arXiv subjects

Robert J. Ravier

Publications and source records attributed to Robert J. Ravier.

6 recordsLinked to original sources

arXiv2021

A Methodology for Exploring Deep Convolutional Features in Relation to Hand-Crafted Features with an Application to Music Audio Modeling

Understanding the features learned by deep models is important from a model trust perspective, especially as deep systems are deployed in the real world. Most recent approaches for deep feature understanding or model explanation focus on highlighting input data features that are relevant for classification decisions. In this work, we instead take the perspective of relating deep features to well-studied, hand-crafted features that are meaningful for the application of interest. We propose a methodology and set of systematic experiments for exploring deep features in this setting, where input feature importance approaches for deep feature understanding do not apply. Our experiments focus on understanding which hand-crafted and deep features are useful for the classification task of interest, how robust these features are for related tasks and how similar the deep features are to the meaningful hand-crafted features. Our proposed method is general to many application areas and we demonstrate its utility on orchestral music audio data.

cs.SD↗

arXiv2021

GeoStat Representations of Time Series for Fast Classification

Recent advances in time series classification have largely focused on methods that either employ deep learning or utilize other machine learning models for feature extraction. Though successful, their power often comes at the requirement of computational complexity. In this paper, we introduce GeoStat representations for time series. GeoStat representations are based off of a generalization of recent methods for trajectory classification, and summarize the information of a time series in terms of comprehensive statistics of (possibly windowed) distributions of easy to compute differential geometric quantities, requiring no dynamic time warping. The features used are intuitive and require minimal parameter tuning. We perform an exhaustive evaluation of GeoStat on a number of real datasets, showing that simple KNN and SVM classifiers trained on these representations exhibit surprising performance relative to modern single model methods requiring significant computational power, achieving state of the art results in many cases. In particular, we show that this methodology achieves good performance on a challenging dataset involving the classification of fishing vessels, where our methods achieve good performance relative to the state of the art despite only having access to approximately two percent of the dataset used in training and evaluating this state of the art.

cs.LG↗

arXiv2020

Eyes on the Prize: Improved Biological Surface Registration via Forward Propagation

Many algorithms for surface registration risk producing significant errors if surfaces are significantly nonisometric. Manifold learning has been shown to be effective at improving registration quality, using information from an entire collection of surfaces to correct issues present in pairwise registrations. These methods, however, are not robust to changes in the collection of surfaces, or do not produce accurate registrations at a resolution high enough for subsequent downstream analysis. We propose a novel algorithm for efficiently registering such collections given initial correspondences with varying degrees of accuracy. By combining the initial information with recent developments in manifold learning, we employ a simple metric condition to construct a measure on the space of correspondences between any pair of shapes in our collection, which we then use to distill soft correspondences. We demonstrate that this measure can improve correspondence accuracy between feature points compared to currently employed, less robust methods on a diverse dataset of surfaces from evolutionary biology. We then show how our methods can be used, in combination with recent sampling and interpolation methods, to compute accurate and consistent homeomorphisms between surfaces.

cs.GR↗

arXiv2020

Distributed Online Convex Optimization with Improved Dynamic Regret

In this paper, we consider the problem of distributed online convex optimization, where a group of agents collaborate to track the global minimizers of a sum of time-varying objective functions in an online manner. Specifically, we propose a novel distributed online gradient descent algorithm that relies on an online adaptation of the gradient tracking technique used in static optimization. We show that the dynamic regret bound of this algorithm has no explicit dependence on the time horizon and, therefore, can be tighter than existing bounds especially for problems with long horizons. Our bound depends on a new regularity measure that quantifies the total change in the gradients at the optimal points at each time instant. Furthermore, when the optimizer is approximatly subject to linear dynamics, we show that the dynamic regret bound can be further tightened by replacing the regularity measure that captures the path length of the optimizer with the accumulated prediction errors, which can be much lower in this special case. We present numerical experiments to corroborate our theoretical results.

math.OC↗

arXiv2019

A Distributed Online Convex Optimization Algorithm with Improved Dynamic Regret

In this paper, we consider the problem of distributed online convex optimization, where a network of local agents aim to jointly optimize a convex function over a period of multiple time steps. The agents do not have any information about the future. Existing algorithms have established dynamic regret bounds that have explicit dependence on the number of time steps. In this work, we show that we can remove this dependence assuming that the local objective functions are strongly convex. More precisely, we propose a gradient tracking algorithm where agents jointly communicate and descend based on corrected gradient steps. We verify our theoretical results through numerical experiments.

math.OC↗

arXiv2015

Sampling Theory with Average Values on the Sierpinski Gasket

In the case of some fractals, sampling with average values on cells is more natural than sampling on points. In this paper we investigate this method of sampling on $SG$ and $SG_{3}$. In the former, we show that the cell graph approximations have the spectral decimation property and prove an analog of the Shannon sampling theorem.. We also investigate the numerical properties of these sampling functions and make conjectures which allow us to look at sampling on infinite blowups of $SG$. In the case of $SG_{3}$, we show that the cell graphs have the spectral decimation property, but show that it is not useful for proving an analogous sampling theorem.

math.AP↗