Solutions to the wave equation on de Sitter-Schwarzschild space with smooth initial data on a Cauchy surface are shown to decay exponentially to a constant at temporal infinity, with corresponding uniform decay on the appropriately compactified space.
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48 results for “temporal decay”
HED Score improves temporal evaluation of detection accuracy.
problem Temporal agnosticism in existing evaluation frameworks for non-stationary processes.
method Measure-theoretic HED Score integrating exponentially decaying kernel over posterior probability stream.
result HED Score achieves 388.8% improvement over ROC/AUC on NSL-KDD benchmark.
Quantum systems with scrambling improve temporal information processing, but scaling requires exponential overhead.
problem Scalability and memory retention of quantum reservoirs in temporal information processing.
method Examined a quantum reservoir processing framework with scrambling reservoirs modeled by high-order unitary designs, analyzed in noiseless and noisy settings.
result Memory retention improves exponentially with reservoir size but worsens with reservoir iterations, requiring exponential shot overhead for scaling.
The probability of default (PD) estimation is an important process for financial institutions. The difficulty of the estimation depends on the correlations between borrowers. In this paper, we introduce a hierarchical Bayesian estimation method using the beta binomial distribution and consider a multi-year case with a …
The paper studies harmonic map heat flow stability and decay rates.
problem Analyzing stability and decay rates of harmonic map heat flow solutions.
method Use of homogeneous Besov space for small initial data and self-similar decay assumption.
result Decay rates for solutions of the harmonic map flow of the form and self-similar decay under stronger initial conditions.
Proposes a new model for complex multivariate event data.
problem Modeling complex multivariate event data with spatio-temporal dynamics.
method Integrates spatial information into latent state evolution through learned temporal and spatial decay dynamics.
result Successfully recovers sensible temporal and spatial intensity structure in multivariate spatio-temporal point patterns.
Parameterized state space models in the form of recurrent networks are often used in machine learning to learn from data streams exhibiting temporal dependencies. To break the black box nature of such models it is important to understand the dynamical features of the input driving time series that are formed in the sta…
T-KAN improves HFT LOB forecasting with learnable splines.
problem Alpha decay in HFT LOB forecasting models.
method T-KAN uses learnable B-spline activation functions to model market signals.
result 19.1% relative improvement in F1-score at k = 100 horizon.
Introduces recency bias to improve time-series forecasting.
problem Lack of recency bias in standard Transformer attention for time-series data.
method Reweights attention scores with a smooth heavy-tailed decay to emphasize nearby observations.
result Recency-biased attention consistently improves sequential modeling and achieves competitive performance on time-series forecasting benchmarks.
We found that factors decay over time, with momentum fitting best.
problem Understanding how factors decay over time and their impact on performance.
method Derived a hyperbolic decay model for factors, tested against linear and exponential alternatives.
result Momentum exhibits hyperbolic decay, outperforming linear and exponential models.
Temporal networks representing a stream of timestamped edges are seemingly ubiquitous in the real-world. However, the massive size and continuous nature of these networks make them fundamentally challenging to analyze and leverage for descriptive and predictive modeling tasks. In this work, we propose a general framewo…
We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with longer memory than those considered in the current literature. We show that severa…
RainfallBench benchmarks GNSS-based precipitation nowcasting models, addressing complex meteorological challenges.
problem Evaluation of precipitation nowcasting models in meteorology is insufficient due to focus on periodic variables.
method RainfallBench dataset and specialized evaluation protocols for multi-scale, multi-resolution, and extreme rainfall events.
result Bi-Focus Precipitation Forecaster (BFPF) enhances rainfall time series forecasting by incorporating domain-specific priors.
Study shows Merton model limits to Poisson process with log-normal intensity, improving default portfolio prediction.
problem Improving prediction of default portfolios using complex models.
method Applying Merton model with log-normal intensity function to Poisson process, discussing temporal correlation effects.
result Power decay model provides better generalization for long-term default portfolio data.
GRU-D detects age-specific missing patterns in vital signs.
problem Temporal missingness in clinical time series data.
method Gated recurrent unit with decay mechanisms (GRU-D) trained on MIMIC-IV vital signs.
result GRU-D achieves AUROC 0.780 and AUPRC 0.810 on bootstrapped data.
Look-Ahead-Bench: a Standardized Benchmark of Look-ahead Bias in Point-in-Time LLMs for Financecs.AI
Look-Ahead-Bench evaluates financial LLMs for lookahead bias, revealing significant differences in model performance.
problem Measuring and mitigating lookahead bias in financial LLMs.
method Standardized benchmark evaluating model behavior in practical financial scenarios, analyzing performance decay across market regimes.
result Standard LLMs exhibit significant lookahead bias, while Pitinf models show improved generalization and reasoning abilities.
Diffusion Transformer Captures Spatial-Temporal Dependencies: A Theory for Gaussian Process Datacs.LG
Diffusion Transformer captures spatial-temporal dependencies in sequential data.
problem Capturing rich spatial and temporal dependencies in sequential data.
method Established theoretical guarantees for diffusion transformers learning Gaussian process data.
result Spatial-temporal dependencies are captured within attention layers of diffusion transformers.
Study on eigenvalue distribution of correlated time series, showing deformation of Marchenko-Pastur distribution.
problem Eigenvalue distribution of Wishart matrix with temporal correlation.
method Analysis of moments and convergence to deformed Marchenko-Pastur distribution for Gaussian process with temporal correlation.
result Eigenvalue distribution converges to deformed Marchenko-Pastur distribution with longer tail and higher peak.
Using a proprietary dataset of meta-orders and prediction signals, and assuming a quasi-linear impact model, we deconvolve market impact from past correlated trades and a predictable return component to elicit the temporal dependence of the market impact of a single daily meta-order, over a ten day horizon in various e…
STAD adapts models to evolving time-based data shifts.
problem Gradual distribution shifts over time challenge existing test-time adaptation methods.
method Bayesian filtering method that learns time-varying dynamics in hidden features.
result STAD excels in handling small batch sizes and label shift on real-world data.
Continuous Hidden Markov Models for Equity Returns
problem Generating synthetic equity returns that match real return characteristics
method Continuous Hidden Markov Models
result Recovered volatility clustering and narrowed kurtosis gap
Transformers simplify modeling of small longitudinal cohort data by reducing parameters and incorporating attention mechanisms.
problem Challenges in modeling longitudinal cohort data due to complex temporal dependencies and large dataset requirements.
method Simplified transformer architecture with attention mechanism, autoregressive model, and kernel-based temporal decay.
result The approach recovers contextual dependencies even with small datasets, identifying temporal patterns in stress and mental health.
Improves spatio-temporal forecasting by reducing errors between training and inference.
problem Accumulation of small errors in Seq2Seq models during inference due to different distributions of training and inference phases.
method Curriculum learning based on Temporal Progressive Growing Sampling to replace some ground-truth context with generated predictions.
result Better models long-term dependencies and outperforms baseline approaches on two datasets.
The study uses the Merton model to estimate PD and finds a phase transition affecting convergence speed.
problem Estimating the probability of default (PD) using limited historical data.
method Adopted the Merton model and analyzed phase transitions in default correlation.
result PD estimation converges slowly when temporal correlation decays by power law less than one.
Improved TD learning with tail averaging and regularization achieves optimal convergence rates.
problem Convergence analysis of TD learning with linear function approximation.
method Tail-averaging and regularization applied to TD learning algorithm.
result Achieves optimal convergence rate in expectation and with high probability.
Sequence models assign probabilities to variable-length sequences such as natural language texts. The ability of sequence models to capture temporal dependence can be characterized by the temporal scaling of correlation and mutual information. In this paper, we study the mutual information of recurrent neural networks …
We consider the off-policy evaluation problem in Markov decision processes with function approximation. We propose a generalization of the recently introduced \emph{emphatic temporal differences} (ETD) algorithm \citep{SuttonMW15}, which encompasses the original ETD(), as well as several other off-policy evaluation …
We study soft persistence (existence in subsequent temporal layers of motifs from the initial layer) of motif structures in Triangulated Maximally Filtered Graphs (TMFG) generated from time-varying Kendall correlation matrices computed from stock prices log-returns over rolling windows with exponential smoothing. We ob…
Recently, a new multi-step temporal learning algorithm, called , unifies -step Tree-Backup (when ) and -step Sarsa (when ) by introducing a sampling parameter . However, similar to other multi-step temporal-difference learning algorithms, needs much memory consumption and computation tim…
Simplicial persistence of financial markets: filtering, generative processes and portfolio riskq-fin.ST
Simplicial persistence measures financial market dynamics, revealing long-term structure evolution.
problem Understanding the long-term structure evolution of financial markets.
method Simplicial persistence, null models, TMFG filtering, thresholding, generative process analysis.
result More liquid markets exhibit slower persistence decay, suggesting higher fragility to systemic shocks.
Beyond the Independence Assumption: Finite-Sample Guarantees for Deep Q-Learning under -Mixingstat.ML
Study shows DQN's performance degrades with temporal dependence in data.
problem Temporal dependence in replayed data affects DQN's performance.
method Modelled -mixing data, derived risk bounds, and empirical validation.
result Temporal dependence leads to a degradation in DQN's performance rate.
TGNN4I model forecasts irregularly observed graph data using ODEs.
problem Forecasting graph-structured data with irregular time steps and partial observations.
method Introduces a time-continuous latent state in each node using ODEs and GRUs, integrating graph neural network layers.
result Validated usefulness of graph structure and time-continuous dynamics in irregular observation settings.
Temporal Difference Learning analysis under non-i.i.d. data and nonlinear approximation.
problem Finite-sample behavior of TD(0) under non-i.i.d. data and nonlinear approximation.
method High-probability, finite-sample analysis of vanilla TD(0) on polynomially mixing Markov data, assuming Holder continuity and bounded generalized gradients.
result Bounds on the convergence rate of TD(0) with high probability, matching known i.i.d. rates and holding even with nonstationary initialization.
The paper analyzes multivariate Hawkes processes and their induced population processes.
problem Analyzing the time-dependent joint probability distribution of multivariate Hawkes processes.
method Exact and asymptotic analysis of general multivariate Hawkes processes and their induced population processes.
result Full characterization of the time-dependent joint transform of the multivariate population process and its intensity process.
SGDm with fixed step-size diverges under covariate shift, similar to a parametric oscillator.
problem SGDm with fixed step-size diverges under covariate shift.
method Approximated learning system as a time-varying system of ODEs and characterized divergence/convergence modes.
result SGDm with fixed step-size can diverge under covariate shift, similar to resonance in oscillators.
In this paper, we present an effective deep prediction framework based on robust recurrent neural networks (RNNs) to predict the likely therapeutic classes of medications a patient is taking, given a sequence of diagnostic billing codes in their record. Accurately capturing the list of medications currently taken by a …
New framework relaxes independence assumption for graph-mixing dependencies.
problem Tackles limitations of existing generalization results for graph-mixing dependencies.
method Proposes a framework where dependencies decay with graph distance, derives generalization bounds leveraging online-to-PAC framework.
result Derives high-probability generalization guarantees that depend on mixing rate and graph's chromatic number.
Stability of catenoid in 4D Minkowski space proven without symmetry assumptions.
problem Stability of the catenoid as a nonflat stationary solution to the HVMC equation in 4D.
method Established asymptotic stability under codimension-1 assumption, using new commutator vector field estimates.
result Catenoid stability in 4D proven without symmetry assumptions, with improved pointwise decay.
Proposes a transformer model with geostatistical inductive bias for spatio-temporal forecasting.
problem Combining probabilistic rigor of geostatistics with flexible deep learning representations.
method Spatially-informed transformer with learnable covariance kernel.
result Successfully recovers spatial decay parameters end-to-end via backpropagation.
Social networks are getting closer to our real physical world. People share the exact location and time of their check-ins and are influenced by their friends. Modeling the spatio-temporal behavior of users in social networks is of great importance for predicting the future behavior of users, controlling the users' mov…
In the online multiple testing problem, p-values corresponding to different null hypotheses are observed one by one, and the decision of whether or not to reject the current hypothesis must be made immediately, after which the next p-value is observed. Alpha-investing algorithms to control the false discovery rate (FDR…
Time-Aware Gated Recurrent Unit Networks for Road Surface Friction Prediction Using Historical Datacs.LG
An accurate road surface friction prediction algorithm can enable intelligent transportation systems to share timely road surface condition to the public for increasing the safety of the road users. Previously, scholars developed multiple prediction models for forecasting road surface conditions using historical data. …
Existing methods for arterial blood pressure (BP) estimation directly map the input physiological signals to output BP values without explicitly modeling the underlying temporal dependencies in BP dynamics. As a result, these models suffer from accuracy decay over a long time and thus require frequent calibration. In t…
We formulate the problem of neural network optimization as Bayesian filtering, where the observations are the backpropagated gradients. While neural network optimization has previously been studied using natural gradient methods which are closely related to Bayesian inference, they were unable to recover standard optim…
Extends Minkowski stability proof to minimal decay assumptions.
problem Global stability of Minkowski spacetime with minimal decay.
method Extends Christodoulou-Klainerman's proof to minimal decay assumptions.
result Exterior stability of Minkowski holds with borderline decay.
New method creates vacuum data at minimal and borderline decay thresholds.
problem Creating vacuum initial data at specific decay thresholds.
method Conical solution-operator method applied to vacuum asymptotically flat initial data.
result Demonstrates global and exterior stability of Minkowski spacetime.
Study introduces new Bernstein inequalities for dependent data in Hilbert spaces.
problem Learning from non-independent and non-identically distributed data.
method Data-dependent Bernstein inequalities tailored for vector-valued processes in Hilbert space.
result Achieved novel risk bounds for covariance operator estimation and operator learning.
Unique solutions found for wave-like decaying null infinity equations.
problem Wave-like decaying null infinity equations with spherically symmetric Einstein-scalar-field.
method Local and global unique solutions for small initial data.
result Sharp decaying condition for unique solutions.