相关论文: Sample Complexity of Data-Driven Stochastic LQR wi…

This paper considers the problem of estimating the cumulative distribution function and probability density function of a random variable using data quantized by uniform and non-uniform quantizers. A simple estimator is proposed based on…

We consider the problem of estimating high-dimensional covariance matrices of $K$-populations or classes in the setting where the sample sizes are comparable to the data dimension. We propose estimating each class covariance matrix as a…

This paper studies the linear quadratic regulator (LQR) problem over an unknown Bernoulli packet loss channel. The unknown loss rate is estimated using finite channel samples and a certainty-equivalence (CE) optimal controller is then…

We consider a robust estimation of linear regression coefficients. In this note, we focus on the case where the covariates are sampled from an $L$-subGaussian distribution with unknown covariance, the noises are sampled from a distribution…

In recent years, large language models (LLMs) have become increasingly prevalent, offering remarkable text generation capabilities. However, a pressing challenge is their tendency to make confidently wrong predictions, highlighting the…

We consider the problem of recovering the unknown noise variance in the linear regression model. To estimate the nuisance (a vector of regression coefficients) we use a family of spectral regularisers of the maximum likelihood estimator.…

We consider the problem of training a deep neural network with nonsmooth regularization to retrieve a sparse and efficient sub-structure. Our regularizer is only assumed to be lower semi-continuous and prox-bounded. We combine an adaptive…

High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…

The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space…

In this paper, we establish sample complexity bounds for learning high-dimensional simplices in $\mathbb{R}^K$ from noisy data. Specifically, we consider $n$ i.i.d. samples uniformly drawn from an unknown simplex in $\mathbb{R}^K$, each…

We establish sample complexity guarantees for estimating the covariance matrix of a strongly log-concave smooth distribution using the unadjusted Langevin algorithm (ULA). We quantitatively compare our complexity estimates on single-chain…

We study the problem of modeling univariate distributions via their quantile functions. We introduce a flexible family of distributions whose quantile function is a linear combination of basis quantiles. Because the model is linear in its…

This work provides several new insights on the robustness of Kearns' statistical query framework against challenging label-noise models. First, we build on a recent result by \cite{DBLP:journals/corr/abs-2006-04787} that showed noise…

Stochastic models in biomolecular contexts can have a state-dependent process noise covariance. The choice of the process noise covariance is an important parameter in the design of a Kalman Filter for state estimation and the theoretical…

Uncertainties have become a major concern in integrated circuit design. In order to avoid the huge number of repeated simulations in conventional Monte Carlo flows, this paper presents an intrusive spectral simulator for statistical circuit…

We investigate the q-voter model with stochastic noise arising from independence on complex networks. Using the pair approximation, we provide a comprehensive, mathematical description of its behavior and derive a formula for the critical…

We study consistency properties of machine learning methods based on minimizing convex surrogates. We extend the recent framework of Osokin et al. (2017) for the quantitative analysis of consistency properties to the case of inconsistent…

In this paper we introduce concepts from uncertainty quantification (UQ) and numerical analysis for the efficient evaluation of stochastic high dimensional Newton iterates. In particular, we develop complex analytic regularity theory of the…

New classes of stochastic differential equations can now be studied using rough path theory (e.g. Lyons et al. [LCL07] or Friz--Hairer [FH14]). In this paper we investigate, from a numerical analysis point of view, stochastic differential…

Surrogate testing techniques have been used widely to investigate the presence of dynamical nonlinearities, an essential ingredient of deterministic chaotic processes. Traditional surrogate testing subscribes to statistical hypothesis…