Related papers: Distributional Shrinkage II: Higher-Order Scores E…
We study the problem of denoising when only the noise level is known, not the noise distribution. Independent noise $Z$ corrupts a signal $X$, yielding the observation $Y = X + \sigma Z$ with known $\sigma \in (0,1)$. We propose…
The first order derivative of a data density can be estimated efficiently by denoising score matching, and has become an important component in many applications, such as image generation and audio synthesis. Higher order derivatives…
We study statistical inference for the optimal transport (OT) map (also known as the Brenier map) from a known absolutely continuous reference distribution onto an unknown finitely discrete target distribution. We derive limit distributions…
We consider two independent binary i.i.d. random strings $X$ and $Y$ of equal length $n$ and the optimal alignments according to a symmetric scoring functions only. We decompose the space of scoring functions into five components. Two of…
We propose a novel algorithm that improves on the previous neural span-based CKY decoder for constituency parsing. In contrast to the traditional span-based decoding, where spans are combined only based on the sum of their scores, we…
We consider the additive version of the matrix denoising problem, where a random symmetric matrix $S$ of size $n$ has to be inferred from the observation of $Y=S+Z$, with $Z$ an independent random matrix modeling a noise. For prior…
This paper studies the convergence rates of optimal transport (OT) map estimators, a topic of growing interest in statistics, machine learning, and various scientific fields. Despite recent advancements, existing results rely on regularity…
We study the problem of estimating a function $T$ given independent samples from a distribution $P$ and from the pushforward distribution $T_\sharp P$. This setting is motivated by applications in the sciences, where $T$ represents the…
Polynomial regression is widely used and can help to express nonlinear patterns. However, considering very high polynomial orders may lead to overfitting and poor extrapolation ability for unseen data. The paper presents a method for…
In this paper, we introduce an alternative method for applying averaging theory of orders $1$ and $2$ in the plane. This is done by combining Taylor expansions of the displacement map with the integral form of the…
There are two major routes to address the ubiquitous family of inverse problems appearing in signal and image processing, such as denoising or deblurring. A first route relies on Bayesian modeling, where prior probabilities are used to…
The de Bruijn graph $G_K$ of a set of strings $S$ is a key data structure in genome assembly that represents overlaps between all the $K$-length substrings of $S$. Construction and navigation of the graph is a space and time bottleneck in…
Denoising stationary process $(X_i)_{i \in Z}$ corrupted by additive white Gaussian noise is a classic and fundamental problem in information theory and statistical signal processing. Despite considerable progress in designing efficient…
We study the problem of causal structure learning from data using optimal transport (OT). Specifically, we first provide a constraint-based method which builds upon lower-triangular monotone parametric transport maps to design conditional…
Message passing algorithms have been tailored for compressive imaging applications by plugging in different types of off-the-shelf image denoisers. These off-the-shelf denoisers mostly rely on some generic or hand-crafted priors for…
This paper is concerned with the problem of nonlinear filtering, i.e., computing the conditional distribution of the state of a stochastic dynamical system given a history of noisy partial observations. Conventional sequential importance…
Unsupervised performance estimation, or evaluating how well models perform on unlabeled data is a difficult task. Recently, a method was proposed by Garg et al. [2022] which performs much better than previous methods. Their method relies on…
The density estimation is one of the core problems in statistics. Despite this, existing techniques like maximum likelihood estimation are computationally inefficient due to the intractability of the normalizing constant. For this reason an…
One of the central objects in the theory of optimal transport is the Brenier map: the unique monotone transformation which pushes forward an absolutely continuous probability law onto any other given law. A line of recent work has analyzed…
We consider the problem of inference in higher-order undirected graphical models with binary labels. We formulate this problem as a binary polynomial optimization problem and propose several linear programming relaxations for it. We compare…