Related papers: Signature inversion for monotone paths

Consider a graph with a set of vertices and oriented edges connecting pairs of vertices. Each vertex is associated with a random variable and these are assumed to be independent. In this setting, suppose we wish to solve the following…

We study how to sample paths of a random walk up to the first time it crosses a fixed barrier, in the setting where the step sizes are iid with negative mean and have a regularly varying right tail. We introduce a desirable property for a…

Deep neural networks often produce miscalibrated probability estimates, leading to overconfident predictions. A common approach for calibration is fitting a post-hoc calibration map on unseen validation data that transforms predicted…

Quantifying the contributions, or weights, of comparisons or single studies to the estimates in a network meta-analysis (NMA) is an active area of research. We extend this to the contributions of paths to NMA estimates. We present a general…

In this paper, we introduce the branched signature model, motivated by the branched rough path framework of [Gubinelli, Journal of Differential Equations, 248(4), 2010], which generalizes the classical geometric rough path. We establish a…

We present a one-way shooting algorithm for transition path sampling that accepts every proposed trajectory, yet samples the correct transition path ensemble for systems with overdamped stochastic dynamics. The method is based on two key…

Transform coding is routinely used for lossy compression of discrete sources with memory. The input signal is divided into N-dimensional vectors, which are transformed by means of a linear mapping. Then, transform coefficients are quantized…

We introduce a novel signature approach for pricing and hedging path-dependent options with instantaneous and permanent market impact under a mean-quadratic variation criterion. Leveraging the expressive power of signatures, we recast an…

We consider a sparse Erd\H{o}s--R\'{e}nyi graph $\mathcal{G}(n,\lambda/n)$ where each edge is independently assigned a random signed weight. For two uniformly chosen vertices, we study the joint distribution of the total weights and…

Modern methods for sampling rugged landscapes in state space mainly rely on knowledge of the relative probabilities of microstates, which is given by the Boltzmann factor for equilibrium systems. In principle, trajectory reweighting…

In this article, I provide significant mathematical evidence in support of the existence of short-time approximations of any polynomial order for the computation of density matrices of physical systems described by arbitrarily smooth and…

Mutational signatures describe the pattern of mutations over the different mutation types. Each mutation type is determined by a base substitution and the flanking nucleotides to the left and right of that base substitution. Due to the…

Traditional Neural machine translation (NMT) involves a fixed training procedure where each sentence is sampled once during each epoch. In reality, some sentences are well-learned during the initial few epochs; however, using this approach,…

The Mapper algorithm does not include a check for whether the cover produced conforms to the requirements of the nerve lemma. To perform a check for obstructions to the nerve lemma, statistical considerations of multiple testing quickly…

Consider a queueing system fed by traffic from $N$ independent and identically distributed marked point processes. We establish several novel sample path large deviations results in the scaled uniform topology for such a system with a small…

We revisit strong approximation theory from a new perspective, culminating in a proof of the Koml\'os-Major-Tusn\'ady embedding theorem for the simple random walk. The proof is almost entirely based on a series of soft arguments and easy…

Let $X$ be a L\'evy process with regularly varying L\'evy measure $\nu$. We obtain sample-path large deviations for scaled processes $\bar X_n(t) \triangleq X(nt)/n$ and obtain a similar result for random walks. Our results yield detailed…

We introduce a proper notion of 2-dimensional signature for images. This object is inspired by the so-called rough paths theory, and it captures many essential features of a 2-dimensional object such as an image. It thus serves as a…

We consider the problem of reconstructing an undirected graph $G$ on $n$ vertices given multiple random noisy subgraphs or "traces". Specifically, a trace is generated by sampling each vertex with probability $p_v$, then taking the…

We consider a walker that at each step keeps the same direction with a probabilitythat depends on the time already spent in the direction the walker is currently moving. In this paper, we study some asymptotic properties of this persistent…