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Found 31 papers, 8 papers with code
An Oblivious Stochastic Composite Optimization Algorithm for Eigenvalue Optimization Problems
For the $L$-smooth case with a feasible set bounded by $D$, we derive a convergence rate of $ O( {L^2 D^2}/{(T^{2}\sqrt{T})} + {(D_0^2+\sigma^2)}/{\sqrt{T}} )$, where $D_0$ is the starting distance to an optimal solution, and $ \sigma^2$ is the stochastic oracle variance.
Vision Transformers, a new approach for high-resolution and large-scale mapping of canopy heights
This model achieves better accuracy than previously used convolutional based approaches (ConvNets) optimized with only a continuous loss function.
Detecting Methane Plumes using PRISMA: Deep Learning Model and Data Augmentation
The new generation of hyperspectral imagers, such as PRISMA, has improved significantly our detection capability of methane (CH4) plumes from space at high spatial resolution (30m).
Optimal Algorithms for Stochastic Complementary Composite Minimization
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting.
Linear Bandits on Uniformly Convex Sets
Linear bandit algorithms yield $\tilde{\mathcal{O}}(n\sqrt{T})$ pseudo-regret bounds on compact convex action sets $\mathcal{K}\subset\mathbb{R}^n$ and two types of structural assumptions lead to better pseudo-regret bounds.
Local and Global Uniform Convexity Conditions
We review various characterizations of uniform convexity and smoothness on norm balls in finite-dimensional spaces and connect results stemming from the geometry of Banach spaces with \textit{scaling inequalities} used in analysing the convergence of optimization methods.
Acceleration Methods
This monograph covers some recent advances in a range of acceleration techniques frequently used in convex optimization.
A Bregman Method for Structure Learning on Sparse Directed Acyclic Graphs
We develop a Bregman proximal gradient method for structure learning on linear structural causal models.
Averaging Atmospheric Gas Concentration Data using Wasserstein Barycenters
Hyperspectral satellite images report greenhouse gas concentrations worldwide on a daily basis.
A Trainable Optimal Transport Embedding for Feature Aggregation and its Relationship to Attention
We address the problem of learning on sets of features, motivated by the need of performing pooling operations in long biological sequences of varying sizes, with long-range dependencies, and possibly few labeled data.
FANOK: Knockoffs in Linear Time
We describe a series of algorithms that efficiently implement Gaussian model-X knockoffs to control the false discovery rate on large scale feature selection problems.
Global Convergence of Frank Wolfe on One Hidden Layer Networks
The classical Frank Wolfe algorithm then converges with rate $O(1/T)$ where $T$ is both the number of neurons and the number of calls to the oracle.
Complexity Guarantees for Polyak Steps with Momentum
In smooth strongly convex optimization, knowledge of the strong convexity parameter is critical for obtaining simple methods with accelerated rates.
Screening Data Points in Empirical Risk Minimization via Ellipsoidal Regions and Safe Loss Functions
We design simple screening tests to automatically discard data samples in empirical risk minimization without losing optimization guarantees.
Ranking and synchronization from pairwise measurements via SVD
Given a measurement graph $G= (V, E)$ and an unknown signal $r \in \mathbb{R}^n$, we investigate algorithms for recovering $r$ from pairwise measurements of the form $r_i - r_j$; $\{i, j\} \in E$.
Regularity as Regularization: Smooth and Strongly Convex Brenier Potentials in Optimal Transport
On the other hand, one of the greatest achievements of the OT literature in recent years lies in regularity theory: Caffarelli showed that the OT map between two well behaved measures is Lipschitz, or equivalently when considering 2-Wasserstein distances, that Brenier convex potentials (whose gradient yields an optimal map) are smooth.
Naive Feature Selection: Sparsity in Naive Bayes
We propose a sparse version of naive Bayes, which can be used for feature selection.
Overcomplete Independent Component Analysis via SDP
Moreover, we conjecture that the proposed program recovers a mixing component at the rate k < p^2/4 and prove that a mixing component can be recovered with high probability when k < (2 - epsilon) p log p when the original components are sampled uniformly at random on the hyper sphere.
Reconstructing Latent Orderings by Spectral Clustering
We tackle the task of retrieving linear and circular orderings in a unifying framework, and show how a latent ordering on the data translates into a filamentary structure on the Laplacian embedding.
Data Structures and Algorithms Genomics
Nonlinear Acceleration of CNNs
The Regularized Nonlinear Acceleration (RNA) algorithm is an acceleration method capable of improving the rate of convergence of many optimization schemes such as gradient descend, SAGA or SVRG.
Online Regularized Nonlinear Acceleration
Regularized nonlinear acceleration (RNA) estimates the minimum of a function by post-processing iterates from an algorithm such as the gradient method.
Frank-Wolfe with Subsampling Oracle
The first algorithm that we propose is a randomized variant of the original FW algorithm and achieves a $\mathcal{O}(1/t)$ sublinear convergence rate as in the deterministic counterpart.
Integration Methods and Optimization Algorithms
We show that accelerated optimization methods can be seen as particular instances of multi-step integration schemes from numerical analysis, applied to the gradient flow equation.
Sharpness, Restart and Acceleration
The {\L}ojasiewicz inequality shows that H\"olderian error bounds on the minimum of convex optimization problems hold almost generically.
Nonlinear Acceleration of Stochastic Algorithms
Here, we study extrapolation methods in a stochastic setting, where the iterates are produced by either a simple or an accelerated stochastic gradient algorithm.
Learning with Clustering Structure
We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation.
SerialRank: Spectral Ranking using Seriation
Intuitively, the algorithm assigns similar rankings to items that compare similarly with all others.
Spectral Ranking using Seriation
We first show that this spectral seriation algorithm recovers the true ranking when all pairwise comparisons are observed and consistent with a total order.
Convex Relaxations for Permutation Problems
Seriation seeks to reconstruct a linear order between variables using unsorted similarity information.
White Functionals for Anomaly Detection in Dynamical Systems
The candidate functionals are estimated in a subset of a reproducing kernel Hilbert space associated with the set where the process takes values.
Support Vector Machine Classification with Indefinite Kernels
In this paper, we propose a method for support vector machine classification using indefinite kernels.
