables, correntropy has been successfully applied in robust machine learning and signal processing to combat large outliers. The…
Large language models (LLMs) have revolutionized natural language processing (NLP), particularly through Retrieval-Augmented Generation (RAG), which enhances LLM capabilities by integrating external knowledge. However, traditional RAG…
Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…
Reinforcement learning utilizing kernel ridge regression to predict the expected value function represents a powerful method with great representational capacity. This setting is a highly versatile framework amenable to analytical results.…
While correlation measures are used to discern statistical relationships between observed variables in almost all branches of data-driven scientific inquiry, what we are really interested in is the existence of causal dependence. Designing…
We present a new framework for learning Granger causality networks for multivariate categorical time series, based on the mixture transition distribution (MTD) model. Traditionally, MTD is plagued by a nonconvex objective,…