相关论文: Decimated generalized Prony systems

This article introduces the concept of optimization learning, a methodology to design optimization proxies that learn the input/output mapping of parametric optimization problems. These optimization proxies are trustworthy by design: they…

Latent neural stochastic differential equations (SDEs) have recently emerged as a promising approach for learning generative models from stochastic time series data. However, they systematically underestimate the noise level inherent in…

Robust methods, though ubiquitous in practice, are yet to be fully understood in the context of regularized estimation and high dimensions. Even simple questions become challenging very quickly. For example, classical statistical theory…

Deep learning models have achieved tremendous success in most of the industries in recent years. The evolution of these models has also led to an increase in the model size and energy requirement, making it difficult to deploy in production…

The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…

We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…

Symmetries are prevalent in deep learning and can significantly influence the learning dynamics of neural networks. In this paper, we examine how exponential symmetries -- a broad subclass of continuous symmetries present in the model…

We obtain general estimates for exponential integrals of the form \[ E_f(y)=\int_{\mathbb{Z}_{p}^{n}}\psi(\sum_{j=1}^r y_j f_j(x))|dx|, \] where the $f_j$ are restricted power series over $\mathbb{Q}_p$, $y_j\in\mathbb{Q}_p$, and $\psi$ a…

Black-box variational inference is widely used in situations where there is no proof that its stochastic optimization succeeds. We suggest this is due to a theoretical gap in existing stochastic optimization proofs: namely the challenge of…

With recent research advancements, deep learning models are becoming attractive and powerful choices for speech enhancement in real-time applications. While state-of-the-art models can achieve outstanding results in terms of speech quality…

The paper addresses the problem of sampling discretization of integral norms of elements of finite-dimensional subspaces satisfying some conditions. We prove sampling discretization results under two standard kinds of assumptions --…

Message passing algorithms have proved surprisingly successful in solving hard constraint satisfaction problems on sparse random graphs. In such applications, variables are fixed sequentially to satisfy the constraints. Message passing is…

Answering complex questions often requires multi-step reasoning in order to obtain the final answer. Most research into decompositions of complex questions involves open-domain systems, which have shown success in using these decompositions…

Local decision rules are commonly understood to be more explainable, due to the local nature of the patterns involved. With numerical optimization methods such as gradient boosting, ensembles of local decision rules can gain good predictive…

Motivated by the poor performance of cross-validation in settings where data are scarce, we propose a novel estimator of the out-of-sample performance of a policy in data-driven optimization.Our approach exploits the optimization problem's…

Denoising diffusion probabilistic models (DDPMs) have shown impressive results on sequence generation by iteratively corrupting each example and then learning to map corrupted versions back to the original. However, previous work has…

Many structured data-fitting applications require the solution of an optimization problem involving a sum over a potentially large number of measurements. Incremental gradient algorithms offer inexpensive iterations by sampling a subset of…

The possibility of detracting the decoherence due to the acceleration process of the two-qutrit system is investigated, where we examined the behaviour of the relative entropy and the non-local information. For this purpose, the accelerated…

We present an optimization framework for learning a fair classifier in the presence of noisy perturbations in the protected attributes. Compared to prior work, our framework can be employed with a very general class of linear and…

Non-adaptive group testing refers to the problem of inferring a sparse set of defectives from a larger population using the minimum number of simultaneous pooled tests. Recent positive results for noiseless group testing have motivated the…