Related papers: Adaptivity in convolution models with partially kn…
In a parametric framework, the paper is devoted to the study of a new estimation procedure for the inverse filter and the level noise in a complex noisy blind discrete deconvolution model. Our estimation method is a consequence of the sharp…
Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…
In this work, we investigate the numerical approximation of the second order non-autonomous semilnear parabolic partial differential equation (PDE) using the finite element method. To the best of our knowledge, only the linear case is…
We study the open-set label shift problem, where the test data may include a novel class absent from training. This setting is challenging because both the class proportions and the distribution of the novel class are not identifiable…
We study the problem of parameter estimation for a univariate discretely observed ergodic diffusion process given as a solution to a stochastic differential equation. The estimation procedure we propose consists of two steps. In the first…
We propose an estimator of a concave cumulative distribution function under the measurement error model, where the non-negative variables of interest are perturbed by additive independent random noise. The estimator is defined as the least…
The estimation of a density profile from experimental data points is a challenging problem, usually tackled by plotting a histogram. Prior assumptions on the nature of the density, from its smoothness to the specification of its form, allow…
A popular approach for modeling and inference in spatial statistics is to represent Gaussian random fields as solutions to stochastic partial differential equations (SPDEs) of the form $L^{\beta}u = \mathcal{W}$, where $\mathcal{W}$ is…
Random smoothing data augmentation is a unique form of regularization that can prevent overfitting by introducing noise to the input data, encouraging the model to learn more generalized features. Despite its success in various…
We investigate the quality of space approximation of a class of stochastic integral equations of convolution type with Gaussian noise. Such equations arise, for example, when considering mild solutions of stochastic fractional order partial…
In this paper, we present an abstract framework to obtain convergence rates for the approximation of random evolution equations corresponding to a random family of forms determined by finite-dimensional noise. The full discretization error…
Despite the large progress in supervised learning with neural networks, there are significant challenges in obtaining high-quality, large-scale and accurately labelled datasets. In such a context, how to learn in the presence of noisy…
Let $X_1,...,X_n$ be i.i.d. observations, where $X_i=Y_i+\sigma Z_i$ and $Y_i$ and $Z_i$ are independent. Assume that unobservable $Y$'s are distributed as a random variable $UV,$ where $U$ and $V$ are independent, $U$ has a Bernoulli…
A popular class of problem in statistics deals with estimating the support of a density from $n$ observations drawn at random from a $d$-dimensional distribution. The one-dimensional case reduces to estimating the end points of a univariate…
We study the long-time behavior of fully discretized semilinear SPDEs with additive space-time white noise, which admit a unique invariant probability measure $\mu$. We show that the average of regular enough test functions with respect to…
Stable distributions provide a flexible framework for modeling heavy-tailed and skewed data, with the stability index $\alpha$ quantifying tail heaviness. We propose a new semiparametric estimator for $\alpha$ that leverages the two-sum…
The noise sensitivity of a Boolean function $f: \{0,1\}^n \rightarrow \{0,1\}$ is one of its fundamental properties. A function of a positive noise parameter $\delta$, it is denoted as $NS_{\delta}[f]$. Here we study the algorithmic problem…
Nearly all identifiability results in unsupervised representation learning inspired by, e.g., independent component analysis, factor analysis, and causal representation learning, rely on assumptions of additive independent noise or…
In this paper, we study the problem of sampling from distributions of the form p(x) \propto e^{-\beta f(x)} for some function f whose values and gradients we can query. This mode of access to f is natural in the scenarios in which such…
We introduce a conditional pseudo-reversible normalizing flow for constructing surrogate models of a physical model polluted by additive noise to efficiently quantify forward and inverse uncertainty propagation. Existing surrogate modeling…