While knowntobesample efficient, these methods havefailed tofully leverage recent advances indeep learning, forcing the use of less efficient but more scalable model-free methods which try to learn the values directly.

While knowntobesample efficient, these methods havefailed tofully leverage recent advances indeep learning, forcing the use of less efficient but more scalable model-free methods which try to learn the values directly.

Channel equalization is fundamental for mitigating distortions such as frequency-selective fading and inter-symbol interference. Unlike standard supervised learning approaches that require costly retraining or fine-tuning for each new task, in-context learning (ICL) adapts to new channels at inference time with only a few examples. However, existing ICL-based equalizers are primarily developed for and evaluated on static channels within the context window. Indeed, to our knowledge, prior principled analyses and theoretical studies of ICL focus exclusively on the stationary setting, where the function remains fixed within the context. In this paper, we investigate the ability of ICL to address non-stationary problems through the lens of time-varying channel equalization. We employ a principled framework for designing efficient attention mechanisms with improved adaptivity in non-stationary tasks, leveraging algorithms from adaptive signal processing to guide better designs. For example, new attention variants can be derived from the Least Mean Square (LMS) adaptive algorithm, a Least Root Mean Square (LRMS) formulation for enhanced robustness, or multi-step gradient updates for improved long-term tracking. Experimental results demonstrate that ICL holds strong promise for non-stationary MIMO equalization, and that attention mechanisms inspired by classical adaptive algorithms can substantially enhance adaptability and performance in dynamic environments. Our findings may provide critical insights for developing next-generation wireless foundation models with stronger adaptability and robustness.

We prove that, for a linear parametrization, gradient descent converges to global optima despite non-linearity and non-convexity introduced by the implicit representation.

ANOVA (Analysis of Variance) is a process to compare the means of more than two groups. It can also be used for comparing the means of two groups. Comparing the means between two groups only can be done using a hypothesis testing method such as a t-test. This article will focus on comparing the means of more than two groups using the Analysis of Variance (ANOVA) method. This method breaks down the overall variability of a given continuous outcome into pieces. One way ANOVA is applicable where groups are defined based on the value of one factor.

Regression is unarguably one of the most used models in data science and statistics. It is prevalent in almost every field in industry and academia. I will go through in this blog the statistical concepts involved in Simple Linear Regression i.e. regression involving only one predictor variable. The readers are assumed to have some basic knowledge of probability theory and statistics, although I have given references to the concepts. Now, we need to estimate the parameters (Beta_0, Beta_1) of model and also the value of sigma squared, which is the variance of error term.

A wild bootstrap method for nonparametric hypothesis tests based on kernel distribution embeddings is proposed. This bootstrap method is used to construct provably consistent tests that apply to random processes, for which the naive permutation-based bootstrap fails. It applies to a large group of kernel tests based on V -statistics, which are degenerate under the null hypothesis, and non-degenerate elsewhere. To illustrate this approach, we construct a two-sample test, an instantaneous independence test and a multiple lag independence test for time series. In experiments, the wild bootstrap gives strong performance on synthetic examples, on audio data, and in performance benchmarking for the Gibbs sampler.

Kernel adaptive filters (KAF) are a class of powerful nonlinear filters developed in Reproducing Kernel Hilbert Space (RKHS). The Gaussian kernel is usually the default kernel in KAF algorithms, but selecting the proper kernel size (bandwidth) is still an open important issue especially for learning with small sample sizes. In previous research, the kernel size was set manually or estimated in advance by Silvermans rule based on the sample distribution. This study aims to develop an online technique for optimizing the kernel size of the kernel least mean square (KLMS) algorithm. A sequential optimization strategy is proposed, and a new algorithm is developed, in which the filter weights and the kernel size are both sequentially updated by stochastic gradient algorithms that minimize the mean square error (MSE). Theoretical results on convergence are also presented. The excellent performance of the new algorithm is confirmed by simulations on static function estimation and short term chaotic time series prediction. Keywords: Kernel methods, kernel adaptive filtering, kernel least mean square, kernel selection.