arXiv research

Investigates second best Einstein manifolds in low dimensions.

Study optimizes best-arm identification with minimax and Bayes strategies.

The goal of a learner, in standard online learning, is to have the cumulative loss not much larger compared with the best-performing function from some fixed class. Numerous algorithms were shown to have this gap arbitrarily close to zero, compared with the best function that is chosen off-line. Nevertheless, many real…

In this paper, we analyze the Wisconsin Diagnostic Breast Cancer Data using Machine Learning classification techniques, such as the SVM, Bayesian Logistic Regression (Variational Approximation), and K-Nearest-Neighbors. We describe each model, and compare their performance through different measures. We conclude that S…

Paper defines and studies measures related to earthquakes and best Lipschitz maps.

Catastrophic forgetting is a problem faced by many machine learning models and algorithms. When trained on one task, then trained on a second task, many machine learning models "forget" how to perform the first task. This is widely believed to be a serious problem for neural networks. Here, we investigate the extent to…

We concerns here with the continuity on the geometry of the second Riemannian L^p-Sobolev best constant B_0(p,g) associated to the AB program. Precisely, for 1 <= p <= 2, we prove that B_0(p,g) depends continuously on g in the C^2-topology. Moreover, this topology is sharp for p = 2. From this discussion, we deduce som…

We consider the stochastic bandit problem in the sublinear space setting, where one cannot record the win-loss record for all $K$ arms. We give an algorithm using $O(1)$ words of space with regret \[ \sum_{i=1}^{K}\frac{1}{Δ_i}\log \frac{Δ_i}Δ\log T \] where $Δ_i$ is the gap between the best arm and arm $i$ and $Δ$ is …

Improved Compressed Sensing by optimizing sparse solutions with mixed integer programming.

New algorithms minimize regret in both adversarial and stochastic contexts.

Two kernel Stein tests control decision errors in non-parametric model comparison.

In this paper, we study stochastic non-convex optimization with non-convex random functions. Recent studies on non-convex optimization revolve around establishing second-order convergence, i.e., converging to a nearly second-order optimal stationary points. However, existing results on stochastic non-convex optimizatio…

Logistic Regression and Support Vector Machine algorithms, together with Linear and Non-Linear Deep Neural Networks, are applied to lending data in order to replicate lender acceptance of loans and predict the likelihood of default of issued loans. A two phase model is proposed; the first phase predicts loan rejection,…

Two new algorithms solve nonconvex-strongly concave problems efficiently.

New strategies for identifying the best arm in bandits with decreasing variances.

We study the optimal placement problem of a stock trader who wishes to clear his/her inventory by a predetermined time horizon t, by using a limit order or a market order. For a diffusive market, we characterize the optimal limit order placement policy and analyze its behavior under different market conditions. In part…

Second-order economic theory considers new variables to improve price volatility predictions.

New algorithms optimize non-smooth, non-convex objectives with improved complexity.

Two methods for model adaptation compared; fine-tuning outperforms Best-of-N in realizable settings.

Study quantile multi-armed bandits for identifying the best arm with a specified quantile level.

Second-order methods improve differential privacy in convex optimization.

Variance reduction techniques like SVRG provide simple and fast algorithms for optimizing a convex finite-sum objective. For nonconvex objectives, these techniques can also find a first-order stationary point (with small gradient). However, in nonconvex optimization it is often crucial to find a second-order stationary…

Optimizes identifying the best arm with fixed samples.

We study a seemingly unexpected and relatively less understood overfitting aspect of a fundamental tool in sparse linear modeling - best subset selection, which minimizes the residual sum of squares subject to a constraint on the number of nonzero coefficients. While the best subset selection procedure is often perceiv…

The motivation of this work is to improve the performance of standard stacking approaches or ensembles, which are composed of simple, heterogeneous base models, through the integration of the generation and selection stages for regression problems. We propose two extensions to the standard stacking approach. In the fir…

New algorithms improve stopping time for best arm identification.

A new method selects clean samples to train DNNs with noisy labels.

This text is a survey on cross-validation. We define all classical cross-validation procedures, and we study their properties for two different goals: estimating the risk of a given estimator, and selecting the best estimator among a given family. For the risk estimation problem, we compute the bias (which can also be …

New methods recover best rank-r approximations from few entries.

Risk management in financial derivative markets requires inevitably the calculation of the different price sensitivities. The literature contains an abundant amount of research works that have studied the computation of these important values. Most of these works consider the well-known Black and Scholes model where th…

Study best-response learning dynamics in zero-sum polymatrix games under full and minimal information settings.

A new algorithm solves minimax problems without needing parameters.

The paper is devoted to weighted $L^p$-Hardy inequalities with best constants on Finsler metric measure manifolds. There are two major ingredients. The first, which is the main part of this paper, is the Hardy inequalities concerned with distance functions in the Finsler setting. In this case, we find that besides the …

In this paper, we consider the problem of prediction with expert advice in dynamic environments. We choose tracking regret as the performance metric and develop two adaptive and efficient algorithms with data-dependent tracking regret bounds. The first algorithm achieves a second-order tracking regret bound, which impr…

Improved Local SGD convergence for general convex objectives with bounded second-order heterogeneity.

Paper proposes a method to find approximate SOSP for nonconvex conic optimization problems.

A new method selects the best feature selection technique for datasets.

New algorithms avoid a dominant lower-order term in heavy-tailed loss settings.

Optimizes pure exploration in linear bandits with a new algorithm.

The paper studies consistency of surrogate loss procedures under constrained classifiers.

This is the second of a series of two technical papers devoted to the analysis of holonomy invariants in strict higher gauge theory with end applications in higher Chern--Simons theory. We provide a definition of trace over a crossed module such to yield surface knot invariants upon application to 2-holonomies. We show…

New concept of proper-calibeating extends classic calibrated forecasts to proper scoring rules.

The Hessian-vector product has been utilized to find a second-order stationary solution with strong complexity guarantee (e.g., almost linear time complexity in the problem's dimensionality). In this paper, we propose to further reduce the number of Hessian-vector products for faster non-convex optimization. Previous a…

Graph-based approach repairs programs from diagnostic feedback.

Paper introduces STSL, a second-order Tweedie sampler for efficient posterior sampling in inverse problems.

COMRADE is a communication-efficient, Byzantine-resilient second-order optimization algorithm.

The study analyzes neural network predictions of knot invariants and finds that braid representations work best.

Paper learns optimal kernels for Gaussian process regression in aerodynamics.