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Found 11 papers, 0 papers with code
Dirichlet Active Learning
This work introduces Dirichlet Active Learning (DiAL), a Bayesian-inspired approach to the design of active learning algorithms.
Using Higher-Order Moments to Assess the Quality of GAN-generated Image Features
The rapid advancement of Generative Adversarial Networks (GANs) necessitates the need to robustly evaluate these models.
Rates of Convergence for Regression with the Graph Poly-Laplacian
In the (special) smoothing spline problem one considers a variational problem with a quadratic data fidelity penalty and Laplacian regularisation.
Eikonal depth: an optimal control approach to statistical depths
Statistical depths provide a fundamental generalization of quantiles and medians to data in higher dimensions.
The Geometry of Adversarial Training in Binary Classification
We establish an equivalence between a family of adversarial training problems for non-parametric binary classification and a family of regularized risk minimization problems where the regularizer is a nonlocal perimeter functional.
Tukey Depths and Hamilton-Jacobi Differential Equations
We prove that this equation possesses a unique viscosity solution and that this solution always bounds the Tukey depth from below.
Adversarial Classification: Necessary conditions and geometric flows
Using the necessary conditions, we derive a geometric evolution equation which can be used to track the change in classification boundaries as $\varepsilon$ varies.
From graph cuts to isoperimetric inequalities: Convergence rates of Cheeger cuts on data clouds
In this work we study statistical properties of graph-based clustering algorithms that rely on the optimization of balanced graph cuts, the main example being the optimization of Cheeger cuts.
Distributed Stochastic Gradient Descent: Nonconvexity, Nonsmoothness, and Convergence to Local Minima
In centralized settings, it is well known that stochastic gradient descent (SGD) avoids saddle points and converges to local minima in nonconvex problems.
Optimization and Control
A maximum principle argument for the uniform convergence of graph Laplacian regressors
This paper investigates the use of methods from partial differential equations and the Calculus of variations to study learning problems that are regularized using graph Laplacians.
A new analytical approach to consistency and overfitting in regularized empirical risk minimization
This work considers the problem of binary classification: given training data $x_1, \dots, x_n$ from a certain population, together with associated labels $y_1,\dots, y_n \in \left\{0, 1 \right\}$, determine the best label for an element $x$ not among the training data.
