arXiv research

A simple log-transform fixes heavy-tailed data for generative models.

Paper derives a simplified formula for Expected Improvement using log-transformed data.

Several classification methods assume that the underlying distributions follow tree-structured graphical models. Indeed, trees capture statistical dependencies between pairs of variables, which may be crucial to attain low classification errors. The resulting classifier is linear in the log-transformed univariate and b…

Firm size data usually do not show the normality that is often assumed in statistical analysis such as regression analysis. In this study we focus on two firm size data: the number of employees and sale. Those data deviate considerably from a normal distribution. To improve the normality of those data we transform them…

Transformers can efficiently approximate nonparametric regression with minimal parameters and sequences.

The study shows conditions for elliptic surfaces without 1-handles.

HFformer outperforms LSTM in high-frequency trading with multiple signals.

The paper improves transformer generalization bounds using rank-dependent covering number bounds.

A new iterative low complexity algorithm has been presented for computing the Walsh-Hadamard transform (WHT) of an $N$ dimensional signal with a $K$-sparse WHT, where $N$ is a power of two and $K = O(N^α)$, scales sub-linearly in $N$ for some $0 < α< 1$. Assuming a random support model for the non-zero transform domain…

We study topological properties of log-symplectic structures and produce examples of compact manifolds with such structures. Notably we show that several symplectic manifolds do not admit log-symplectic structures and several log-symplectic manifolds do not admit symplectic structures, for example #m CP^2 # n bar(CP^2)…

Unsupervised learning of probabilistic models is a central yet challenging problem in machine learning. Specifically, designing models with tractable learning, sampling, inference and evaluation is crucial in solving this task. We extend the space of such models using real-valued non-volume preserving (real NVP) transf…

New linear flows using exponential of linear transformations improve generative models.

Proposes a new Huber loss combining absolute and quadratic properties.

Computes Vafa-Witten invariants of 3-manifolds.

End-to-end neural network based approaches to audio modelling are generally outperformed by models trained on high-level data representations. In this paper we present preliminary work that shows the feasibility of training the first layers of a deep convolutional neural network (CNN) model to learn the commonly-used l…

The paper revisits expected signatures in semimartingale models, providing new formulae and simplifying complexity.

Analytical pricing formulas and Greeks are obtained for European and American basket put options using Mellin transforms. We assume assets are driven by geometric Brownian motion which exhibit correlation and pay a continuous dividend rate. A novel approach to numerical Mellin inversion is achieved via the fast Fourier…

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

This paper compares Transformers and RNNs in various tasks, showing size differences.

New private algorithms for online learning improve regret in high privacy regimes.

Algorithm learns means of spherical Gaussian mixtures efficiently in low dimensions.

A new method uses Transformers for efficient prediction of marked point processes.

Transformation models are a very important tool for applied statisticians and econometricians. In many applications, the dependent variable is transformed so that homogeneity or normal distribution of the error holds. In this paper, we analyze transformation models in a high-dimensional setting, where the set of potent…

Paper uses Transformers to predict intraday volume ratio with high accuracy.

Deep signature/log-signature FBSDE algorithm improves accuracy and training time.

We study revenue optimization learning algorithms for repeated second-price auctions with reserve where a seller interacts with multiple strategic bidders each of which holds a fixed private valuation for a good and seeks to maximize his expected future cumulative discounted surplus. We propose a novel algorithm that h…

Study of circle homeomorphisms with square summable diamond shears.

We solve a class of control problems with fuel constraint by means of the log-Laplace transforms of $J$-functionals of Dawson-Watanabe superprocesses. This solution is related to the superprocess solution of quasilinear parabolic PDEs with singular terminal condition. For the probabilistic verification proof, we develo…

Improves sequence modeling with a flow-based recurrent mixture density network.

New sampling method using regularized Wasserstein proximal for Gibbs distributions.

In this paper we consider a jump-diffusion dynamic whose parameters are driven by a continuous time and stationary Markov Chain on a finite state space as a model for the underlying of European contingent claims. For this class of processes we firstly outline the Fourier transform method both in log-price and log-strik…

Resurgence of Joyce structures gauged to a standard form using gauge transformations.

A new model detects financial bubbles with high accuracy.

We aim to model unknown file processing. As the content of log files often evolves over time, we established a dynamic statistical model which learns and adapts processing and parsing rules. First, we limit the amount of unstructured text by focusing only on those frequent patterns which lead to the desired output tabl…

Multisections generalize trisections for 4-manifolds, allowing complex operations and explicit diagrams.

Exposes new connections between weighted Kähler-Ricci solitons and Ricci-flat Kähler cone metrics.

This paper is the first arising from our project announced in math.AG/0211094, "Affine manifolds, log structures, and mirror symmetry." We aim to study mirror symmetry by studying the log structures of Illusie-Fontaine and Kato on degenerations of Calabi-Yau manifolds. The basic idea is that one can associate to certai…

The square root of Fredholm determinants causes numerical instabilities in option pricing models.

GBHT uses gradient boosting for density estimation with theoretical guarantees.

Large Transformer models routinely achieve state-of-the-art results on a number of tasks but training these models can be prohibitively costly, especially on long sequences. We introduce two techniques to improve the efficiency of Transformers. For one, we replace dot-product attention by one that uses locality-sensiti…

Transformers approximate Bayesian posteriors but not exactly.

Develops a functional generalization of Eldan's stochastic localization for optimization and privacy.

Log-Normal Multiplicative Dynamics improves low-precision training of neural networks.

In this study we suggest a portfolio selection framework based on option-implied information and multivariate non-Gaussian models. The proposed models incorporate skewness, kurtosis and more complex dependence structures among stocks log-returns than the simple correlation matrix. The two models considered are a multiv…

A new transformer model uses Monte Carlo methods for sequence prediction.

Study large deviations in fractional volatility models with non-Gaussian volatility.

Study develops ensemble machine learning framework for predicting groundwater heavy metal pollution.

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…