This paper explores twisted Lagrangian tori in C^2 and their Hamiltonian stationarity.
problem Understanding the Hamiltonian stationarity of twisted Lagrangian tori in C^2.
method Investigation of differential geometry of twisted tori, including product and Chekanov's exotic tori.
result Only product tori are minimal under Hamiltonian deformations, indicating Chekanov's exotic tori are not area minimal.
L-HNNs improve Bayesian inference by reducing gradient requirements and improving ESS.
problem Efficient Bayesian inference with complex target densities.
method Latent Hamiltonian Neural Networks (L-HNNs) with NUTS, incorporating online error monitoring.
result L-HNNs in NUTS with online error monitoring required 1--2 orders of magnitude fewer numerical gradients and improved ESS by an order of magnitude.
Bayesian optimization uses BNNs as efficient surrogate models for expensive function evaluations.
problem Optimizing expensive objective functions using Gaussian process surrogates.
method Study of Bayesian neural networks (BNNs) as alternatives to standard Gaussian process (GP) surrogates for optimization.
result Infinite-width BNNs are particularly promising, especially in high dimensions.
TSFMs embed non-stationary time series data, revealing specific types of changes.
problem Understanding non-stationarity in TSFMs' embedding spaces.
method Examined mean shifts, variance changes, linear trends, and persistence in TSFMs.
result Different TSFMs exhibit distinct failure modes in detecting non-stationarity.
Deep RL agents suffer from transient non-stationarity, which ITER mitigates.
problem Transient non-stationarity in deep RL agents affects generalization.
method Iterated Relearning (ITER) transfers knowledge between networks to reduce non-stationarity.
result ITER improves deep RL agents' performance on generalization benchmarks.
TimeBridge addresses non-stationarity in long-term time series forecasting.
problem Non-stationarity in multivariate time series leads to spurious regressions and obscures long-term relationships.
method TimeBridge segments series into patches, applying Integrated Attention for short-term non-stationarity and Cointegrated Attention for long-term cointegration.
result TimeBridge achieves state-of-the-art performance in both short-term and long-term forecasting.
This paper compares stationarity in Bitcoin and S&P500 price indices.
problem Comparing stationarity in cryptocurrency and traditional stock market indices.
method Wide sense stationarity defined; Wiener-Khinchin Theorem applied; stationarity achieved through detrending and normalization of price returns.
result S&P500 price return achieves stationarity for 28 years with specific normalization windows, while Bitcoin's stationarity varies by segment and volatility.
New algorithm speeds up HMC by generating a warm start in O(d^1/4) iterations.
problem Unclear how many iterations of HMC are needed for high-dimensional sampling.
method Developed a non-Metropolized HMC that generates a warm start in O(d^1/4) iterations, followed by Metropolized HMC.
result Final complexity of O(d^1/4) is the fastest algorithm for high-accuracy sampling under strong log-concavity assumptions.
We use variational Gaussian approximations to analyze parametric models with unknown data-generating distributions.
problem Analyzing inference and learning in parametric models with unknown or intractable data-generating distributions.
method Replica method with variational Gaussian approximation in grand canonical formalism.
result Stationarity conditions adaptively determine parameters of the trial Hamiltonian for each dataset.
The paper explores various stationarity concepts in non-smooth optimization.
problem Understanding stationarity in non-smooth optimization problems.
method Introduction and discussion of different stationarity concepts for non-convex non-smooth functions.
result Clarification of the relationship among different stationarity concepts and their relevance in iterative methods.
Improved stock return prediction model handles noise and non-stationarity.
problem Predicting stock returns with robustness to noise and non-stationarity.
method Extended AROW algorithm to handle synchronous mini-batch updates and applied it to stock return prediction.
result The new model outperforms classical approaches in backtesting on S\&P500 stocks.
This paper considers regression tasks involving high-dimensional multivariate processes whose structure is dependent on some {known} graph topology. We put forth a new definition of time-vertex wide-sense stationarity, or joint stationarity for short, that goes beyond product graphs. Joint stationarity helps by reducin…
Master algorithm fails to detect non-stationarity in practical settings.
problem Non-Stationary Reinforcement Learning without prior knowledge.
method Master algorithm tested under various conditions, including piecewise stationary multi-armed bandits.
result Master's non-stationarity detection is ineffective for practical horizons, leading to performance similar to random restarting.
NOHD optimizes multi-agent systems by decomposing dynamics into irrotational and solenoidal components.
problem Non-stationarity and conflicting interests in multi-agent learning problems.
method NOHD (Newton Optimization on Helmholtz Decomposition) decomposes system dynamics into irrotational and solenoidal components.
result NOHD ensures quadratic convergence in purely irrotational and solenoidal systems and attracts to stable fixed points in general multi-agent systems.
Study classifies stock price data into stationary and non-stationary periods for mechanical trading.
problem Classifying stock price fluctuations into stationary and non-stationary periods for trading.
method Stationarity analysis using KM2O-Langevin theory and trend-based indicators for stationary periods, oscillator-based indicators for non-stationary periods. result Back testing confirms the strategy is a safe trading strategy with small maximum drawdown.
Study large deviation in stationarized fully lifted blirp interpolation.
problem Understanding atypical solutions in random optimization problems.
method Large deviation theory applied to fully lifted blirp interpolation.
result Elegant relations uncovered for fundamental interpolating parameters.
Study non-stationary bandits with resource constraints.
problem Maximize reward in a non-stationary environment with resource constraints.
method Propose new non-stationarity measure and use primal-dual analysis.
result Upper and lower bounds for non-stationary BwK problem.
Neural population activity often exhibits rich variability and temporal structure. This variability is thought to arise from single-neuron stochasticity, neural dynamics on short time-scales, as well as from modulations of neural firing properties on long time-scales, often referred to as "non-stationarity". To better …
Paper tackles uncertainty prediction for deep sequential regression.
problem Challenges in generating accurate uncertainty estimates for deep recurrent networks.
method Flexible method that generates symmetric and asymmetric uncertainty estimates without stationarity assumptions.
result Outperforms competitive baselines on both drift and non-drift scenarios.
Framework isolates causal effects from time series data, improving accuracy under non-stationarity and autocorrelation.
problem Causal inference in non-stationary, autocorrelated time series data.
method Decomposes time series into trend, seasonal, and residual components; performs component-specific causal analysis.
result Framework more accurately recovers ground-truth causal structure than state-of-the-art baselines, especially under strong non-stationarity and temporal autocorrelation.
Study uses RL to optimize dynamic portfolios, addressing non-stationarity and constraints.
problem Non-stationarity and investment constraints in dynamic portfolio optimization.
method Reinforcement learning with regime change variables and practical constraints integration.
result Enhanced prediction accuracy through incorporation of regime change variables.
SplitSGD dynamically adjusts learning rate based on stationarity detection.
problem Optimizing learning rates for stochastic optimization.
method SplitSGD uses a simple stationarity detection method to adjust learning rates.
result SplitSGD improves generalization and outperforms other adaptive methods.
Model analyzes RFQ markets using stochastic control to optimize dealer performance and inventory.
problem Optimizing market making in aggregator-routed RFQ markets with varying dealer performance scores.
method Two-tier stochastic control model that separates RFQ-level price competition from macro routing.
result Optimal controls can be expressed through derivatives of reduced Hamiltonians, leading to interpretable mappings from optimal win probabilities to optimal offsets.
This article develops a statistical test for the null hypothesis of strict stationarity of a discrete time stochastic process in the frequency domain. When the null hypothesis is true, the second order cumulant spectrum is zero at all the discrete Fourier frequency pairs in the principal domain. The test uses a window …
Develops RL algorithm for lifelong non-stationary environments.
problem Challenges of reinforcement learning in environments with persistent change.
method Formalizes lifelong non-stationarity, uses latent variable models, and leverages online learning and probabilistic inference.
result Substantial improvement in performance over non-reasoning approaches in lifelong non-stationary environments.
Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the latter suffers from intractable computation and can lead to overfitting. Taking the i…
New method for estimating and optimizing MDPs without stationarity.
problem Challenges in offline contextual MDP estimation without stationarity.
method Introduces a new adaptive estimation and cost optimization approach for contextual MDPs.
result First robust, theoretically backed method for offline contextual MDP estimation.
New conditions for ACD model consistency and normality.
problem Random number of durations in ACD model.
method Additional sufficient conditions for consistency and normality of QMLE.
result Finite mean of durations is required for consistency and normality.
Study on fake stationary Volterra Heston model for non-stationary processes.
problem Non-stationary nature of true Volterra equations.
method Weak notion of stationarity (fake stationary regime) for inhomogeneous affine Stochastic Volterra equations.
result Existence of limiting distributions in the long run, which may depend on initial state.
Graph-based methods for signal processing have shown promise for the analysis of data exhibiting irregular structure, such as those found in social, transportation, and sensor networks. Yet, though these systems are often dynamic, state-of-the-art methods for signal processing on graphs ignore the dimension of time, tr…
Proposes a probabilistic framework for stationary topological signals on simplicial complexes.
problem Complex data structures require new models and tools.
method Generalizes stationarity to topological signals on simplicial complexes.
result Defines topological power spectral density (PSD) for stationary signals.
Solves POMDPs with recurrent neural networks and natural policy gradient.
problem Non-stationarity in optimal policies of POMDPs.
method Integrates recurrent neural networks into natural policy gradient and temporal difference learning.
result Non-asymptotic theoretical guarantees for global optimality up to function approximation.
This work generalizes Hamiltonian mechanics using closed differential forms.
problem Hidden invariants in classical Hamiltonian mechanics.
method Establishes a novel correspondence between generalized Hamiltonian mechanics and multisymplectic geometry.
result Key theorems linking classical and generalized Hamiltonian systems.
A new QHR model extends HR model with a quadratic variance function.
problem Modeling volatility with greater flexibility and stationarity.
method Introducing a quadratic variance function to the HR model, maintaining Markovian property.
result Stationary distribution of the QHR model is Pearson type IV.
S&P 500 index data sampled at one-minute intervals over the course of 11.5 years (January 1989- May 2000) is analyzed, and in particular the Hurst parameter over segments of stationarity (the time period over which the Hurst parameter is almost constant) is estimated. An asymptotically unbiased and efficient estimator …
Classifies Hamiltonian and quasi-Hamiltonian manifolds with specific group actions.
problem Classifying specific types of manifolds under group actions.
method General classification of multiplicity free manifolds, focusing on rank one.
result Obtained numerous new concrete examples of quasi-Hamiltonian manifolds.
Study investigates Hamiltonian systems in fibered almost-symplectic manifolds.
problem Existence and properties of non-vertical fully-Hamiltonian vector fields in almost symplectic manifolds with Lagrangian fibrations.
method Investigates vector fields in 2n-dimensional almost symplectic manifolds with Lagrangian fibrations, focusing on partially-Hamiltonian and fully-Hamiltonian vector fields.
result Non-vertical fully-Hamiltonian vector fields exist under certain genericity conditions and can be reduced to families of symplectic-Hamiltonian vector fields.
A simple baseline outperforms deep learning methods in transportation forecasting.
problem The importance of stationarity and recurrent patterns in transportation data.
method A naive baseline based on average weekly patterns and linear regression.
result The baseline method achieves comparable or better results than state-of-the-art deep learning approaches.
Holographic energy equals Hamiltonian energy.
problem Equating holographic and Hamiltonian energies.
method Relative holographic and Hamiltonian energy comparison.
result Holographic energy is identical to Hamiltonian energy.
Develops Hamiltonian Score Matching and Generative Flows for machine learning.
problem Estimating score functions and designing generative models.
method Introduces Hamiltonian velocity predictors (HVPs) for score matching and generative flows.
result Hamiltonian Generative Flows (HGFs) rival leading generative modeling techniques.
Improved analysis for fair federated learning reduces dependence on noise floor.
problem Asymptotic stationarity in group fair federated learning with reduced noise floor dependence.
method DS FedProxGrad framework with inexact local proximal solutions and fairness regularization.
result Algorithm converges asymptotically to stationarity without dependence on a noise floor.
Summing Hamiltonian manifolds with a common submanifold.
problem Combining Hamiltonian manifolds with a shared submanifold.
method Establishing symplectic reduction and comparing Chern classes.
result Symplectic reduction of the sum agrees with the sum of reductions.
Proposes a new algorithm for graph-based semi-parametric contextual bandits.
problem Non-stationarity in human behavior and social interaction.
method SemiGraphTS algorithm for graph-based semi-parametric reward model.
result Derives an upper bound of cumulative regret for graph-based semi-parametric model.
The study examines stability of Hamiltonian Poisson integrators on both integrable and non-integrable systems.
problem Investigating stability properties of Hamiltonian Poisson integrators.
method Examples of Lotka-Volterra dynamics and numerical investigations of a non-integrable system are used.
result The existence of a modified Hamiltonian is crucial for the stability of Hamiltonian Poisson integrators.
The paper studies co-Hamiltonian diffeomorphisms on compact cosymplectic manifolds.
problem Fix-point theory and co-Hamiltonian diffeomorphisms on compact cosymplectic manifolds.
method Fix-point theory, Arnold's conjecture, co-Hofer norms, topologies, approximations lemmas.
result Minimum number of fix points for co-Hamiltonian diffeomorphisms is at least 1.
This paper addresses Gaussian Process regression over probability measures, revealing a non-stationarity issue between Euclidean and Wasserstein kernels.
problem Non-stationarity issue between Euclidean and Wasserstein kernels in Gaussian Process regression over probability measures.
method Assuming Euclidean input space, applying algebraic transformation based on uncovered non-stationarity relationship to create a non-stationary and Wasserstein-based Gaussian Process model.
result An algebraic transformation simplifies learning a non-stationary Gaussian Process model over probability measures.
Algorithm adapts to non-stationary rewards without prior knowledge.
problem Optimizing decisions in non-stationary environments without prior knowledge of changes.
method Optimization-based algorithm that restarts when non-stationarity is detected.
result Achieves tighter dynamic regret bound and is nearly minimax optimal.
New algorithms improve MCMC efficiency for complex distributions.
problem High variance and low effective sample size in MCMC samplers.
method Antithetic Riemannian Manifold and Quantum-Inspired Hamiltonian Monte Carlo.
result Improved effective sample size and variance reduction.