arXiv research

A new method uses deep learning to efficiently sample rare transitions for estimating committor functions.

Develops a flexible model for regime transitions in time series data.

The study proves unique harmonic functions and combinatorial properties of vertex-transitive graphs.

Neural models learn continuous-time Markov chain transition rates from data.

The equivalence of principal bundles with transitive Lie groupoids due to Ehresmann is a well known result. A remarkable generalisation of this equivalence, due to Mackenzie, is the equivalence of principal bundle extensions with those transitive Lie groupoids over the total space of a principal bundle, which also admi…

We derive the exact solution of a one-dimensional Markov functional model with log-normally distributed interest rates in discrete time. The model is shown to have two distinct limiting states, corresponding to small and asymptotically large volatilities, respectively. These volatility regimes are separated by a phase …

New neural processes use stacked Markov operators to improve flexibility.

New algorithm achieves data-dependent regret bounds in MDPs with unknown transitions.

In this paper we study how to learn stochastic, multimodal transition dynamics in reinforcement learning (RL) tasks. We focus on evaluating transition function estimation, while we defer planning over this model to future work. Stochasticity is a fundamental property of many task environments. However, discriminative f…

We focus on variational inference in dynamical systems where the discrete time transition function (or evolution rule) is modelled by a Gaussian process. The dominant approach so far has been to use a factorised posterior distribution, decoupling the transition function from the system states. This is not exact in gene…

New algorithms achieve no-regret learning even with adversarial transitions and losses.

The existence of nonconstant harmonic Dirichlet functions on a Cayley graph of a discrete group is equivalent to the nonvanishing of the first L2-cohomology of the given group. It was first proven by Cheeger and Gromov that such functions do not exists on the Cayley-graph of an amenable group. The result was extended u…

A multi-task GP model tracks time-varying transition probabilities between two states.

The committor function is a central object of study in understanding transitions between metastable states in complex systems. However, computing the committor function for realistic systems at low temperatures is a challenging task, due to the curse of dimensionality and the scarcity of transition data. In this paper,…

Predicting labels of nodes in a network, such as community memberships or demographic variables, is an important problem with applications in social and biological networks. A recently-discovered phase transition puts fundamental limits on the accuracy of these predictions if we have access only to the network topology…

Proposes a method for approximating transition densities of SDEs driven by gamma processes.

New methods use machine learning to simulate rare transitions in molecular systems.

FourNet approximates financial transition densities using Fourier transforms.

Deep reinforcement learning method finds rare events in complex systems.

Study phase transitions with prescribed mean curvature in Riemannian manifolds.

We obtain explicit formulas for the trivialization functions of the ${\rm SU}(3)$ principal bundle $G_2 \to S^6$ over two affine charts. We also calculate the explicit transition function of this fibration over the equator of the six-sphere. In this way we obtain a new proof of the known fact that this fibration corres…

PQR estimates reward functions from actions and states without assuming state-only rewards.

Abstract: Investigates the role of activation functions in neural networks and their physical basis.

The paper develops ML algorithms for calibrating credit rating transition models for high and low default portfolios.

New algorithms reduce regret in reinforcement learning with MNL approximations.

Study shows strong min-max principle for phase transitions.

ISOKANN learns collective variables and effective dynamics for metastable transitions.

Develops a new framework for conditional independence.

Study on phase transitions on surfaces using Allen-Cahn equation.

A new method for ILO with transition model disparity using an intermediary policy.

Study shows Merton model limits to Poisson process with log-normal intensity, improving default portfolio prediction.

e-GGPs learn graph vertex transitions over time.

We present a global optimization algorithm for clustering data given the ratio of likelihoods that each pair of data points is in the same cluster or in different clusters. To define a clustering solution in terms of pairwise relationships, a necessary and sufficient condition is that belonging to the same cluster sati…

ML PCA detects phase transitions in muon spectroscopy data.

We identify a new variational inference scheme for dynamical systems whose transition function is modelled by a Gaussian process. Inference in this setting has either employed computationally intensive MCMC methods, or relied on factorisations of the variational posterior. As we demonstrate in our experiments, the fact…

In this paper, we study the sensitivity of the spectral clustering based community detection algorithm subject to a Erdos-Renyi type random noise model. We prove phase transitions in community detectability as a function of the external edge connection probability and the noisy edge presence probability under a general…

Efficient RL algorithm for multinomial logistic MDPs with provable guarantees.

Study on neural networks' storage capacity and solution space structure.

Develops CLTs for Markov chain transition probabilities and policies.

Wide neural networks become linear, but adding bottlenecks makes them bilinear or multilinear.

A new RL paradigm reduces state-action-value function approximation inefficiency.

Generative Stochastic Networks (GSNs) have been recently introduced as an alternative to traditional probabilistic modeling: instead of parametrizing the data distribution directly, one parametrizes a transition operator for a Markov chain whose stationary distribution is an estimator of the data generating distributio…

Paper tackles transfer RL under unobserved context, developing methods to reduce bias.

New algorithm reduces suboptimality in imitation learning to nearly optimal levels.

Value functions struggle to represent transition dynamics, impacting statistical efficiency.

A new method learns robust policies from offline data with latent structures.

Study refracted skew Brownian motion, find densities and asymptotics.

PCA improves detection of phase transitions in muon spectroscopy data from various materials.