arXiv research

Quadratic models explain neural network behavior during training.

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

We provide explicit solutions of certain forward-backward stochastic differential equations (FBSDEs) with quadratic growth. These particular FBSDEs are associated with quadratic term structure models of interest rates and characterize the zero-coupon bond price. The results of this paper are naturally related to simila…

Deep learning solves high-dimensional quadratic hedging problems.

Inspired by complexity and diversity of biological neurons, our group proposed quadratic neurons by replacing the inner product in current artificial neurons with a quadratic operation on input data, thereby enhancing the capability of an individual neuron. Along this direction, we are motivated to evaluate the power o…

Paper connects MoE and self-attention, proposing active-attention.

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

A new QHR model extends HR model with a quadratic variance function.

The paper solves a utility-based hedging problem with quadratic costs.

The paper extends a variance gamma model to quadratic functions, reducing arbitrage and computational costs.

Paper optimizes estimation of quadratic functionals in nonparametric IV models.

We discuss the class of "Quadratic Normal Volatility" models, which have drawn much attention in the financial industry due to their analytic tractability and flexibility. We characterize these models as the ones that can be obtained from stopped Brownian motion by a simple transformation and a change of measure that o…

Proposes a new framework for invariant quadratic P&L predictions in option books.

We consider a square-integrable semimartingale and investigate the convex order relations between its discrete, continuous and predictable quadratic variation. As the main results, we show that if the semimartingale has conditionally independent increments and symmetric jump measure, then its discrete realized variance…

Using Vovk's outer measure, which corresponds to a minimal superhedging price, the existence of quadratic variation is shown for "typical price paths" in the space of càdlàg functions possessing a mild restriction on the jumps directed downwards. In particular, this result includes the existence of quadratic variation …

We consider the tensor completion problem of predicting the missing entries of a tensor. The commonly used CP model has a triple product form, but an alternate family of quadratic models, which are the sum of pairwise products instead of a triple product, have emerged from applications such as recommendation systems. N…

In this paper, we consider a discrete time economy where we assume that the short term interest rate follows a quadratic term structure of a regime switching asset process. The possible non-linear structure and the fact that the interest rate can have different economic or financial trends justify the interest of Regim…

The paper proposes a method to select clusters, models, and algorithms based on quadratic discriminant scores.

New quadratic forms expand and rotate linear endomorphisms in geometric theory.

We construct a finitely presented group $G$ with non-quadratic Dehn function $f$ majorizable by a quadratic function on arbitrary long intervals.

Gaussian equivalence fails for simple polynomial embeddings in quadratic scaling RF models.

We introduce and establish the main properties of QHawkes ("Quadratic" Hawkes) models. QHawkes models generalize the Hawkes price models introduced in E. Bacry et al. (2014), by allowing all feedback effects in the jump intensity that are linear and quadratic in past returns. A non-parametric fit on NYSE stock data sho…

The paper classifies biharmonic quadratic maps between spheres, proving their energy density properties.

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

Study optimal hedging for claims with random weights in discrete time.

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 …

We prove that the model-free typical (in the sense of Vovk) càdlàg price paths with mildly restricted downward jumps possess quadratic variation which does not depend on the specific sequence of partitions as long as these partitions are obtained from stopping times such that the oscillations of a path on the consecuti…

The study examines how quadratic inequalities affect distances in length spaces.

The paper studies optimal transport in linear quadratic systems and derives interpolation inequalities.

We consider a proximal operator given by a quadratic function subject to bound constraints and give an optimization algorithm using the alternating direction method of multipliers (ADMM). The algorithm is particularly efficient to solve a collection of proximal operators that share the same quadratic form, or if the qu…

Consider an analytic map of a neighborhood of 0 in a vector space to a Euclidean space. Suppose that this map takes all germs of lines passing through 0 to germs of circles. Such a map is called rounding. We introduce a natural equivalence relation on roundings and prove that any rounding, whose differential at 0 has r…

Abstract: Survey on quadratic Hessian equations, their properties, and open problems.

We consider support recovery in the quadratic logistic regression setting - where the target depends on both p linear terms $x_i$ and up to $p^2$ quadratic terms $x_i x_j$. Quadratic terms enable prediction/modeling of higher-order effects between features and the target, but when incorporated naively may involve solvi…

New conic quadratic formulations improve outlier detection in regression models.

Quadratic regression involves modeling the response as a (generalized) linear function of not only the features $x^{j_1}$ but also of quadratic terms $x^{j_1}x^{j_2}$. The inclusion of such higher-order "interaction terms" in regression often provides an easy way to increase accuracy in already-high-dimensional problem…

This paper classifies quadratic form parameters over integers and computes their Witt groups.

RL and DTSOC for final quadratic hedging performance studied.

Deep learning calibrates a rough Heston model to match implied volatilities.

Abstract perspective on quadratic programming for optimal portfolio allocation.

Proposes QDF to improve multi-step time-series forecasting.

The paper models asset pricing in a partially observed market using mean field game theory and exponential quadratic Gaussian framework.

Classifies extended Abelian Chern-Simons theories using quadratic modules.

Finite intersection numbers between horizontal foliations of quadratic differentials.

We attempt to unveil the fine structure of volatility feedback effects in the context of general quadratic autoregressive (QARCH) models, which assume that today's volatility can be expressed as a general quadratic form of the past daily returns. The standard ARCH or GARCH framework is recovered when the quadratic kern…

Python package for projecting onto quadratic hypersurfaces.

Proposes sparse QSVM for better generalization and interpretability.

Paper develops methods for non-quadratic loss low-rank matrix recovery.