Related papers: On truncated variation, upward truncated variation…
With the increasing interest in applying the methodology of difference-of-convex (dc) optimization to diverse problems in engineering and statistics, this paper establishes the dc property of many well-known functions not previously known…
We investigate some previously unexplored (or underexplored) computational aspects of total variation (TV) distance. First, we give a simple deterministic polynomial-time algorithm for checking equivalence between mixtures of product…
While disentangled representations have shown promise in generative modeling and representation learning, their downstream usefulness remains debated. Recent studies re-defined disentanglement through a formal connection to symmetries,…
Several implications of well-known fluctuation theorems, on the statistical properties of the entropy production, are studied using various approaches. We begin by deriving a tight lower bound on the variance of the entropy production for a…
This paper studies the winding of a continuously differentiable Gaussian stationary process $f:\mathbb{R}\to\mathbb{C}$ in the interval $[0,T]$. We give formulae for the mean and the variance of this random variable. The variance is shown…
We study the convergence rate of randomly truncated stochastic algorithms, which consist in the truncation of the standard Robbins-Monro procedure on an increasing sequence of compact sets. Such a truncation is often required in practice to…
We study the convergence rate of randomly truncated stochastic algorithms, which consist in the truncation of the standard Robbins-Monro procedure on an increasing sequence of compact sets. Such a truncation is often required in practice to…
We consider estimating the shared mean of a sequence of heavy-tailed random variables taking values in a Banach space. In particular, we revisit and extend a simple truncation-based mean estimator first proposed by Catoni and Giulini. While…
In the setting of a metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we show that the total variation of functions of bounded variation is lower semicontinuous with respect to $L^1$-convergence in…
In the analysis of Markov chains and processes, it is sometimes convenient to replace an unbounded state space with a "truncated" bounded state space. When such a replacement is made, one often wants to know whether the equilibrium behavior…
Temporal difference learning with linear function approximation is a popular method to obtain a low-dimensional approximation of the value function of a policy in a Markov Decision Process. We give a new interpretation of this method in…
This paper is devoted to a systematic study and characterizations of the fundamental notions of variational and strong variational convexity for lower semicontinuous functions. While these notions have been quite recently introduced by…
This work considers the use of Total variation (TV) minimization in the recovery of a given gradient sparse vector from Gaussian linear measurements. It has been shown in recent studies that there exist a sharp phase transition behavior in…
Consistency models have recently been introduced to accelerate sampling from diffusion models by directly predicting the solution (i.e., data) of the probability flow ODE (PF ODE) from initial noise. However, the training of consistency…
Total variation regularization and total variation flows (TVF) have been widely applied for image enhancement and denoising. To include a generic preservation of crossing curvilinear structures in TVF we lift images to the homogeneous space…
This paper is devoted to the study of travelling fronts of reaction-diffusion equations with periodic advection in the whole plane $\mathbb R^2$. We are interested in curved fronts satisfying some "conical" conditions at infinity. We prove…
We discuss a one-dimensional model of a fluctuating interface with a dynamic exponent $z=1$. The events that occur are adsorption, which is local, and desorption which is non-local and may take place over regions of the order of the system…
Truncated Levy flights are stochastic processes which display a crossover from a heavy-tailed Levy behavior to a faster decaying probability distribution function (pdf). Putting less weight on long flights overcomes the divergence of the…
This article considers exponential families of truncated multivariate normal distributions with one-sided truncation for some or all coordinates. We observe that if all components are one-sided truncated then this family is not full. The…
For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution.…