arXiv research

PAC-Bayesian bounds for stochastic LTI systems derived.

Improved price bounds for multi-asset derivatives using market option data.

The paper analyzes risk estimation methods and derives bounds for OCE risk.

Study dynamic trading in options to improve price bounds for exotic derivatives.

We derive bounds for a notion of adversarial risk, designed to characterize the robustness of linear and neural network classifiers to adversarial perturbations. Specifically, we introduce a new class of function transformations with the property that the risk of the transformed functions upper-bounds the adversarial r…

Sharp bounds on heat kernel derivatives on incomplete manifolds.

Estimates for covariant derivatives and Riesz transforms on differential forms.

Enhanced $H$-consistency bounds derived under relaxed conditions.

New bounds on continuous random variables' right-tail probabilities.

Data-driven models are subject to model errors due to limited and noisy training data. Key to the application of such models in safety-critical domains is the quantification of their model error. Gaussian processes provide such a measure and uniform error bounds have been derived, which allow safe control based on thes…

Paper derives an error bound for stochastic LTI systems.

Sharp bounds derived for eigenvalues on specific geometric spaces.

The study examines how including additional call option prices affects model-independent price bounds for exotic derivatives.

Improved bounds for Monte Carlo Rademacher Averages using self-bounding functions.

In this note, Black--Scholes implied volatility is expressed in terms of various optimisation problems. From these representations, upper and lower bounds are derived which hold uniformly across moneyness and call price. Various symmetries of the Black--Scholes formula are exploited to derive new bounds from old. These…

Study on signatures of positive braids with bounds derived.

Paper derives PAC-Bayesian bounds for LTI systems learning from empirical data.

Entropy study on synthetic spaces with curvature bounds.

In this note, we obtain the asymptotic estimate for the time derivative of the $Φ$-entropy in terms of the lower bound on the Bakry-Emery $Γ_2$ curvature. In the cases of Hyperbolic space and Heisenberg group, we show that the time derivative of the $Φ$-entropy is non-increasing, and we also get sharp asymptotic bound …

Theory for deep neural network approximation of score function and its derivatives.

We use surrogate losses to obtain several new regret bounds and new algorithms for contextual bandit learning. Using the ramp loss, we derive new margin-based regret bounds in terms of standard sequential complexity measures of a benchmark class of real-valued regression functions. Using the hinge loss, we derive an ef…

In this paper we study a model-based approach to calculating approximately optimal policies in Markovian Decision Processes. In particular, we derive novel bounds on the loss of using a policy derived from a factored linear model, a class of models which generalize numerous previous models out of those that come with s…

Logistic regression gets a new, simpler uniform bound.

Sharp bounds derived for test error of finite-rank kernel ridge regression.

New method uses logical relations to derive bounds and inequality constraints from causal models.

Sharp bounds for curve isoperimetric deficit derived.

Exact bounds derived for neural network outputs with noisy inputs.

In this paper, we propose a novel uniform generalization bound on the time and inverse temperature for stochastic gradient Langevin dynamics (SGLD) in a non-convex setting. While previous works derive their generalization bounds by uniform stability, we use Rademacher complexity to make our generalization bound indepen…

We derive a lower bound on the size of finite non-cyclic quotients of the braid group that is superexponential in the number of strands. We also derive a similar lower bound for nontrivial finite quotients of the commutator subgroup of the braid group.

New bounds derived using conditional $f$-information for machine learning models.

We develop a technique for deriving data-dependent error bounds for transductive learning algorithms based on transductive Rademacher complexity. Our technique is based on a novel general error bound for transduction in terms of transductive Rademacher complexity, together with a novel bounding technique for Rademacher…

Kernel smoothing on unknown manifolds with bounds and asymptotic normality.

Unified derivation of PAC-Bayes and MI bounds for general VC classes with fast rates.

Derivatives on the Chicago Board Options Exchange volatility index (VIX) have gained significant popularity over the last decade. The pricing of VIX derivatives involves evaluating the square root of the expected realised variance which cannot be computed by direct Monte Carlo methods. Least squares Monte Carlo methods…

Unified framework for deriving generalization bounds in supervised learning.

We suggest a general oracle-based framework that captures different parallel stochastic optimization settings described by a dependency graph, and derive generic lower bounds in terms of this graph. We then use the framework and derive lower bounds for several specific parallel optimization settings, including delayed …

We derive and analyze learning algorithms for apprenticeship learning, policy evaluation, and policy gradient for average reward criteria. Existing algorithms explicitly require an upper bound on the mixing time. In contrast, we build on ideas from Markov chain theory and derive sampling algorithms that do not require …

We consider the problem of learning a dictionary matrix from a number of observed signals, which are assumed to be generated via a linear model with a common underlying dictionary. In particular, we derive lower bounds on the minimum achievable worst case mean squared error (MSE), regardless of computational complexity…

We consider option pricing in a regime-switching diffusion market. As the market is incomplete, there is no unique price for a derivative. We apply the good-deal pricing bounds idea to obtain ranges for the price of a derivative. As an illustration, we calculate the good-deal pricing bounds for a European call option a…

Derives exact formula for Minkowski sum of ellipsoids in N-space.

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

We present a general method for deriving collapsed variational inference algo- rithms for probabilistic models in the conjugate exponential family. Our method unifies many existing approaches to collapsed variational inference. Our collapsed variational inference leads to a new lower bound on the marginal likelihood. W…

We study the K-armed dueling bandit problem, a variation of the standard stochastic bandit problem where the feedback is limited to relative comparisons of a pair of arms. The hardness of recommending Copeland winners, the arms that beat the greatest number of other arms, is characterized by deriving an asymptotic regr…

Develops a framework for consistent pricing of interest rate derivatives.

The paper establishes bounds for transductive learning using information theory.

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

Derives gradient bounds for f-heat equations on manifolds with Bakry-Emery Ricci curvature.

We give a unified statement and proof of a class of wellknown mean value inequalities for nonnegative functions with a nonlinear bound on the Laplacian. We generalize these to domains with boundary, requiring a (possibly nonlinear) bound on the normal derivative at the boundary. These inequalities give rise to an energ…