arXiv research

Unified approach to domain generalization by aligning gradients and Hessians.

Unified framework for distribution shift estimation, explanation, and improvement.

Develops efficient methods for approximating densities of financial models with jumps.

The paper uses moment matching method for pricing spread options under Lévy models.

We extend the notion of multi-moment map to geometries defined by closed forms of arbitrary degree. We give fundamental existence and uniqueness results and discuss a number of essential examples, including geometries related to special holonomy. For forms of degree four, multi-moment maps are guaranteed to exist and a…

The paper derives risk measures for metalog distributions.

Developed moment estimators for affine stochastic volatility models.

We develop a family of techniques to align word embeddings which are derived from different source datasets or created using different mechanisms (e.g., GloVe or word2vec). Our methods are simple and have a closed form to optimally rotate, translate, and scale to minimize root mean squared errors or maximize the averag…

Proposes DWMD for better matching of hidden representations across domains.

Introduces generalized moment maps for almost Hermitian settings.

Paper improves basket option pricing for log-normal models.

We propose a new family of specification tests called kernel conditional moment (KCM) tests. Our tests are built on a novel representation of conditional moment restrictions in a reproducing kernel Hilbert space (RKHS) called conditional moment embedding (CMME). After transforming the conditional moment restrictions in…

The paper refines and generalizes worst-case law invariant convex risk measures.

Python package ajdmom simplifies moment formula derivation for jump diffusions.

The paper derives formulas for moments of a Student t distribution and applies them to quantify $L_p$-quantiles.

Moment Pooling reduces latent space dimensions in machine learning models.

We introduce a kernel method for manifold alignment (KEMA) and domain adaptation that can match an arbitrary number of data sources without needing corresponding pairs, just few labeled examples in all domains. KEMA has interesting properties: 1) it generalizes other manifold alignment methods, 2) it can align manifold…

ITSPACE improves covariance alignment faster than other methods.

A new method for aligning multiple distributions efficiently.

We find the exact worst-case tail probability for bounded kurtosis.

We deal with the efficient parallelization of Bayesian global optimization algorithms, and more specifically of those based on the expected improvement criterion and its variants. A closed form formula relying on multivariate Gaussian cumulative distribution functions is established for a generalized version of the mul…

Paper addresses online alignment of large language models under uncertain preference feedback.

Weibull weight-scale parameter $λ$ evolves during AdamW training, with alignment, injection, and decay forces driving its growth and relaxation.

Unsupervised domain adaptation aims to transfer and adapt knowledge learned from a labeled source domain to an unlabeled target domain. Key components of unsupervised domain adaptation include: (a) maximizing performance on the target, and (b) aligning the source and target domains. Traditionally, these tasks have eith…

A new method reduces the computational burden of safety alignment for large language models.

Learning rate needs to decrease with higher data moments for effective ICA in high dimensions.

Estimation of the operational risk capital under the Loss Distribution Approach requires evaluation of aggregate (compound) loss distributions which is one of the classic problems in risk theory. Closed-form solutions are not available for the distributions typically used in operational risk. However with modern comput…

Exact tail probability bounds for bounded kurtosis.

AOT aligns LLMs on distributional preferences via optimal transport.

A tractable pseudo-metric for non-parametric distributions via SPD geometry.

Sharp threshold found for aligning Gaussian-weighted graphs.

Adaptive importance sampling is a class of techniques for finding good proposal distributions for importance sampling. Often the proposal distributions are standard probability distributions whose parameters are adapted based on the mismatch between the current proposal and a target distribution. In this work, we prese…

Derives a series expansion for Asian option pricing with polynomial jump-diffusion moments.

Paper identifies tensor ranks via prior predictive matching, solving system of equations.

In this paper we propose a closed-form approximation for the price of basket options under a multivariate Black-Scholes model, based on Taylor expansions and the calculation of mixed exponential-power moments of a Gaussian distribution. Our numerical results show that a second order expansion provides accurate prices o…

Paper derives analytical formulas for NLD-CEV moments with regime switching.

Geometric framework detects concept frustration between human concepts and machine representations.

We present a framework for compactly summarizing many recent results in efficient and/or biologically plausible online training of recurrent neural networks (RNN). The framework organizes algorithms according to several criteria: (a) past vs. future facing, (b) tensor structure, (c) stochastic vs. deterministic, and (d…

A new sliced IGW distance for Gromov-Wasserstein alignment.

The paper characterizes functions of shallow ReLU NN denoisers under minimal norm constraints.

Associated to any manifold equipped with a closed form of degree >1 is an `L-infinity algebra of observables' which acts as a higher/homotopy analog of the Poisson algebra of functions on a symplectic manifold. In order to study Lie group actions on these manifolds, we introduce a theory of homotopy moment maps. Such a…

Paper characterizes optimal language model alignment methods.

We propose a novel method for closed-form predictive distribution modeling with neural nets. In quantifying prediction uncertainty, we build on Evidential Deep Learning, which has been impactful as being both simple to implement and giving closed-form access to predictive uncertainty. We employ it to model aleatoric un…

Iteratively reweighted least squares (IRLS) is a widely-used method in machine learning to estimate the parameters in the generalised linear models. In particular, IRLS for L1 minimisation under the linear model provides a closed-form solution in each step, which is a simple multiplication between the inverse of the we…

The paper examines optimal insurance design using Lambda-Value-at-Risk.

Improves inference-time alignment for diffusion models without updating weights.

In an efficient stock market, the log-returns and their time-dependent variances are often jointly modelled by stochastic volatility models (SVMs). Many SVMs assume that errors in log-return and latent volatility process are uncorrelated, which is unrealistic. It turns out that if a non-zero correlation is included in …

We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial moments. We establish parametric conditions which guarantee existen…