arXiv research

Paper finds optimal shapes for minimizing average lengths of billiard trajectories in specific polygons.

Algorithm learns mixtures of Markov chains and MDPs from short trajectories.

Geometric Brownian motion (GBM) is a key model for representing self-reproducing entities. Self-reproduction may be considered the definition of life [5], and the dynamics it induces are of interest to those concerned with living systems from biology to economics. Trajectories of GBM are distributed according to the we…

Algorithm learns stochastic system dynamics from data.

The paper develops a new theory to understand deep learning optimization.

We use splines and the Sasaki metric to analyze and compare manifold-valued trajectories.

Geometric Brownian motion (GBM) is a model for systems as varied as financial instruments and populations. The statistical properties of GBM are complicated by non-ergodicity, which can lead to ensemble averages exhibiting exponential growth while any individual trajectory collapses according to its time-average. A com…

We introduce a mixed-effects model to learn spatiotempo-ral patterns on a network by considering longitudinal measures distributed on a fixed graph. The data come from repeated observations of subjects at different time points which take the form of measurement maps distributed on a graph such as an image or a mesh. Th…

Estimates causal effects from patient trajectories using DeepACE model.

Improved trajectory prediction for team sports using sparse outputs.

LSS learns molecular trajectories from MD data.

This paper proposes recurrent neuron networks (RNNs) for a fingerprinting indoor localization using WiFi. Instead of locating user's position one at a time as in the cases of conventional algorithms, our RNN solution aims at trajectory positioning and takes into account the relation among the received signal strength i…

Stochastic gradient descent's long-term fluctuations are described by a diffusion limit.

Averaging recent model checkpoints speeds up training time.

A new framework for averaging spatio-temporal signals using optimal transport and soft alignments.

Sharp bounds established for Federated Averaging (FedAvg), improving convergence rates.

Learning the parameters of a (potentially partially observable) random field model is intractable in general. Instead of focussing on a single optimal parameter value we propose to treat parameters as dynamical quantities. We introduce an algorithm to generate complex dynamics for parameters and (both visible and hidde…

A new method, based on the original theory of conservation of sum of kinetic and potential energy defined for prices is proposed and applied on Dow Jones Industrials Average (DJIA). The general trends averaged over months or years gave a roughly conserved total energy, with three different potential energies, i.e. posi…

We propose a method to learn a distribution of shape trajectories from longitudinal data, i.e. the collection of individual objects repeatedly observed at multiple time-points. The method allows to compute an average spatiotemporal trajectory of shape changes at the group level, and the individual variations of this tr…

Adaptive stopping in MCMC using classifier-based dynamics

Improved averaging method for noisy observations converges strongly.

A framework learns multiscale dynamics from single trajectories using normalizing flows.

Hamiltonian dynamics-based algorithms achieve deterministic and accelerated convergence for convex optimization.

We propose a minimal theory of non-linear price impact based on a linear (latent) order book approximation, inspired by diffusion-reaction models and general arguments. Our framework allows one to compute the average price trajectory in the presence of a meta-order, that consistently generalizes previously proposed pro…

Deep neural networks are typically trained by optimizing a loss function with an SGD variant, in conjunction with a decaying learning rate, until convergence. We show that simple averaging of multiple points along the trajectory of SGD, with a cyclical or constant learning rate, leads to better generalization than conv…

Patient subtyping based on temporal observations can lead to significantly nuanced subtyping that acknowledges the dynamic characteristics of diseases. Existing methods for subtyping trajectories treat the evolution of clinical observations as a homogeneous process or employ data available at regular intervals. In real…

In this work we study generalization of neural networks in gradient-based meta-learning by analyzing various properties of the objective landscapes. We experimentally demonstrate that as meta-training progresses, the meta-test solutions, obtained after adapting the meta-train solution of the model, to new tasks via few…

Drone optimizes collaborative learning for neural networks.

In this paper, we propose new conditions guaranteeing that the trajectories of a mechanical control system can track any curve on the configuration manifold. We focus on systems that can be represented as forced affine connection control systems and we generalize the sufficient conditions for tracking known in the lite…

Presently the most successful approaches to semi-supervised learning are based on consistency regularization, whereby a model is trained to be robust to small perturbations of its inputs and parameters. To understand consistency regularization, we conceptually explore how loss geometry interacts with training procedure…

New model explains why metaorder impact estimation is hard with public data.

DSPI connects natural policy gradient to policy iteration, proving global convergence.

Paper develops methods for statistical inference in SGD with infinite variance.

Here we present DIVE: Data-driven Inference of Vertexwise Evolution. DIVE is an image-based disease progression model with single-vertex resolution, designed to reconstruct long-term patterns of brain pathology from short-term longitudinal data sets. DIVE clusters vertex-wise biomarker measurements on the cortical surf…

Patients initially diagnosed with early mild cognitive impairment (eMCI) are known to be a clinically heterogeneous group with very subtle patterns of brain atrophy. To examine the boarders between normal controls (NC) and eMCI, Magnetic Resonance Imaging (MRI) was extensively used as a non-invasive imaging modality to…

New measure EC assesses node contributions in nonlinear, time-varying systems.

Today, despite decades of developments in medicine and the growing interest in precision healthcare, vast majority of diagnoses happen once patients begin to show noticeable signs of illness. Early indication and detection of diseases, however, can provide patients and carers with the chance of early intervention, bett…

The wide variety of motions performed by the human arm during daily tasks makes it desirable to find representative subsets to reduce the dimensionality of these movements for a variety of applications, including the design and control of robotic and prosthetic devices. This paper presents a novel method and the result…

We consider the problem of finding optimal strategies that maximize the average growth-rate of multiplicative stochastic processes. For a geometric Brownian motion the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction o…

Federated Q-learning achieves linear speedup with heterogeneity, improving sample complexity.

Paper presents a probabilistic framework for diffusion synchronization.

A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph into a large network. We propose two complementary MCMC algorithms for sampling random graph homomorphisms and establish bounds on their mixing times and the …

RL and DTSOC for final quadratic hedging performance studied.

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…

The energy in a square membrane $Ω$ subject to constant viscous damping on a subset $ω\subset Ω$ decays exponentially in time as soon as $ω$ satisfies a geometrical condition known as the "Bardos-Lebeau-Rauch" condition. The rate $τ(ω)$ of this decay satisfies $τ(ω)= 2 \min(-μ(ω), g(ω))$ (see Lebeau [Math. Phys. Stud. …

New algorithm for robust circular coordinates in recurrent time series data.

The paper tackles video prediction by estimating conditional densities implicitly.

Optimal energy trading strategy for intraday markets using Hawkes processes.