Related papers: Memory properties of transformations of linear pro…
Time series often exhibit non-ergodic behaviour that complicates forecasting and inference. This article proposes a likelihood-based approach for estimating ergodicity transformations that addresses such challenges. The method is broadly…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Dynamic linear regression models forecast the values of a time series based on a linear combination of a set of exogenous time series while incorporating a time series process for the error term. This error process is often assumed to…
We construct a two-sample test for comparison of long memory parameters based on ratios of two rescaled variance (V/S) statistics studied in [Giraitis L., Leipus, R., Philippe, A., 2006. A test for stationarity versus trends and unit roots…
We present a Gaussian process machine learning model to predict the transformation temperature and lattice parameters of ZrO$_2$-based ceramics. Our overall goal is to search for a shape memory ceramic with a reversible transformation and…
Gaussian Processes (GPs) are widely recognized as powerful non-parametric models for regression and classification. Traditional GP frameworks predominantly operate under the assumption that the inputs are either accurately known or subject…
We discuss a class of conditionally heteroscedastic time series models satisfying the equation $r_t= \zeta_t \sigma_t$, where $\zeta_t$ are standardized i.i.d. r.v.'s and the conditional standard deviation $\sigma_t$ is a nonlinear function…
Model selection in Gaussian processes scales prohibitively with the size of the training dataset, both in time and memory. While many approximations exist, all incur inevitable approximation error. Recent work accounts for this error in the…
Identification of a linear time-invariant dynamical system from partial observations is a fundamental problem in control theory. Particularly challenging are systems exhibiting long-term memory. A natural question is how learn such systems…
Memory is the fundamental form of temporal complexity: when present but uncontrollable, it manifests as non-Markovian noise; conversely, if controllable, memory can be a powerful resource for information processing. Memory effects arise…
Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…
Morse projections are well-known in chemistry and allow one, within a Morse potential approximation, to redefine the potential in a simple quadratic form. The latter, being a non-linear transform, is also very helpful for machine learning…
We study the long-term memory in diverse stock market indices and foreign exchange rates using the Detrended Fluctuation Analysis(DFA). For all daily and high-frequency market data studied, no significant long-term memory property is…
A large class of linear memory differential equations in one dimension, where the evolution depends on the whole history, can be equivalently described as a projection of a Markov process living in a higher dimensional space. Starting with…
We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a…
The Transformer architecture has revolutionized deep learning on sequential data, becoming ubiquitous in state-of-the-art solutions for a wide variety of applications. Yet vanilla Transformers are notoriously resource-expensive, requiring…
We introduce a two-parameter deformation of the classical Bosonic, Fermionic, and Boltzmann Fock spaces that is a refinement of the $q$-Fock space of [BS91]. Starting with a real, separable Hilbert space $H$, we construct the $(q,t)$-Fock…
Any repeated use of a fixed experimental instrument is subject to memory effects. We design an estimation method uncovering the details of the underlying interaction between the system and the internal memory without having any experimental…
The correlation length-scale next to the noise variance are the most used hyperparameters for the Gaussian processes. Typically, stationary covariance functions are used, which are only dependent on the distances between input points and…