Related papers: CFTM: Continuous time fractional topic model
In this paper, we develop the continuous time dynamic topic model (cDTM). The cDTM is a dynamic topic model that uses Brownian motion to model the latent topics through a sequential collection of documents, where a "topic" is a pattern of…
Fractional Brownian motion (fBm) is a centered self-similar Gaussian process with stationary increments, which depends on a parameter $H \in (0, 1)$ called the Hurst index. The use of time-changed processes in modeling often requires the…
We present Fractional Diffusion Bridge Models (FDBM), a novel generative diffusion bridge framework driven by an approximation of the rich and non-Markovian fractional Brownian motion (fBM). Real stochastic processes exhibit a degree of…
Fractional Brownian motion (fBm) is a canonical model for long-memory phenomena. In the presence of large amounts of potentially memory-bearing data, the data are often averaged, which can change the structure of the underlying…
Fractional Brownian motion (fBm) has been used as a theoretical framework to study real time series appearing in diverse scientific fields. Because its intrinsic non-stationarity and long range dependence, its characterization via the Hurst…
We introduce the first continuous-time score-based generative model that leverages fractional diffusion processes for its underlying dynamics. Although diffusion models have excelled at capturing data distributions, they still suffer from…
This article introduces a novel construction of the two-dimensional fractional Brownian motion (2D fBm) with dependent components. Unlike similar models discussed in the literature, our approach uniquely accommodates the full range of model…
There is a lack of quantitative measures to evaluate the progression of topics through time in dynamic topic models (DTMs). Filling this gap, we propose a novel evaluation measure for DTMs that analyzes the changes in the quality of each…
The linear fractional stable motion (LFSM) extends the fractional Brownian motion (fBm) by considering $\alpha$-stable increments. We propose a method to forecast future increments of the LFSM from past discrete-time observations, using the…
In this paper we introduce a new approach to topic modelling that scales to large datasets by using a compact representation of the data and by leveraging the GPU architecture. In this approach, topics are learned directly from the…
Monitoring online customer reviews is important for business organisations to measure customer satisfaction and better manage their reputations. In this paper, we propose a novel dynamic Brand-Topic Model (dBTM) which is able to…
We propose here a testing methodology based on the autocovariance, detrended moving average, and time-averaged mean-squared displacement statistics for tempered fractional Brownian motions (TFBMs) which are related to the notions of…
In continual learning, our aim is to learn a new task without forgetting what was learned previously. In topic models, this translates to learning new topic models without forgetting previously learned topics. Previous work either…
Millions of online discussions are generated everyday on social media platforms. Topic modelling is an efficient way of better understanding large text datasets at scale. Conventional topic models have had limited success in online…
Despite the success of fractional Brownian motion (fBm) in modeling systems that exhibit anomalous diffusion due to temporal correlations, recent experimental and theoretical studies highlight the necessity for a more comprehensive approach…
We present algorithms for topic modeling based on the geometry of cross-document word-frequency patterns. This perspective gains significance under the so called separability condition. This is a condition on existence of novel-words that…
Time series forecasting models are becoming increasingly prevalent due to their critical role in decision-making across various domains. However, most existing approaches represent the coupled temporal patterns, often neglecting the…
A multivariate fractional Brownian motion (mfBm) with component-wise Hurst exponents is used to model and forecast realized volatility. We investigate the interplay between correlation coefficients and Hurst exponents and propose a novel…
Dynamic topic modeling facilitates the identification of topical trends over time in temporal collections of unstructured documents. We introduce a novel unsupervised neural dynamic topic model named as Recurrent Neural Network-Replicated…
The fractional Brownian motion (fBm) extends the standard Brownian motion by introducing some dependence between non-overlapping increments. Consequently, if one considers for example that log-prices follow an fBm, one can exploit the…