arXiv research

We derive caplet volatilities for quadratic models, providing an asymptotic approximation.

Recently, deep learning has achieved huge successes in many important applications. In our previous studies, we proposed quadratic/second-order neurons and deep quadratic neural networks. In a quadratic neuron, the inner product of a vector of data and the corresponding weights in a conventional neuron is replaced with…

This paper concerns a method of selecting a subset of features for a sequential logit model. Tanaka and Nakagawa (2014) proposed a mixed integer quadratic optimization formulation for solving the problem based on a quadratic approximation of the logistic loss function. However, since there is a significant gap between …

The paper debiases mini-batch approximations in deep learning for more accurate optimization and uncertainty quantification.

Closed-form polynomial approximations replace MLPs in transformers, enabling new interpretability methods.

We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are mostly not scalable. In this paper, we develop a method that transforms the quadra…

Novel approximation hierarchy for sparse quadratic programs.

The paper proves signatures of non-geometric rough paths can approximate functionals uniformly.

A new method for exponentially weighted moving models using approximations.

QLA improves Bayesian uncertainty estimation for DNNs without increasing computational cost.

The runtime for Kernel Partial Least Squares (KPLS) to compute the fit is quadratic in the number of examples. However, the necessity of obtaining sensitivity measures as degrees of freedom for model selection or confidence intervals for more detailed analysis requires cubic runtime, and thus constitutes a computationa…

A new method automatically and dynamically sets learning rates in deep learning.

Market maker optimizes SPX and VIX spread using quadratic rough Heston model.

Method solves complex optimization problems with high probability bounds.

We consider an application involving a financial quadratic portfolio of options, when the joint underlying log-returns changes with multivariate elliptic distribution. This motivates the needs for methods for the approximation of multiple integrals over hyperboloids. A transformation is used to reduce the hyperboloid i…

New findings on kernel regression in the quadratic regime, improving understanding of machine learning models.

Quadratic models explain neural network behavior during training.

New algorithm learns LQR with $O(\sqrt{T})$ regret using Langevin dynamics and excitation.

Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including…

In the setting of exponential investors and uncertainty governed by Brownian motions we first prove the existence of an incomplete equilibrium for a general class of models. We then introduce a tractable class of exponential-quadratic models and prove that the corresponding incomplete equilibrium is characterized by a …

Paper uses Koopman operator and Nyström method for efficient nonlinear control.

A sampling-based optimization method for quadratic functions is proposed. Our method approximately solves the following $n$-dimensional quadratic minimization problem in constant time, which is independent of $n$: $z^*=\min_{\mathbf{v} \in \mathbb{R}^n}\langle\mathbf{v}, A \mathbf{v}\rangle + n\langle\mathbf{v}, \mathr…

New method for CMS derivatives pricing using Watanabe's expansions.

The paper explores the geometry of algebraic numbers and their roots.

This article proposes a new approximation scheme for quadratic-growth BSDEs in a Markovian setting by connecting a series of semi-analytic asymptotic expansions applied to short-time intervals. Although there remains a condition which needs to be checked a posteriori, one can avoid altogether time-consuming Monte Carlo…

New lower bounds improve logistic log-likelihood optimization and inference.

We study the space of "link maps": the space of maps of a disjoint union of compact, closed manifolds P_1, . . ., P_k into a manifold N whose images are pairwise disjoint. We apply the manifold calculus of functors developed by Goodwillie and Weiss to study the difference between it and its linear and quadratic approxi…

Quantum algorithm speeds up Lasso regression by quadratically faster per iteration.

Study Markov chain gradient descent in Hilbert spaces for quadratic loss.

QENDy learns quadratic dynamics from nonlinear systems data.

AQFC method estimates mesh curvatures using quadratic surfaces.

Paper approximates Kelly betting for wealth growth.

Markov's theorem classifies the worst irrational numbers with respect to rational approximation and the indefinite binary quadratic forms whose values for integer arguments stay farthest away from zero. The main purpose of this paper is to present a new proof of Markov's theorem using hyperbolic geometry. The main ingr…

The Mean-Variance Criterion is equivalent to Second-order Stochastic Dominance under symmetric Elliptical distributions.

The paper tackles learning smooth distance functions using query-based methods.

PDHAMS improves sampling for discrete distributions with quadratic potential functions.

Quadratic points of a surface in the projective 3-space are the points which can be exceptionally well approximated by a quadric. They are also singularities of a 3-web in the elliptic part and of a line field in the hyperbolic part of the surface. We show that generically the index of the 3-web at a quadratic point is…

A fast, robust AMP algorithm for quadratic optimization problems.

Actor-critic finds Nash in mean-field games with linear-quadratic costs.

We consider the problem of numerical approximation for forward-backward stochastic differential equations with drivers of quadratic growth (qgFBSDE). To illustrate the significance of qgFBSDE, we discuss a problem of cross hedging of an insurance related financial derivative using correlated assets. For the convergence…

IntHT solves sparse quadratic regression in sub-quadratic time and space.

Model liquidity premia using a risk-sharing economy with quadratic costs.

In this paper we study decomposition methods based on separable approximations for minimizing the augmented Lagrangian. In particular, we study and compare the Diagonal Quadratic Approximation Method (DQAM) of Mulvey and Ruszczyński and the Parallel Coordinate Descent Method (PCDM) of Richtárik and Takáč. We show that …

HA-SME models SGD dynamics with Hessian info for better escaping behaviors.

A new method improves adversarial robustness and interpretability with reduced training time.

This note gives a simple analysis of a randomized approximation scheme for matrix multiplication proposed by Sarlos (2006) based on a random rotation followed by uniform column sampling. The result follows from a matrix version of Bernstein's inequality and a tail inequality for quadratic forms in subgaussian random ve…

Improved pricing method for American options in various models.

The paper develops an expansion for optimizing portfolios with small quadratic transaction costs.