arXiv research

Adversarial online nonparametric regression achieves optimal rates with locally adaptive learning.

Study approximates unknown function levels with queries.

The purpose of these notes is to explain parts of Gromov's survey of Carnot-Carathedory spaces, in the light of subsequent results of M. Rumin. Among the rich material provided by Gromov, most of which pertains to analysis on metric spaces, we choose to concentrate on the H{ö}lder equivalence problem for Carnot manifol…

Novel graph-based method detects R-peaks in noisy ECG signals without preprocessing.

A variant of Gromov's H{ö}lder-equivalence problem, motivated by a pinching problem in Riemannian geometry, is discussed. A partial result is given. The main tool is a general coarea inequality satisfied by packing energies of maps.

This paper explores four different visualization techniques for long short-term memory (LSTM) networks applied to continuous-valued time series. On the datasets analysed, we find that the best visualization technique is to learn an input deletion mask that optimally reduces the true class score. With a specific focus o…

Develops a method to interpret deep learning models by identifying key features.

In the context of stochastic continuum-armed bandits, we present an algorithm that adapts to the unknown smoothness of the objective function. We exhibit and compute a polynomial cost of adaptation to the H{ö}lder regularity for regret minimization. To do this, we first reconsider the recent lower bound of Locatelli an…

We study finite energy classes of quasiplurisubharmonic (qpsh) functions in the setting of toric compact K{ä}hler manifolds. We characterize toric qpsh functions and give necessary and sufficient conditions for them to have finite (weighted) energy, both in terms of the associated convex function in R n , and through t…

Let $S$ be a closed oriented surface of genus at least $2$, and denote by $\mathcal{T}(S)$ its Teichm{ü}ller space. For any isotopy class of closed curves $γ$, we compute the first three derivatives of the length function $\ell\_γ:\mathcal{T}(S)\rightarrow\mathbf{R}\_+$ in the shearing coordinates associated to a maxim…

We consider the problem of online nonparametric regression with arbitrary deterministic sequences. Using ideas from the chaining technique, we design an algorithm that achieves a Dudley-type regret bound similar to the one obtained in a non-constructive fashion by Rakhlin and Sridharan (2014). Our regret bound is expre…

A new model classifies multi-lead ECGs better than single-channel models.

In this paper we provide an alternative framework to tackle the first-best Principal-Agent problem under CARA utilities. This framework leads to both a proof of existence and uniqueness of the solution to the Risk-Sharing problem under very general assumptions on the underlying contract space. Our analysis relies on an…

Validates economic scenarios using statistical tests on stochastic processes.

We find a local solution to the Ricci flow equation under a negative lower bound for many known curvature conditions. The flow exists for a uniform amount of time, during which the curvature stays bounded below by a controllable negative number. The curvature conditions we consider include 2-non-negative and weakly $\t…

This paper presents a novel signal compression algorithm based on the Blaschke unwinding adaptive Fourier decomposition (AFD). The Blaschke unwinding AFD is a newly developed signal decomposition theory. It utilizes the Nevanlinna factorization and the maximal selection principle in each decomposition step, and achieve…

Electrocardiogram (ECG) can be reliably used as a measure to monitor the functionality of the cardiovascular system. Recently, there has been a great attention towards accurate categorization of heartbeats. While there are many commonalities between different ECG conditions, the focus of most studies has been classifyi…

Study shows zero-shot super-resolution in neural operators is impossible in many cases.

Efficient classifier with uncertainty bounds for safety-critical applications.

Efficient algorithms for contextual bandits with smooth regret in continuous action spaces.

The classification of electrocardiographic (ECG) signals is a challenging problem for healthcare industry. Traditional supervised learning methods require a large number of labeled data which is usually expensive and difficult to obtain for ECG signals. Active learning is well-suited for ECG signal classification as it…

The reservoir computing paradigm is employed to classify heartbeat anomalies online based on electrocardiogram signals. Inspired by the principles of information processing in the brain, reservoir computing provides a framework to design, train, and analyze recurrent neural networks (RNNs) for processing time-dependent…

General lower bounds on neural network approximation in L^p norm.

Compact neural network for ECG classification reduces resource needs.

A new framework for semi-supervised learning using pseudo-representation labeling.

This paper selects features in deep neural networks with theoretical guarantees.

New algorithms for interactive learning match minimax bounds efficiently.

Atrial fibrillation is a cardiac arrhythmia that affects an estimated 33.5 million people globally and is the potential cause of 1 in 3 strokes in people over the age of 60. Detection and diagnosis of atrial fibrillation (AFIB) is done noninvasively in the clinical environment through the evaluation of electrocardiogra…

Generative adversarial network system improves ECG arrhythmia classification.

This work improves interpretability and calibration of complex-valued neural networks using Newton-Puiseux analysis.

Introduces a space of almost complex structures for complex Lie group bundles.

Generative compression technique reduces neural network size and improves performance on microcontrollers.

A criterion for training-free time-lagged spectral embeddings of multivariate time series