arXiv research

New method accelerates optimization in fixed time, improving convergence rates.

GenFlow optimizes faster, avoiding saddle points in fixed time.

Develops variable-lag Granger causality for more accurate time series analysis.

Develops variable-lag Granger causality and Transfer Entropy for time series analysis.

HOPE improves SSMs for long-memory tasks with robust initialization and training.

We describe a Markov latent state space (MLSS) model, where the latent state distribution is a decaying mixture over multiple past states. We present a simple sampling algorithm that allows to approximate such high-order MLSS with fixed time and memory costs.

New algorithm reduces expert prediction regret for two experts.

Paper studies continuous prediction with experts' advice using differential equations.

In this paper, we establish a framework for the analysis of linear parabolic equations on conical surfaces and use them to study the conical Ricci flow. In particular, we prove the long time existence of the conical Ricci flow for general cone angle and show that this solution has the optimal regularity, namely, the ti…

A coordinate-free proof of the Maximum Principle is provided in the specific case of an optimal control problem with fixed time. Our treatment heavily relies on a special notion of variation of curves that consist of a concatenation of integral curves of time-dependent vector fields with unit time component, and on the…

We study a specific \textit{combinatorial pure exploration stochastic bandit problem} where the learner aims at finding the set of arms whose means are above a given threshold, up to a given precision, and \textit{for a fixed time horizon}. We propose a parameter-free algorithm based on an original heuristic, and prove…

Study geometric flows with varying parameters and prove continuous dependence.

A new framework reduces traffic congestion by 36%.

In the compagnion paper [Marginal density expansions for diffusions and stochastic volatility, part I] we discussed density expansions for multidimensional diffusions $(X^1,...,X^d)$, at fixed time $T$ and projected to their first $l$ coordinates, in the small noise regime. Global conditions were found which replace th…

We introduce a simple approach for testing the reliability of homogeneous generators and the Markov property of the stochastic processes underlying empirical time series of credit ratings. We analyze open access data provided by Moody's and show that the validity of these assumptions - existence of a homogeneous genera…

We study quaternionic stochastic areas processes associated with Brownian motions on the quaternionic rank-one symmetric spaces $\mathbb{H}H^n$ and $\mathbb{H}P^n$. The characteristic functions of fixed-time marginals of these processes are computed and allows for the explicit description of their corresponding large-t…

This paper extends Markovian projections to semimartingales with jumps.

A pairs trading model with time-varying volatility using stochastic control.

Estimates drift functions in SDEs using denoising diffusion models.

Models for sequential data such as the recurrent neural network (RNN) often implicitly model a sequence as having a fixed time interval between observations and do not account for group-level effects when multiple sequences are observed. We propose a model for grouped sequential data based on the RNN that accounts for …

Recent work on Bayesian optimization has shown its effectiveness in global optimization of difficult black-box objective functions. Many real-world optimization problems of interest also have constraints which are unknown a priori. In this paper, we study Bayesian optimization for constrained problems in the general ca…

We study two-dimensional stochastic differential equations (SDEs) of McKean--Vlasov type in which the conditional distribution of the second component of the solution given the first enters the equation for the first component of the solution. Such SDEs arise when one tries to invert the Markovian projection developed …

Given discrete time observations over a fixed time interval, we study a nonparametric Bayesian approach to estimation of the volatility coefficient of a stochastic differential equation. We postulate a histogram-type prior on the volatility with piecewise constant realisations on bins forming a partition of the time in…

The paper develops deep learning models for personalized treatment rules in survival analysis.

We consider an investor who seeks to maximize her expected utility derived from her terminal wealth relative to the maximum performance achieved over a fixed time horizon, and under a portfolio drawdown constraint, in a market with local stochastic volatility (LSV). In the absence of closed-form formulas for the value …

Kernel Induced Random Survival Forests (KIRSF) is a statistical learning algorithm which aims to improve prediction accuracy for survival data. As in Random Survival Forests (RSF), Cumulative Hazard Function is predicted for each individual in the test set. Prediction error is estimated using Harrell's concordance inde…

Many algorithms for data analysis exist, especially for classification problems. To solve a data analysis problem, a proper algorithm should be chosen, and also its hyperparameters should be selected. In this paper, we present a new method for the simultaneous selection of an algorithm and its hyperparameters. In order…

We propose a framework to study the optimal liquidation strategy in a limit order book for large-tick stocks, with spread equal to one tick. All order book events (market orders, limit orders and cancellations) occur according to independent Poisson processes, with parameters depending on price move directions. Our goa…

Extends PPI to sequential setting, improving inference over time.

Paper proposes deep learning for operators in semigroups, improving dynamical system modeling.

The method of cointegration in regression analysis is based on an assumption of stationary increments. Stationary increments with fixed time lag are called integration I(d). A class of regression models where cointegration works was identified by Granger and yields the ergodic behavior required for equilibrium expectat…

Let (X,L) be a polarized compact manifold, i.e. L is an ample line bundle over X and denote by H the infinite dimensional space of all positively curved Hermitian metrics on L equipped with the Mabuchi metric. In this short note we show, using Bedford-Taylor type envelope techniques developed in the authors previous wo…

The Trouvé group $\mathcal G_{\mathcal A}$ from image analysis consists of the flows at a fixed time of all time-dependent vectors fields of a given regularity $\mathcal A(\mathbb R^d,\mathbb R^d)$. For a multitude of regularity classes $\mathcal A$, we prove that the Trouvé group $\mathcal G_{\mathcal A}$ coincides wi…

New method predicts spatio-temporal data with short and long-range dependence.

Study optimal portfolios in a non-Markovian regime-switching model with random time horizon.

The influence of Commodity Trading Advisors (CTA) on the price process is explored with the help of a simple model. CTA managers are taken to be Kelly optimisers, which invest a fixed proportion of their assets in the risky asset and the remainder in a riskless asset. This requires regular adjustment of the portfolio w…

Study local expansions of continuous-time processes using Ito signature properties.

This paper models short rates with jumps using PDEs.

Reinforcement learning is explored as a candidate machine learning technique to enhance existing analytical solutions for optimal trade execution with elements from the market microstructure. Given a volume-to-trade, fixed time horizon and discrete trading periods, the aim is to adapt a given volume trajectory such tha…

We consider the optimal stopping problem $v^{(\eps)}:=\sup_{τ\in\mathcal{T}_{0,T}}\mathbb{E}B_{(τ-\eps)^+}$ posed by Shiryaev at the International Conference on Advanced Stochastic Optimization Problems organized by the Steklov Institute of Mathematics in September 2012. Here $T>0$ is a fixed time horizon, $(B_t)_{0\le…

Continuous time Bayesian networks (CTBNs) describe structured stochastic processes with finitely many states that evolve over continuous time. A CTBN is a directed (possibly cyclic) dependency graph over a set of variables, each of which represents a finite state continuous time Markov process whose transition model is…

Paper presents robust confidence sequences for means with known moment bounds and arbitrary corruption.

Optimizes trading large volumes of volatile assets with fast mean-reverting volatility.

We study a novel multi-armed bandit problem that models the challenge faced by a company wishing to explore new strategies to maximize revenue whilst simultaneously maintaining their revenue above a fixed baseline, uniformly over time. While previous work addressed the problem under the weaker requirement of maintainin…

A method for learning with autoregressive chain-of-thoughts.

We quantitatively investigate the ideas behind the often-expressed adage `it takes volume to move stock prices', and study the statistical properties of the number of shares traded $Q_{Δt}$ for a given stock in a fixed time interval $Δt$. We analyze transaction data for the largest 1000 stocks for the two-year period 1…

Binary embedding of high-dimensional data requires long codes to preserve the discriminative power of the input space. Traditional binary coding methods often suffer from very high computation and storage costs in such a scenario. To address this problem, we propose Circulant Binary Embedding (CBE) which generates bina…

uHMC achieves fast mixing in high dimensions with gradient evaluations.