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Anomaly detection (AD) has garnered ample attention in security research, as such algorithms complement existing signature-based methods but promise detection of never-before-seen attacks. Cyber operations manage a high volume of…

In this paper we study nonlinear $q$-voter model with stochastic driving on a complete graph. We investigate two types of stochasticity that, using the language of social sciences, can be interpreted as different kinds of nonconformity.…

Change point analysis has applications in a wide variety of fields. The general problem concerns the inference of a change in distribution for a set of time-ordered observations. Sequential detection is an online version in which new data…

The waiting time needed for a stock market index to undergo a given percentage change in its value is found to have an up-down asymmetry, which, surprisingly, is not observed for the individual stocks composing that index. To explain this,…

Mixture models provide a flexible representation of heterogeneity in a finite number of latent classes. From the Bayesian point of view, Markov Chain Monte Carlo methods provide a way to draw inferences from these models. In particular,…

In this paper we propose a new approach for sequential monitoring of a parameter of a $d$-dimensional time series, which can be estimated by approximately linear functionals of the empirical distribution function. We consider a…

We develop a new tool, the time inhomogeneous Poisson equation in the whole space and with a terminal condition at infinity, to study the asymptotic behavior of the non-autonomous multi-scale stochastic system with irregular coefficients,…

Competition between alternative states is an essential process in social and biological networks. Neutral competition can be represented by an unbiased random drift process in which the states of vertices (e.g., opinions, genotypes, or…

In this article we propose a novel MCMC method based on deterministic transformations T: X x D --> X where X is the state-space and D is some set which may or may not be a subset of X. We refer to our new methodology as Transformation-based…

We consider the problems of parameter estimation for several models of threshold ergodic diffusion processes in the asymptotics of large samples. These models are the direct continuous time analogues of the well-known in time series…

We study a simple model of how social behaviors, like trends and opinions, propagate in networks where individuals adopt the trend when they are informed by threshold $T$ neighbors who are adopters. Using a dynamic message-passing…

The hidden Markov model (HMM) provides a powerful framework for inference in time-varying environments, where the underlying state evolves according to a Markov chain. To address the optimal filtering problem in general dynamic settings, we…

We study Markov population processes on large graphs, with the local state transition rates of a single vertex being linear function of its neighborhood. A simple way to approximate such processes is by a system of ODEs called the…

In such different domains as neurosciences, spin glasses, social science, economics and finance, large ensemble of interacting individuals following (mainstream) or opposing (hipsters) to the majority are ubiquitous. In these systems,…

We study consensus processes on the complete graph of $n$ nodes. Initially, each node supports one from up to n opinions. Nodes randomly and in parallel sample the opinions of constant many nodes. Based on these samples, they use an update…

Benchmarking anomaly detection approaches for multivariate time series is a challenging task due to a lack of high-quality datasets. Current publicly available datasets are too small, not diverse and feature trivial anomalies, which hinders…

A broad set of empirical phenomenon in the study of social, economic and machine behaviour can be modelled as complex systems with averaging dynamics. However many of these models naturally result in consensus or consensus-like outcomes. In…

Mean-field, ensemble-chain, and adaptive samplers have historically been viewed as distinct approaches to Monte Carlo sampling. In this paper, we present a unifying {two-system} framework that brings all three under one roof. In our…

Under the environment of big data streams, it is a common situation where the variable set of a model may change according to the condition of data streams. In this paper, we propose a homogenization strategy to represent the heterogenous…

Data-driven methods that detect anomalies in times series data are ubiquitous in practice, but they are in general unable to provide helpful explanations for the predictions they make. In this work we propose a model-agnostic algorithm that…