Related papers: Error Bounds for Radial Network Topology Learning …

An additive noise channel is considered, in which the distribution of the noise is nonparametric and unknown. The problem of learning encoders and decoders based on noise samples is considered. For uncoded communication systems, the problem…

Causal discovery algorithms infer causal relations from data based on several assumptions, including notably the absence of measurement error. However, this assumption is most likely violated in practical applications, which may result in…

The canonical range resolution limit in radar, sonar, and lidar systems is found to be a special case of a more general resolution limit. The general limit indicates that it is possible to surpass the canonical limit in moderate (of order…

High-dimensional models often have a large memory footprint and must be quantized after training before being deployed on resource-constrained edge devices for inference tasks. In this work, we develop an information-theoretic framework for…

The accuracy of deep learning, i.e., deep neural networks, can be characterized by dividing the total error into three main types: approximation error, optimization error, and generalization error. Whereas there are some satisfactory…

We develop a new class of distance-aware error bounds that tightly characterize the approximation error of spline neural networks. Our bottom-up approach analyzes the error bound of each neuron (a spline) and then extends it to the full…

Recurrent Neural Networks (RNNs) have achieved great success in the prediction of sequential data. However, their theoretical studies are still lagging behind because of their complex interconnected structures. In this paper, we establish a…

Efficient operation of distribution grids in the smart-grid era is hindered by the limited presence of real-time nodal and line meters. In particular, this prevents the easy estimation of grid topology and associated line parameters that…

Compression is a key step to deploy large neural networks on resource-constrained platforms. As a popular compression technique, quantization constrains the number of distinct weight values and thus reducing the number of bits required to…

An information-theoretic upper bound on the generalization error of supervised learning algorithms is derived. The bound is constructed in terms of the mutual information between each individual training sample and the output of the…

The optimization foundations of deep linear networks have recently received significant attention. However, due to their inherent non-convexity and hierarchical structure, analyzing the loss functions of deep linear networks remains a…

This paper studies the possibility of upper bounding the position error of an estimate for range based positioning algorithms in wireless sensor networks. In this study, we argue that in certain situations when the measured distances…

In this work we present some results that allow to improve the decoding radius in solving polynomial linear systems with errors in the scenario where errors are additive and randomly distributed over a finite field. The decoding radius…

Characterization of quantum systems from experimental data is a central problem in quantum science and technology. But which measurements should be used to gather data in the first place? While optimal measurement choices can be worked out…

Numerous studies have shown that label noise can lead to poor generalization performance, negatively affecting classification accuracy. Therefore, understanding the effectiveness of classifiers trained using deep neural networks in the…

This paper provides statistical guarantees on the accuracy of dynamical models learned from dependent data sequences. Specifically, we develop uniform error bounds that apply to quantized models and imperfect optimization algorithms…

The optimal design of neural networks is a critical problem in many applications. Here, we investigate how dynamical systems with polynomial nonlinearities can inform the design of neural systems that seek to emulate them. We propose a…

A problem of reconstruction of the topology and the respective edge resistance values of an unknown circular planar passive resistive network using limitedly available resistance distance measurements is considered. We develop a multistage…

This article studies the achievable guarantees on the error rates of certain learning algorithms, with particular focus on refining logarithmic factors. Many of the results are based on a general technique for obtaining bounds on the error…

In many quantum tasks, there is an unknown quantum object that one wishes to learn. An online strategy for this task involves adaptively refining a hypothesis to reproduce such an object or its measurement statistics. A common evaluation…