arXiv subjects

Archi Roy

Publications and source records attributed to Archi Roy.

6 recordsLinked to original sources

arXiv2026

A model of opinion dynamics evolving via a preferential attachment mechanism involving multiple extractions

We study a model of opinion dynamics / social learning / peer-review-based market economics on an evolving network, wherein i) each of the first $N$ agents adopts one of two available opinions arbitrarily, and ii) the $(n+1)$-st agent, for $n\geqslant N$, upon arrival, draws a sample of size $k_{n}$, with replacement, from the past agents, such that the $i$-th agent (for $i\leqslant n$) is included in the sample with probability proportional to the number of times they were previously sampled and agreed with. The $(n+1)$-st agent then decides which opinion to adopt i) based on the proportion of sampled agents conforming to each of the two opinions, and ii) according to a stochastic update rule that involves a memory parameter and a rather general reinforcement function. We study both i) the scenario where $k_{n}=k$ remains fixed with $n$, and ii) the scenario where $k_{n}$ grows at a suitable rate with $n$. This model can be represented as an evolving preferential attachment network wherein each vertex is endowed with one of two possible states, and all edges are directed. It can also be framed as a variant of the celebrated elephant random walk. We study the asymptotics of this stochastic process -- in particular, the almost sure convergence, and in case of fixed sample sizes, second order fluctuations, of the relative dominance of each opinion, the influence capital and overall network activity.

math.PR↗

arXiv2026

ANGLE: Angular Neural Generative Learning via Engression

Circular data, representing angles or directions, are frequently encountered in computer vision, biology, geology, and meteorology. Traditional regression targets the conditional mean, which is often geometrically misleading for circular responses under multimodal, skewed, or asymmetric data structures. To address these limitations, a lightweight deep generative framework, namely ANGLE, is introduced for non-parametric distributional regression on the circle. The full conditional distribution of an angular response, given Euclidean and circular covariates, is learned through a generative map optimized via a generalized circular energy score (GCES) loss. Desirable theoretical properties, including the strict propriety of the loss and the rotational equivariance of the estimators, are established. Furthermore, both pre- and post-additive noise models are accommodated. A unified toolbox is provided for advancing previously underexplored challenges in circular statistics: extrapolation, sufficient dimension reduction, and conditional distribution equality testing. The framework's efficacy is demonstrated through extensive simulations and real-world applications. Specifically, the proposal is utilized for object pose estimation from imagery and wind direction prediction, which are integral to surveillance, autonomous vehicles, and energy systems, respectively. Superior predictive performance and robust uncertainty quantification of the proposed method in these tasks are revealed.

stat.ML↗

arXiv2026

Elephant random walk with attributed steps and extractions of random sizes

We study a model of market economics wherein the $(n+1)$-st customer, for each $n\geqslant N$, with $N$ being a prespecified positive integer, draws a sample of (random) size $K_{n}$, either with replacement or without, from the customers of the past. Each sampled customer is queried as to which of the two products, A and B, available in the oligopolistic market, they chose, and whether they are satisfied or not with their choice. The $(n+1)$-st customer now employs a stochastic rule, based on the information collected from the sampled customers, to decide which of the two products to buy. The probability that a customer is satisfied with the product they have purchased equals $q_{1}$ when the product is A, and $q_{2}$ when it is B, independent of all else. The resulting stochastic process may be represented as a variant of the celebrated elephant random walk, with the relative performance (in terms of sale) of A with respect to B, up to and including the $n$-th sale, captured by the position $S_{n}$ of the walker at time $n$. We study the almost sure convergence of $S_{n}/n$, as well as the convergence in distribution of suitably scaled versions of $S_{n}$ (where the scaling depends on the regime we are in).

math.PR↗

arXiv2026

A nonparametric approach to understand multivariate quantile dynamics in financial time series

Over the last decade, nonparametric methods have gained increasing attention for modeling complex data structures due to their flexibility and minimal structural assumptions. In this paper, we study a general multivariate nonparametric regression framework that encompasses a broad class of parametric models commonly used in financial econometrics. Both the response and the covariate processes are allowed to be multivariate with fixed finite dimensions, and the framework accommodates temporal dependence, thereby introducing additional modeling and theoretical hurdles. To address these challenges, we adopt a functional dependence structure which permits flexible dynamic behavior while maintaining tractable asymptotic analysis. Within this setting, we establish strong and weak convergence results for the estimators of the conditional mean and volatility functions. In addition, we investigate conditional geometric quantiles in the multivariate time series context and prove their consistency under mild regularity conditions. The finite sample performance is examined through comprehensive simulation studies, and the methodology is illustrated by modeling the stock returns of Maersk and Lockheed Martin as a nonparametric function of a geopolitical risk index.

stat.ME↗

arXiv2025

Elephant random walks with multiple extractions and general reinforcement functions

We consider a generalized model of elephant random walks wherein the walker, during the $(n+1)$-st time-stamp, draws from the past (i.e. the set $\{1,2,\ldots,n\}$) a sample of $k$ time-stamps, either with replacement or without, where $k$ may either remain fixed as $n$ grows, or $k=k(n)$ may grow with $n$. Letting $\{U_{n,1}, U_{n,2}, \ldots, U_{n,k}\}$ denote the time-stamps sampled, the step taken by the walker during the $(n+1)$-st time-stamp, denoted $X_{n+1}$, is a $\pm 1$-valued random variable whose distribution depends on the proportion of $(+1)$-valued steps out of $X_{U_{n,1}},X_{U_{n,2}},\ldots,X_{U_{n,k}}$ via a reinforcement function $f$. In this paper, we investigate the asymptotic behaviour, i.e. strong and weak convergence, of this random walk model under suitable assumptions made on the function $f$ (as well as on the sequence $\{k(n)\}$ when the sample size varies with $n$).

math.PR↗

arXiv2024

Nonparametric method of structural break detection in stochastic time series regression model

We propose a novel nonparametric test to detect structural breaks in the conditional mean and/or variance of a time series. Our method does not assume any specific parametric form for the dependence structure of the regressor, the time series model, or the distribution of the noise. This flexibility allows our algorithm to be applicable to a wide range of framework. We further apply the proposed test to accurately localize the changepoints and establish theoretical guarantees showing that the estimated structural breaks are consistent, meaning they lie sufficiently close to the true breakpoints when a sufficiently large sample is available. The effectiveness of the proposed algorithm is demonstrated through an extensive simulation study encompassing a diverse range of time series structures, including light, moderately heavy, and heavy tailed distributions. We also show a real-life example, where an application to Bitcoin prices and Google search volume illustrates how the procedure can identify changes in the conditional relationship between market attention and price dynamics.

stat.ME↗