arXiv research

Strong stability of ergodic iterations proven without ergodic driving sequence.

Learned factor graphs improve inference from time sequences using neural networks.

Memory-based models can learn to approximate Bayes-optimal predictors for non-stationary data.

We prove a bubble tree convergence theorem for a sequence of closed Hamiltonian Stationary Lagrangian surfaces with bounded areas and Willmore energies in a complete K{ä}hler surface. We also prove two strong compactness theorems on the space of Hamiltonian stationary Lagrangian tori in $\mathbb C^2$ and $\mathbb{CP}^2…

Estimates stationary mass and frequency from non-i.i.d. data.

For stationary harmonic maps between Riemannian manifolds, we provide a necessary and sufficient condition for the uniform interior and boundary gradient estimates in terms of the total energy of maps. We also show that if analytic target manifolds do not carry any harmonic S^2, then the singular sets of stationary map…

Estimates missing mass in Markovian sequences with linear runtime and near-optimal risk.

Process Monitoring involves tracking a system's behaviors, evaluating the current state of the system, and discovering interesting events that require immediate actions. In this paper, we consider monitoring temporal system state sequences to help detect the changes of dynamic systems, check the divergence of the syste…

We build a sequence of empirical measures on the space D(R_+,R^d) of R^d-valued càdlàg functions on R_+ in order to approximate the law of a stationary R^d-valued Markov and Feller process (X_t). We obtain some general results of convergence of this sequence. Then, we apply them to Brownian diffusions and solutions to …

New definition resolves ambiguity in non-stationary bandit classification.

Optimal switching regret for all segmentations in online convex optimisation.

Unsupervised framework learns symmetry from time sequences.

We study online prediction of bounded stationary ergodic processes. To do so, we consider the setting of prediction of individual sequences and build a deterministic regression tree that performs asymptotically as well as the best L-Lipschitz constant predictors. Then, we show why the obtained regret bound entails the …

For a sequence of immersed connected closed Hamiltonian stationary Lagrangian submaniolds in $\mathbb{C}^{n}$ with uniform bounds on their volumes and the total extrinsic curvatures, we prove that a subsequence converges either to a point or to a Hamiltonian stationary Lagrangian $n$-varifold locally uniformly in $C^{k…

Green functions on stationary varifolds established with inequalities and convergence results.

In this paper, we study the stochastic gradient descent (SGD) method for the nonconvex nonsmooth optimization, and propose an accelerated SGD method by combining the variance reduction technique with Nesterov's extrapolation technique. Moreover, based on the local error bound condition, we establish the linear converge…

Framework selects optimal historical data windows for non-stationary learning.

We consider a non-stationary sequential stochastic optimization problem, in which the underlying cost functions change over time under a variation budget constraint. We propose an $L_{p,q}$-variation functional to quantify the change, which yields less variation for dynamic function sequences whose changes are constrai…

Bandit Convex Optimization (BCO) is a fundamental framework for modeling sequential decision-making with partial information, where the only feedback available to the player is the one-point or two-point function values. In this paper, we investigate BCO in non-stationary environments and choose the \emph{dynamic regre…

We revisit the classical Douglas-Rachford (DR) method for finding a zero of the sum of two maximal monotone operators. Since the practical performance of the DR method crucially depends on the stepsizes, we aim at developing an adaptive stepsize rule. To that end, we take a closer look at a linear case of the problem a…

A Markov Decision Process (MDP) is a popular model for reinforcement learning. However, its commonly used assumption of stationary dynamics and rewards is too stringent and fails to hold in adversarial, nonstationary, or multi-agent problems. We study an episodic setting where the parameters of an MDP can differ across…

Study tackles non-stationary bandit convex optimization with new algorithms.

New algorithms minimize dynamic regret in non-stationary online learning.

The paper proves an energy identity for harmonic maps near singularities.

Faster convergence of kernel mean embeddings using variance information.

Formula derived for blow-up of quaternionic maps on Hyperkähler manifolds.

In this paper, we introduce a method for segmenting time series data using tools from Bayesian nonparametrics. We consider the task of temporal segmentation of a set of time series data into representative stationary segments. We use Gaussian process (GP) priors to impose our knowledge about the characteristics of the …

Video sequences contain rich dynamic patterns, such as dynamic texture patterns that exhibit stationarity in the temporal domain, and action patterns that are non-stationary in either spatial or temporal domain. We show that a spatial-temporal generative ConvNet can be used to model and synthesize dynamic patterns. The…

Algorithm minimizes control regret for non-stationary LQR systems.

We characterize stationary solutions to McKean-Vlasov equations on the circle.

This paper provides an algorithm for simulating improper (or noncircular) complex-valued stationary Gaussian processes. The technique utilizes recently developed methods for multivariate Gaussian processes from the circulant embedding literature. The method can be performed in $\mathcal{O}(n\log_2 n)$ operations, where…

Constructs minimal immersions with singularities.

Deep learning model predicts traffic flows across entire network for multiple steps ahead.

Paper proposes a hybrid model for financial time series prediction using sentiment analysis.

Study non-stationary distributions, proving risk bounds for density estimation.

New algorithms reduce dynamic regret for convex and smooth functions in non-stationary environments.

New algorithm reduces decision switching in dynamic environments.

We adapt the Douglas-Rachford (DR) splitting method to solve nonconvex feasibility problems by studying this method for a class of nonconvex optimization problem. While the convergence properties of the method for convex problems have been well studied, far less is known in the nonconvex setting. In this paper, for the…

Algorithm reduces regret in non-stationary bandits and meta-learning with optimal arms.

The goal of a learner, in standard online learning, is to have the cumulative loss not much larger compared with the best-performing function from some fixed class. Numerous algorithms were shown to have this gap arbitrarily close to zero, compared with the best function that is chosen off-line. Nevertheless, many real…

Established recurrent neural networks are well-suited to solve a wide variety of prediction tasks involving discrete sequences. However, they do not perform as well in the task of dynamical system identification, when dealing with observations from continuous variables that are unevenly sampled in time, for example due…

New insights into $p$-widths of surfaces, proving optimality and calculating constants.

New model controls memory in seq2seq tasks, revealing learning regimes.

Unified approach for non-stationary linear bandits with dynamic regret.

In this paper, we study the proximal gradient algorithm with extrapolation for minimizing the sum of a Lipschitz differentiable function and a proper closed convex function. Under the error bound condition used in [19] for analyzing the convergence of the proximal gradient algorithm, we show that there exists a thresho…

We consider the problem of minimizing the sum of a smooth function $h$ with a bounded Hessian, and a nonsmooth function. We assume that the latter function is a composition of a proper closed function $P$ and a surjective linear map $\cal M$, with the proximal mappings of $τP$, $τ> 0$, simple to compute. This problem i…

New algorithms for GLMs adapt to non-stationary contexts.

Estimates and infers multi-stage stationary treatment policies with variable selection.