Related papers: Random sampling of long-memory stationary processe
We consider Stochastic Volatility processes with heavy tails and possible long memory in volatility. We study the limiting conditional distribution of future events given that some present or past event was extreme (i.e. above a level which…
Catastrophic forgetting - the tendency of neural networks to forget previously learned data when learning new information - remains a central challenge in continual learning. In this work, we adopt a behavioral approach, observing a…
Driven by applications in telecommunication networks, we explore the simulation task of estimating rare event probabilities for tandem queues in their steady state. Existing literature has recognized that importance sampling methods can be…
Memorization impacts the performance of deep learning algorithms. Prior works have studied memorization primarily in the context of generalization and privacy. This work studies the memorization effect on incremental learning scenarios.…
Density Ratio Estimation has attracted attention from the machine learning community due to its ability to compare the underlying distributions of two datasets. However, in some applications, we want to compare distributions of random…
Reservoir computing is a machine learning paradigm that uses a structure called a reservoir, which has nonlinearities and short-term memory. In recent years, reservoir computing has expanded to new functions such as the autonomous…
We find the asymptotic distribution of the sample autocovariances of long-memory processes in cases of finite and infinite fourth moment. Depending on the interplay of assumptions on moments and the intensity of dependence, there are three…
Rank-deficient stationary stochastic vector processes are present in many problems in network theory and dynamic factor analysis. In this paper we study hidden dynamical relations between the components of a discrete-time stochastic vector…
We propose a simple model for sample space reducing (SSR) stochastic process, where the dynamical variable denoting the size of the state space is continuous. In general, one can view the model as a multiplicative stochastic process, with a…
Continual learning is the process of training machine learning models on a sequence of tasks where data distributions change over time. A well-known obstacle in this setting is catastrophic forgetting, a phenomenon in which a model…
It recently has been found that methods of the statistical theories of spectra can be a useful tool in the analysis of spectra far from levels of Hamiltonian systems. Several examples originate from areas, such as quantitative linguistics…
This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…
One of the features of many-body quantum systems with Hilbert-space fragmentation is the existence of stationary states manifesting quantum jamming. It was recently shown that these are "states with memory", in which, e.g., measuring a…
Dynamical sampling deals with signals that evolve in time under the action of a linear operator. The purpose of the present paper is to analyze the performance of the basic dynamical sampling algorithms in the finite dimensional case and…
Continual Learning (CL) is the research field addressing learning without forgetting when the data distribution is not static. This paper studies spurious features' influence on continual learning algorithms. We show that continual learning…
We introduce and simulate a two dimensional probabilistic model of granular matter at vanishing pressure. The model exhibits a perfectly sharp random loose packing density, a phenomenon that should be verifiable for real granular matter.
Persistent neural activity associated with working memory (WM) lasts for a limited time duration. Current theories suggest that its termination is \textit{actively} obtained via inhibitory currents, and there is currently no theory…
We investigate a nonlinear dynamical system which ``remembers'' preselected values of a system parameter. The deterministic version of the system can encode many parameter values during a transient period, but in the limit of long times,…
Traditional studies of memory for meaningful narratives focus on specific stories and their semantic structures but do not address common quantitative features of recall across different narratives. We introduce a statistical ensemble of…
In random sequential adsorption (RSA), objects are deposited randomly, irreversibly, and sequentially; attempts leading to an overlap with previously deposited objects are discarded. The process continues until the system reaches a jammed…