Related papers: Affine forward variance models
In this work, we propose the Generative Latent Flow (GLF), an algorithm for generative modeling of the data distribution. GLF uses an Auto-encoder (AE) to learn latent representations of the data, and a normalizing flow to map the…
We show the existence of a broad class of affine Markov processes in the cone of positive self-adjoint Hilbert-Schmidt operators. Such processes are well-suited as infinite dimensional stochastic volatility models. The class of processes we…
In the past, normalizing generative flows have emerged as a promising class of generative models for natural images. This type of model has many modeling advantages: the ability to efficiently compute log-likelihood of the input data, fast…
Diffusion models recently developed for generative AI tasks can produce high-quality samples while still maintaining diversity among samples to promote mode coverage, providing a promising path for learning stochastic closure models.…
Diffusion models have recently attained significant interest within the community owing to their strong performance as generative models. Furthermore, its application to inverse problems have demonstrated state-of-the-art performance.…
Diffusion models are proficient at generating high-quality images. They are however effective only when operating at the resolution used during training. Inference at a scaled resolution leads to repetitive patterns and structural…
The analytical tractability of affine (short rate) models, such as the Vasicek and the Cox-Ingersoll-Ross models, has made them a popular choice for modelling the dynamics of interest rates. However, in order to account properly for the…
Motivated by recent results of Tao-Ziegler [Discrete Anal. 2016] and Greenfeld-Tao (2022 preprint) on concatenating affine-linear functions along subgroups of an abelian group, we show three results on recovering affine-linearity of…
It is well-known that affine Hecke algebras are very useful to describe the smooth representations of any connected reductive p-adic group G, in terms of the supercuspidal representations of its Levi subgroups. The goal of this paper is to…
Diffusion and flow-based models are ubiquitously used for generative modelling and density estimation. They admit a deterministic probability flow ordinary differential equation (PF-ODE), analogous to continuous normalizing flows (CNFs),…
We propose Functional Flow Matching (FFM), a function-space generative model that generalizes the recently-introduced Flow Matching model to operate in infinite-dimensional spaces. Our approach works by first defining a path of probability…
We propose a family of multivariate Gaussian process models for correlated outputs, based on assuming that the likelihood function takes the generic form of the multivariate exponential family distribution (EFD). We denote this model as a…
Stochastic processes generated by non-stationary distributions are difficult to represent with conventional models such as Gaussian processes. This work presents Recurrent Autoregressive Flows as a method toward general stochastic process…
We present adversarial flow models, a class of generative models that belongs to both the adversarial and flow families. Our method supports native one-step and multi-step generation and is trained with an adversarial objective. Unlike…
Normalizing flows are a class of probabilistic generative models which allow for both fast density computation and efficient sampling and are effective at modelling complex distributions like images. A drawback among current methods is…
Wall-bounded turbulent flows are chaotic and multiscale, rendering real-time prediction at high Reynolds numbers computationally prohibitive in applications such as wind farms. Classical data assimilation methods are based on repeated…
As an effective data preprocessing step, feature selection has shown its effectiveness to prepare high-dimensional data for many machine learning tasks. The proliferation of high di-mension and huge volume big data, however, has brought…
This Ph.D. thesis explores approximations and regularity for the Heston stochastic volatility model through three interconnected works. The first work focuses on developing high-order weak approximations for the Cox-Ingersoll-Ross (CIR)…
Affine point processes are a class of simple point processes with self- and mutually-exciting properties, and they have found useful applications in several areas. In this paper, we obtain large-time asymptotic expansions in large…
We revisit affine diffusion processes on general and on the canonical state space in particular. A detailed study of theoretic and applied aspects of this class of Markov processes is given. In particular, we derive admissibility conditions…