arXiv research

The paper derives upper bounds on eigenvalues of Laplace-Beltrami operator on hyperbolic surfaces.

Upper bound found for Steklov eigenvalue of a surface of revolution.

This paper is devoted to regret lower bounds in the classical model of stochastic multi-armed bandit. A well-known result of Lai and Robbins, which has then been extended by Burnetas and Katehakis, has established the presence of a logarithmic bound for all consistent policies. We relax the notion of consistence, and e…

We consider the problem of finding a consistent upper price bound for exotic options whose payoff depends on the stock price at two different predetermined time points (e.g. Asian option), given a finite number of observed call prices for these maturities. A model-free approach is used, only taking into account that th…

In this paper we use continued fractions to study a partial order on the set of 2-bridge knots derived from the work of Ohtsuki, Riley, and Sakuma. We establish necessary and sufficient conditions for any set of 2-bridge knots to have an upper bound with respect to the partial order. Moreover, given any 2-bridge knot K…

Upper bounds for Steklov eigenvalues in subgraphs of polynomial growth Cayley graphs.

It is a theorem of Bers that any closed hyperbolic surface admits a pants decomposition consisting of curves of bounded length where the bound only depends on the topology of the surface. The question of the quantification of the optimal constants has been well studied and the best upper bounds to date are linear in ge…

The paper develops estimators for variance in graph structures using fused lasso.

The condensed nearest neighbor (CNN) algorithm is a heuristic for reducing the number of prototypical points stored by a nearest neighbor classifier, while keeping the classification rule given by the reduced prototypical set consistent with the full set. I present an upper bound on the number of prototypical points ac…

The paper bounds eigenvalues and integrals of eigenfunctions on hyperbolic manifolds.

Novel Orlicz regrets consistently bound environmental variable statistics.

The study establishes risk bounds for distributional regression estimators.

New bounds for balanced classification improve understanding of imbalanced datasets.

We study revenue optimization learning algorithms for repeated posted-price auctions where a seller interacts with a single strategic buyer that holds a fixed private valuation for a good and seeks to maximize his cumulative discounted surplus. For this setting, first, we propose a novel algorithm that never decreases …

An equilateral stick number $s_{=}(K)$ of a knot $K$ is defined to be the minimal number of sticks required to construct a polygonal knot of $K$ which consists of equal length sticks. Rawdon and Scharein [12] found upper bounds for the equilateral stick numbers of all prime knots through 10 crossings by using algorithm…

Paper establishes a universal growth rate for smooth surrogate losses in classification.

Improved linear upper bound for ribbonlength of knots.

Study tightens bounds for interpolating noisy data using minimum l1-norm.

Study magnetic Laplacian eigenvalues on contact manifolds.

The paper proposes methods to estimate MCMC quality with couplings, bounding Wasserstein distance.

Researchers find a way to price American options without relying on specific asset price models.

Multithreshold Entropy Linear Classifier (MELC) is a recent classifier idea which employs information theoretic concept in order to create a multithreshold maximum margin model. In this paper we analyze its consistency over multithreshold linear models and show that its objective function upper bounds the amount of mis…

Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective function downhill. Such a simple principle is widely applicable and has been very popu…

This paper consider penalized empirical loss minimization of convex loss functions with unknown non-linear target functions. Using the elastic net penalty we establish a finite sample oracle inequality which bounds the loss of our estimator from above with high probability. If the unknown target is linear this inequali…

The paper bounds solutions to complex optimization problems with uncertain data.

UCB exploration improves best arm identification in fixed-budget settings.

This paper proves an upper limit on rational points on curves.

A novel post-hoc calibration method reduces neural network calibration errors.

We extend nonparametric models to handle extrapolation, providing bounds for inference.

We study the off-policy evaluation problem---estimating the value of a target policy using data collected by another policy---under the contextual bandit model. We consider the general (agnostic) setting without access to a consistent model of rewards and establish a minimax lower bound on the mean squared error (MSE).…

Upper bound for Laplacian eigenvalue via conformal volume.

Proposes efficient bounds for causal effect estimation under weak confounding.

In this paper we introduce and analyze the learning scenario of \emph{coupled nonlinear dimensionality reduction}, which combines two major steps of machine learning pipeline: projection onto a manifold and subsequent supervised learning. First, we present new generalization bounds for this scenario and, second, we int…

Paper proposes a new UCB approach for estimating maximum mean.

Upper bounds on Einstein metrics on homogeneous spaces.

Paper improves Bayesian regret bounds for Thompson Sampling in reinforcement learning.

In this paper we study time-consistent risk measures for returns that are given by a GARCH(1,1) model. We present a construction of risk measures based on their static counterparts that overcomes the lack of time-consistency. We then study in detail our construction for the risk measures Value-at-Risk (VaR) and Average…

Upper bounds for volume spectrum depend on volume, dimension, and a conformal invariant.

A framework for ranking with abstention, offering theoretical guarantees and practical effectiveness.

This paper analyzes regret bounds for Gaussian process Thompson sampling.

We analyze variational inference for highly symmetric graphical models such as those arising from first-order probabilistic models. We first show that for these graphical models, the tree-reweighted variational objective lends itself to a compact lifted formulation which can be solved much more efficiently than the sta…

Upper bounds for CV errors apply to lasso and other models.

We show that any space with a positive upper curvature bound has in a small neighborhood of any point a closely related metric with a negative upper curvature bound.

New upper bound for Neumann Laplacian eigenvalues on convex domains.

Sharp upper bounds found for Steklov eigenvalues of a specific hypersurface.

New bounds derived for KG algorithm's performance in finite time.

Study proves upper bounds for solutions on Riemannian manifolds.

New method improves adversarial training robustness.