arXiv subjects

Robert Ravier

Publications and source records attributed to Robert Ravier.

8 recordsLinked to original sources

arXiv2021

Improved Automated Machine Learning from Transfer Learning

In this paper, we propose a neural architecture search framework based on a similarity measure between some baseline tasks and a target task. We first define the notion of the task similarity based on the log-determinant of the Fisher Information matrix. Next, we compute the task similarity from each of the baseline tasks to the target task. By utilizing the relation between a target and a set of learned baseline tasks, the search space of architectures for the target task can be significantly reduced, making the discovery of the best candidates in the set of possible architectures tractable and efficient, in terms of GPU days. This method eliminates the requirement for training the networks from scratch for a given target task as well as introducing the bias in the initialization of the search space from the human domain.

cs.LG↗

arXiv2020

Task-Aware Neural Architecture Search

The design of handcrafted neural networks requires a lot of time and resources. Recent techniques in Neural Architecture Search (NAS) have proven to be competitive or better than traditional handcrafted design, although they require domain knowledge and have generally used limited search spaces. In this paper, we propose a novel framework for neural architecture search, utilizing a dictionary of models of base tasks and the similarity between the target task and the atoms of the dictionary; hence, generating an adaptive search space based on the base models of the dictionary. By introducing a gradient-based search algorithm, we can evaluate and discover the best architecture in the search space without fully training the networks. The experimental results show the efficacy of our proposed task-aware approach.

cs.LG↗

arXiv2020

Approximating the Riemannian Metric from Point Clouds via Manifold Moving Least Squares

The approximation of both geodesic distances and shortest paths on point cloud sampled from an embedded submanifold $\mathcal{M}$ of Euclidean space has been a long-standing challenge in computational geometry. Given a sampling resolution parameter $ h $, state-of-the-art discrete methods yield $ O(h) $ provable approximations. In this paper, we investigate the convergence of such approximations made by Manifold Moving Least-Squares (Manifold-MLS), a method that constructs an approximating manifold $\mathcal{M}^h$ using information from a given point cloud that was developed by Sober \& Levin in 2019. In this paper, we show that provided that $\mathcal{M}\in C^{k}$ and closed (i.e. $\mathcal{M}$ is a compact manifold without boundary) the Riemannian metric of $ \mathcal{M}^h $ approximates the Riemannian metric of $ \mathcal{M}, $. Explicitly, given points $ p_1, p_2 \in \mathcal{M}$ with geodesic distance $ \rho_{\mathcal{M}}(p_1, p_2) $, we show that their corresponding points $ p_1^h, p_2^h \in \mathcal{M}^h$ have a geodesic distance of $ \rho_{\mathcal{M}^h}(p_1^h,p_2^h) = \rho_{\mathcal{M}}(p_1, p_2)(1 + O(h^{k-1})) $ (i.e., the Manifold-MLS is nearly an isometry). We then use this result, as well as the fact that $ \mathcal{M}^h $ can be sampled with any desired resolution, to devise a naive algorithm that yields approximate geodesic distances with a rate of convergence $ O(h^{k-1}) $. We show the potential and the robustness to noise of the proposed method on some numerical simulations.

math.NA↗

arXiv2019

Learning Partial Differential Equations from Data Using Neural Networks

We develop a framework for estimating unknown partial differential equations from noisy data, using a deep learning approach. Given noisy samples of a solution to an unknown PDE, our method interpolates the samples using a neural network, and extracts the PDE by equating derivatives of the neural network approximation. Our method applies to PDEs which are linear combinations of user-defined dictionary functions, and generalizes previous methods that only consider parabolic PDEs. We introduce a regularization scheme that prevents the function approximation from overfitting the data and forces it to be a solution of the underlying PDE. We validate the model on simulated data generated by the known PDEs and added Gaussian noise, and we study our method under different levels of noise. We also compare the error of our method with a Cramer-Rao lower bound for an ordinary differential equation. Our results indicate that our method outperforms other methods in estimating PDEs, especially in the low signal-to-noise regime.

cs.LG↗

arXiv2019

Prediction in Online Convex Optimization for Parametrizable Objective Functions

Many techniques for online optimization problems involve making decisions based solely on presently available information: fewer works take advantage of potential predictions. In this paper, we discuss the problem of online convex optimization for parametrizable objectives, i.e. optimization problems that depend solely on the value of a parameter at a given time. We introduce a new regularity for dynamic regret based on the accuracy of predicted values of the parameters and show that, under mild assumptions, accurate prediction can yield tighter bounds on dynamic regret. Inspired by recent advances on learning how to optimize, we also propose a novel algorithm to simultaneously predict and optimize for parametrizable objectives and study its performance using simulated and real data.

math.OC↗

arXiv2018

Quantifying Gerrymandering in North Carolina

Using an ensemble of redistricting plans, we evaluate whether a given political districting faithfully represents the geo-political landscape. Redistricting plans are sampled by a Monte Carlo algorithm from a probability distribution that adheres to realistic and non-partisan criteria. Using the sampled redistricting plans and historical voting data, we produce an ensemble of elections that reveal geo-political structure within the state. We showcase our methods on the two most recent districtings of NC for the U.S. House of Representatives, as well as a plan drawn by a bipartisan redistricting panel. We find the two state enacted plans are highly atypical outliers whereas the bipartisan plan accurately represents the ensemble both in partisan outcome and in the fine scale structure of district-level results.

physics.soc-ph↗

arXiv2017

Evaluating Partisan Gerrymandering in Wisconsin

We examine the extent of gerrymandering for the 2010 General Assembly district map of Wisconsin. We find that there is substantial variability in the election outcome depending on what maps are used. We also found robust evidence that the district maps are highly gerrymandered and that this gerrymandering likely altered the partisan make up of the Wisconsin General Assembly in some elections. Compared to the distribution of possible redistricting plans for the General Assembly, Wisconsin's chosen plan is an outlier in that it yields results that are highly skewed to the Republicans when the statewide proportion of Democratic votes comprises more than 50-52% of the overall vote (with the precise threshold depending on the election considered). Wisconsin's plan acts to preserve the Republican majority by providing extra Republican seats even when the Democratic vote increases into the range when the balance of power would shift for the vast majority of redistricting plans.

stat.AP↗

arXiv2017

Redistricting: Drawing the Line

We develop methods to evaluate whether a political districting accurately represents the will of the people. To explore and showcase our ideas, we concentrate on the congressional districts for the U.S. House of representatives and use the state of North Carolina and its redistrictings since the 2010 census. Using a Monte Carlo algorithm, we randomly generate over 24,000 redistrictings that are non-partisan and adhere to criteria from proposed legislation. Applying historical voting data to these random redistrictings, we find that the number of democratic and republican representatives elected varies drastically depending on how districts are drawn. Some results are more common, and we gain a clear range of expected election outcomes. Using the statistics of our generated redistrictings, we critique the particular congressional districtings used in the 2012 and 2016 NC elections as well as a districting proposed by a bipartisan redistricting commission. We find that the 2012 and 2016 districtings are highly atypical and not representative of the will of the people. On the other hand, our results indicate that a plan produced by a bipartisan panel of retired judges is highly typical and representative. Since our analyses are based on an ensemble of reasonable redistrictings of North Carolina, they provide a baseline for a given election which incorporates the geometry of the state's population distribution.

stat.AP↗