Study evaluates local explanation methods for time series forecasting.
problem Lack of local interpretability methods for multivariate time series forecasting.
method Proposed two novel evaluation metrics: Area Over the Perturbation Curve for Regression and Ablation Percentage Threshold.
result Comprehensive comparison of local explanation models on two datasets.
We investigate the local fractal properties of the financial time series based on the evolution of the Warsaw Stock Exchange Index (WIG) connected with the largest developing financial market in Europe. Calculating the local Hurst exponent for the WIG time series we find an interesting dependence between the behavior o…
This study improves estimation of locally stationary functional time series using NW method.
problem Accurately capturing time-dependence in locally stationary functional time series with time-varying covariates.
method Nadaraya-Watson (NW) estimation procedure for the conditional distribution of LSFTS.
result Established convergence rates of NW estimator for LSFTS with respect to Wasserstein distance.
A new model detects and localizes anomalies in multivariate time series data.
problem Anomaly diagnosis in multivariate time series data, especially localization.
method Attention Low-Rank Transformer (ALoRa-T) with low-rank regularization and Attention Low-Rank score.
result The proposed method significantly outperforms state-of-the-art methods in anomaly detection and localization.
Global models outperform local models in forecasting intermittent time series.
problem Forecasting intermittent time series with zeros in supply chains.
method Comparison of state-of-the-art probabilistic local and global models on five datasets.
result TiDE, a simple neural network architecture, achieves the best accuracy among global models.
CaLoNet integrates spatial and local correlations for multivariate time series classification.
problem Ignoring spatial and local correlations in multivariate time series classification.
method Model spatial correlations using causality modeling, extract local correlations, integrate into graph neural network.
result Competitive performance compared to state-of-the-art methods on UEA datasets.
Efficient method classifies locally stationary time series based on second-order characteristics.
problem Classifying locally stationary time series for various applications.
method Autoregressive approximation, ensemble aggregation, distance-based threshold.
result Zero misclassification error rate asymptotically for mildly differing second-order characteristics.
Study local foliations of surfaces with constant mean curvature and constant expansion in space-time.
problem Characterize surfaces with constant mean curvature and constant expansion in space-time.
method Use Lyapunov Schmidt reduction in an n+1 dimensional manifold to construct and prove the uniqueness of foliations.
result Construct and prove the uniqueness of local foliations of surfaces with constant mean curvature and constant expansion.
Locally symplectic structure found on Kerr space-time.
problem Understanding Kerr space-time using geodesics.
method Identifying locally conformally symplectic structure using characteristic classes and Kerr-Schild coordinates.
result Definition of cobordism category of contact 3-manifolds and locally conformally symplectic cobordisms.
Global methods outperform local in forecasting groups of time series, even in heterogeneous datasets.
problem Forecasting groups of time series, especially in heterogeneous datasets.
method Local methods consider each series separately, global methods fit a single model to all series.
result Global methods can outperform local methods in forecasting groups of time series, even in heterogeneous datasets.
This paper proposes an in-depth re-thinking of neural computation that parallels apparently unrelated laws of physics, that are formulated in the variational framework of the least action principle. The theory holds for neural networks that are also based on any digraph, and the resulting computational scheme exhibits …
Local polynomial regression (Fan and Gijbels 1996) is an important class of methods for nonparametric density estimation and regression problems. However, straightforward implementation of local polynomial regression has quadratic time complexity which hinders its applicability in large-scale data analysis. In this pap…
We define a random-matrix ensemble given by the infinite-time covariance matrices of Ornstein-Uhlenbeck processes at different temperatures coupled by a Gaussian symmetric matrix. The spectral properties of this ensemble are shown to be in qualitative agreement with some stylized facts of financial markets. Through the…
Following a hedging based approach to model free financial mathematics, we prove that it should be possible to make an arbitrarily large profit by investing in those one-dimensional paths which do not possess local times. The local time is constructed from discrete approximations, and it is shown that it is α-Hölder …
Local-HDP learns independent topics for each 3D object category in real-time.
problem Learning independent topics for each 3D object category in real-time.
method Local-Hierarchical Dirichlet Process (Local-HDP) with online variational inference.
result Local-HDP outperforms other approaches in accuracy, scalability, and memory efficiency.
New method calibrates local volatility models to marginal distributions.
problem Calibrating local volatility models to specific marginal distributions.
method Inspired by volatility interpolation, constructs time-homogeneous or continuous local volatility functions.
result Efficient numerical algorithms for constructing local volatility functions.
In this paper, we give the first detailed proof of the short-time existence of Deane Yang's local Ricci flow. Then using the local Ricci flow, we prove short-time existence of the Ricci flow on noncompact manifolds, whose Ricci curvature has global lower bound and sectional curvature has only local average integral bou…
Langevin dynamics (LD) has been proven to be a powerful technique for optimizing a non-convex objective as an efficient algorithm to find local minima while eventually visiting a global minimum on longer time-scales. LD is based on the first-order Langevin diffusion which is reversible in time. We study two variants th…
Study smooth mappings between manifolds and their properties.
problem Understanding mappings between manifolds with various dimensions and boundaries.
method Analyzes mappings Cα in terms of iterated directional derivatives and smooth structures. result Establishes a canonical smooth manifold structure for mappings under certain conditions.
We investigate finite-time decoupled convergence in nonlinear two-time-scale stochastic approximation.
problem Achieving decoupled convergence in nonlinear two-time-scale stochastic approximation.
method Nested local linearity assumption, suitable step size selection, convergence analysis of matrix cross term, fourth-order moment convergence rates.
result Finite-time decoupled convergence rates can be achieved in nonlinear two-time-scale stochastic approximation with proper step size selection.
Model financial default cascades on sparse graphs via hitting times.
problem Capturing systemic risk in large, sparsely-connected financial networks.
method Dynamic particle systems with hitting times and convergence theory.
result Characterization of default time distribution in tree-like networks.
We study the detailed path-wise behavior of the discrete-time Langevin algorithm for non-convex Empirical Risk Minimization (ERM) through the lens of metastability, adopting some techniques from Berglund and Gentz (2003. For a particular local optimum of the empirical risk, with an arbitrary initialization, we show tha…
It is well known that mean-variance portfolio selection is a time-inconsistent optimal control problem in the sense that it does not satisfy Bellman's optimality principle and therefore the usual dynamic programming approach fails. We develop a time- consistent formulation of this problem, which is based on a local not…
PerCDL learns personalized dictionaries for physiological signals combining global and local structures.
problem Representing datasets with both global and local structures in human physiological signals.
method Personalized Convolutional Dictionary Learning (PerCDL) that combines a global and personalized local dictionary.
result PerCDL effectively learns interpretable representations for human locomotion data.
Paper approximates rough stochastic local volatility models for efficient computation.
problem No unified method for rough stochastic local volatility models.
method Semimartingale and continuous-time Markov chain approximation.
result Fast CTMC algorithm with weak convergence proved.
In this work we prove the fact that, for a short time, it is possible to construct a smooth parametrized family of isometric embeddings of an arbitrary smooth parametrized family of Riemannian metrics on a smooth closed manifold into an Euclidean space. In order to prove this statement we work out stability estimates w…
The paper details local forms of morphisms in colored supermanifolds.
problem Understanding local forms of morphisms in colored supermanifolds.
method Detailed account of Z2n-differential calculus and local theorems. result Detailed insights into local forms of morphisms in colored supermanifolds.
Meta-GLAR combines global deep representations with local adaptation for improved forecasting accuracy.
problem Joint learning from related time series boosts accuracy but fails for out-of-sample forecasting.
method Meta-GLAR uses a meta-learning approach to adapt RNN representations for each time series.
result Meta-GLAR outperforms state-of-the-art methods in out-of-sample forecasting accuracy.
BN refines local partition geometry in piecewise-affine networks during training.
problem Understanding the effect of BN on the function realized during training in piecewise-affine networks.
method Analyzing the geometry of switching hyperplanes and affine-region partition conditioned on a mini-batch.
result BN increases expected local partition refinement in ReLU and piecewise-affine networks.
Study local expansions of continuous-time processes using Ito signature properties.
problem Analyzing local expansions of continuous-time processes and their moments.
method Using the Ito signature, a basis of iterated integrals, to conduct expansions of the process' characteristic function.
result Explicit coefficients and stochastic representations for asymptotics as time shrinks or diverges.
Paper develops sparse learning for heavy-tailed time series with locally stationary dynamics.
problem Sparse learning for high-dimensional heavy-tailed locally stationary time series.
method Additive modeling with kernel smoothing, sparsity-inducing penalized estimation.
result Prediction-error bounds and convergence rates for different sparsity structures.
This paper is devoted to problem of detecting critical events at finiacial markets using methods of multifractal analysis. Namely, the local regularity of time-series is studied. As a result, one can find out a special behavior or signal of regularity before crashes. This spesial behaviour of local Hoelder exponents in…
We construct locally homogeneous 6-dimensional nearly Kähler manifolds as quotients of homogeneous nearly Kähler manifolds M by freely acting finite subgroups of Aut0(M). We show that non-trivial such groups do only exists if M=S3×S3. In that case we classify all freely acting subgroups of $Aut_0(M)=SU (…
M-CaStLe discovers causal structures in multivariate space-time data.
problem Challenges in causal graph discovery for high-dimensional gridded data.
method Generalizes CaStLe to multivariate analyses, using local embeddings and pooling spatial replicates.
result More accurately recovers multivariate causal structure and identifies physical dynamics.
Consider an integral Brakke flow (μt), t∈[0,T], inside some ball in Euclidean space. If μ0 has small height, its measure does not deviate too much from that of a plane and if μT is non-empty, then Brakke's local regularity theorem yields that (μt) is actually smooth and graphical inside a smaller b…
A new algorithm speeds up EEG source localization using ℓ1 regularization.
problem Challenging inverse problem in mapping EEG readings to brain activity.
method Formulated as a graphical generalized elastic net inverse problem, solved with a variable projected algorithm (VPAL).
result VPAL provides faster and more accurate EEG source localization compared to existing methods.
In this paper, we take a new approach for time of arrival geo-localization. We show that the main sources of error in metropolitan areas are due to environmental imperfections that bias our solutions, and that we can rely on a probabilistic model to learn and compensate for them. The resulting localization error is val…
Calculates local Granger causality for Gaussian and nonlinear systems.
problem Understanding causal influence in complex systems.
method Vector autoregression and information-theoretic approach.
result Local Granger causality offers a robust and fast method for time-directed information transfer.
Local existence and uniqueness of Bakry-Émery Ricci flow solutions on finite graphs.
problem Analyzing the behavior of Ricci flow on finite graphs.
method Local existence and uniqueness proof for solutions of the Bakry-Émery Ricci flow.
result Local existence and uniqueness of solutions to the Ricci flow on finite graphs.
In modeling multivariate time series, it is important to allow time-varying smoothness in the mean and covariance process. In particular, there may be certain time intervals exhibiting rapid changes and others in which changes are slow. If such time-varying smoothness is not accounted for, one can obtain misleading inf…
We calculate eigenvector overlaps between intersecting time periods of covariance matrices.
problem Analyzing overlapping time periods in covariance matrices.
method Girko linearisation and extended local laws.
result Computed eigenvector overlaps for intersecting time intervals.
Fractional porous media equations yield q-Gaussian solutions for stock price returns.
problem Modeling stock price returns using fractional porous media equations.
method Analyzed three types of fractional extensions of the porous media equation.
result Local and non-local fractional extensions fit S&P 500 data better than classical models.
Method extracts time-localized clusters to explain deep learning models in ECG analysis.
problem Limited understanding of deep learning models in ECG analysis.
method Extracts time-localized clusters from model's internal representations.
result Enhances trust in AI-driven diagnostics and reveals clinically relevant patterns.
InstantEmbedding efficiently generates node representations with less computation and memory.
problem Efficiently generating local node representations for large graphs.
method Local PageRank computations in sublinear time.
result Significantly faster and less memory-intensive than traditional methods.
Localized Kasner-like singularities constructed in spacetime.
problem Constructing localized singular solutions to Einstein vacuum equations.
method First order symmetric hyperbolic formulation, adapted orthonormal frame.
result Localized Kasner-like singularities with refined uniqueness and general asymptotic data.
Local gluing connects flow lines in finite time intervals.
problem Connecting flow lines in finite time intervals.
method Functional analytic approach to define local gluing map.
result Explicit construction of local gluing map in Euclidean case; intricate construction in non-Euclidean case.
Defines speculative bubbles in discrete-time models based on discounted stock price losing mass.
problem Characterizing speculative bubbles in discrete-time models.
method Introduces a new definition based on discounted stock price behavior and provides probabilistic characterizations.
result Speculative bubbles in discrete time are linked to solutions of a linear Volterra integral equation.
Study local exploration on dynamic graphs with time-varying edges.
problem Learning optimal actions in a network with changing connections.
method Local explore-then-commit algorithms under a structural condition ensuring intrinsic walk stability.
result Sublinear expected regret for reward-aware strategies.