arXiv research

New method learns stochastic process representations without exact reconstruction.

This work tackles representation learning by introducing stochastic competition-based activations.

Study multi-task learning with low-rank representation in stochastic linear bandits.

Paper analyzes error in stochastic approximation for discontinuous functions.

New approach solves utility maximization problems using Delta family.

ST-MAML tackles task ambiguity in meta-learning by encoding tasks with stochastic representations.

We present a deep recurrent neural network architecture to solve a class of stochastic optimal control problems described by fully nonlinear Hamilton Jacobi Bellmanpartial differential equations. Such PDEs arise when one considers stochastic dynamics characterized by uncertainties that are additive and control multipli…

Study forward investment performance in semimartingale markets with stochastic factors.

The article provides representations of exchange option prices under SVJD dynamics.

In this article I will prove new representation for the Levi-Civita connection in terms of the stochastic flow corresponding to Brownian motion on manifold.

Paper introduces PRMs to learn non-Markovian stochastic rewards for reinforcement learning.

In the context of stochastic volatility models, we study representation formulas in terms of expectations for the power series' coefficients associated to the call price-function. As in a recent paper by Antonelli and Scarlatti the expansion is done w.r.t. the correlation between the noises driving the underlying asset…

A semi-supervised framework using stochastic interpolation and latent representations.

Contrastive learning harms minority group representations, affecting downstream tasks.

We extend Stochastic Gradient Variational Bayes to perform posterior inference for the weights of Stick-Breaking processes. This development allows us to define a Stick-Breaking Variational Autoencoder (SB-VAE), a Bayesian nonparametric version of the variational autoencoder that has a latent representation with stocha…

Simplified calculus for semimartingales makes complex transformations easier.

Study on how optimal representations emerge during deep learning training, focusing on the role of implicit regularization.

This paper studies a class of non$-$Markovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a $Z-$constrained BSDE, with dynamics associated to a non singular underlying forward process. Du…

π-GNN learns soft permutations for graph representations, improving graph classification and regression.

The paper develops a deep signature approach for option pricing under non-Markovian stochastic volatility models.

Paper applies theorem to find optimal investment boundary in stochastic capacity expansion.

Enhances deep kernel learning with stochastic latent variables for better model regularization.

Representations are fundamental to artificial intelligence. The performance of a learning system depends on the type of representation used for representing the data. Typically, these representations are hand-engineered using domain knowledge. More recently, the trend is to learn these representations through stochasti…

The paper explains emergent phenomena in deep learning using entropic forces.

Study max- and min-stability under first-order stochastic dominance, finding new functional characterizations.

Unified kernel framework extends to stochastic systems, improving numerical stability.

Contrastive learning struggles with class collapse and feature suppression, revealing bias towards simpler solutions.

We develop a stochastic target representation for Ricci flow and normalized Ricci flow on smooth, compact surfaces, analogous to Soner and Touzi's representation of mean curvature flow. We prove a verification/uniqueness theorem, and then consider geometric consequences of this stochastic representation. Based on this …

We prove a geometrically meaningful stochastic representation of the derivative of the heat semigroup on sub-Riemannian manifolds with tranverse symmetries. This representation is obtained from the study of Bochner-Weitzenbock type formulas for sub-Laplacians on 1-forms. As a consequence, we prove new hypoelliptic heat…

New algorithm improves learning efficiency in multi-task contextual bandits.

Graph convolutional networks adapt the architecture of convolutional neural networks to learn rich representations of data supported on arbitrary graphs by replacing the convolution operations of convolutional neural networks with graph-dependent linear operations. However, these graph-dependent linear operations are d…

Although stochastic approximation learning methods have been widely used in the machine learning literature for over 50 years, formal theoretical analyses of specific machine learning algorithms are less common because stochastic approximation theorems typically possess assumptions which are difficult to communicate an…

The paper provides an efficient method to price path-dependent derivatives using multiscale stochastic volatility models.

In an incomplete market, with incompleteness stemming from stochastic factors imperfectly correlated with the underlying stocks, we derive representations of homothetic (power, exponential and logarithmic) forward performance processes in factor-form using ergodic BSDE. We also develop a connection between the forward …

Revisits stochastic collocation with exponential splines for option pricing.

Developed a diffusion model on spherical data, addressing geometric and stochastic challenges.

Researchers develop explicit approximations for European put options in stochastic volatility models.

This paper addresses law invariant coherent risk measures and their Kusuoka representations. By elaborating the existence of a minimal representation we show that every Kusuoka representation can be reduced to its minimal representation. Uniqueness -- in a sense specified in the paper -- of the risk measure's Kusuoka r…

Optimizes portfolios with constraints and stochastic factors, deriving explicit solutions.

SSDMs generate quantum states directly, outperforming classical methods.

New method finds balanced clusters in graphs using auxiliary information.

In this paper we investigate general linear stochastic volatility models with correlated Brownian noises. In such models the asset price satisfies a linear SDE with coefficient of linearity being the volatility process. This class contains among others Black-Scholes model, a log-normal stochastic volatility model and H…

High-dimensional representations often have a lower dimensional underlying structure. This is particularly the case in many decision making settings. For example, when the representation of actions is generated from a deep neural network, it is reasonable to expect a low-rank structure whereas conventional structures l…

Proof confirms perfect representation in deep learning models.

Given a second order partial differential operator $L$ satisfying the strong Hörmander condition with corresponding heat semigroup $P_t$, we give two different stochastic representations of $dP_t f$ for a bounded smooth function $f$. We show that the first identity can be used to prove infinite lifetime of a diffusion …

Deep reinforcement learning (RL) algorithms can use high-capacity deep networks to learn directly from image observations. However, these high-dimensional observation spaces present a number of challenges in practice, since the policy must now solve two problems: representation learning and task learning. In this work,…

Optimal estimator derived for partially observable LTI systems.

GENESIS-V2 infers unordered object representations without iterative refinement.