Related papers: Parameter Estimation of Long Memory Stochastic Pro…

This paper investigates the continuous-time limit of score-driven models with long memory. By extending score-driven models to incorporate infinite-lag structures with coefficients exhibiting heavy-tailed decay, we establish their weak…

In this paper, we investigate a semiparametric regression model under the context of treatment effects via a localized neural network (LNN) approach. Due to a vast number of parameters involved, we reduce the number of effective parameters…

Consider observing a collection of discrete events within a network that reflect how network nodes influence one another. Such data are common in spike trains recorded from biological neural networks, interactions within a social network,…

Although stochastic approximation learning methods have been widely used in the machine learning literature for over 50 years, formal theoretical analyses of specific machine learning algorithms are less common because stochastic…

We present data-dependent learning bounds for the general scenario of non-stationary non-mixing stochastic processes. Our learning guarantees are expressed in terms of a data-dependent measure of sequential complexity and a discrepancy…

We introduce Pairwise Distance-Diffusion Analysis (PDDA), a geometric framework for estimating the Hurst exponent from distance plots of long-memory stochastic processes. A single construction yields two complementary routes: R/S-PDDA, a…

Time series prediction with deep learning methods, especially long short-term memory neural networks (LSTMs), have scored significant achievements in recent years. Despite the fact that the LSTMs can help to capture long-term dependencies,…

Deep Neural Networks (DNNs) rely on inherent fluctuations in their internal parameters (weights and biases) to effectively navigate the complex optimization landscape and achieve robust performance. While these fluctuations are recognized…

In this study, we develop a new theory of estimating Hurst parame- ter using conic multivariate adaptive regression splines (CMARS) method. We concentrate on the strong solution of stochastic differentional equations (SDEs) driven by…

Fueled by their remarkable ability to tackle diverse tasks across multiple domains, large language models (LLMs) have grown at an unprecedented rate, with some recent models containing trillions of parameters. This growth is accompanied by…

We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…

Spatio-temporal data are ubiquitous in the agricultural, ecological, and environmental sciences, and their study is important for understanding and predicting a wide variety of processes. One of the difficulties with modeling spatial…

We investigate the problem of joint statistical estimation of several parameters for a stochastic differential equation driven by an additive fractional Brownian motion. Based on discrete-time observations of the model, we construct an…

Recent advances in statistical inference have significantly expanded the toolbox of probabilistic modeling. Historically, probabilistic modeling has been constrained to (i) very restricted model classes where exact or approximate…

Recurrent neural networks (RNNs) have many advantages over more traditional system identification techniques. They may be applied to linear and nonlinear systems, and they require fewer modeling assumptions. However, these neural network…

When fine-tuning Deep Neural Networks (DNNs) to new data, DNNs are prone to overwriting network parameters required for task-specific functionality on previously learned tasks, resulting in a loss of performance on those tasks. We propose…

Long range dependence or long memory is a feature of many processes in the natural world, which provides important insights on the underlying mechanisms that generate the observed data. The usual tools available to characterize the…

This paper reviews recent developments of robust estimation in linear time series models, with short and long memory correlation structures, in the presence of additive outliers. Based on the manuscripts Fajardo et al. (2009) and…

In this article, we present a novel inference framework for estimating the parameters of Continuous-State Branching Processes (CSBPs). We do so by leveraging their subordinator representation. Our method reformulates the estimation problem…

Hyper-parameters (HPs) are an important part of machine learning (ML) model development and can greatly influence performance. This paper studies their behavior for three algorithms: Extreme Gradient Boosting (XGB), Random Forest (RF), and…